Anthropomotron

Estimate:
Stature
Body Mass
MNI and MLNI

About
Sources

Version 2.1.1

Welcome to Anthropomotron

Please select an option from the menu to the left.

Choose one of the methods of stature estimation from the menu above.

Choose a reference sample below to see what criteria are available. Scroll to the bottom to read about the chosen reference sample.

Estimated Stature:
Confidence Interval:

Background:

Data were derived from the Denver Growth Study radiographs of mostly middle to upper middle class European Americans from the Denver area between 1941 and 1967 (Ruff 2007, p. 699).

Sources:

This page uses sources from Ruff (2007) and Robbins Schug (2013).

Choose a reference sample below to see what criteria are available. See the Background section to read about the chosen reference sample.

Estimated Stature:
Confidence Interval:

Notes:
Background:

Sources:

This page uses sources from Pearson (1899), Trotter and Gleser (1952, 1958, 1977), Olivier (1976), Sjøvold (1990), Sciulli and Giesen (1993), Ousley (1995), del Angel and Cisneros (2004), Bidmos (2008), Raxter et al. (2008), Auerbach and Ruff (2010), Pomeroy and Stock (2012), Ruff et al. (2012), and Lee et al. (2014).

Choose a reference sample below.

Estimated Stature:

Please choose a technique

Sources:

This page uses sources from Fully (1956) and Raxter et al. (2006, 2007).

Choose one of three methods of mass estimation from the menu above. On smaller devices, lengthy menu items need to be viewed in landscape mode.

Estimated Body Mass:
Confidence Interval:

Technique:

Ruff and colleagues describe the measurement as the "superoinferor breadth of the femoral head," (2012:604).
Sources:

This page uses sources from Ruff et al. (1991), Auerbach and Ruff (2004), and Ruff et al. (2012).

Estimated Body Mass:

Technique:

Bi-iliac breadth is the maximum mediolateral breadth (Ruff 2007).
Sources:

This page uses sources from Ruff et al. (2005).

Estimated Body Mass:
Confidence Interval:

Technique:

Use "the maximum mediolateral breadth of the distal metaphyseal surface of the femoral diaphysis... [t]aken between the most medially and laterally projecting points on the metaphyseal surface, close to but not necessarily perpendicular to the long axis of the shaft," (Ruff 2007:699)
Sources:

This page uses sources from Ruff (2007) and Robbins Schug et al. (2013).

Estimated Body Mass:
Confidence Interval:

Technique:

The maximum superioinferior femoral head breadth was used "perpendicular to the femoral head-neck axis," (Ruff et al., 2007:699).
Sources:

This page uses sources from Ruff (2007) and Robbins Schug et al. (2013).

Estimated Body Mass:

Technique:

Bi-iliac breadth is the maximum mediolateral breadth (Ruff 2007). Long bone lengths are the macimum, including the epiphyses.
Sources:

This page uses sources from Ruff (2007).

Estimated Body Mass:

Technique:

Measurements were taken at 45.5% diaphyseal length (Robbins et al., 2010)
Sources:

This page uses sources from Robbins et al. (2010) and Robbins Schug et al. (2013).

Estimated Body Mass:
Prediction Interval:

Technique:

The DPP is "the greatest dorsoplantar diameter with the arms of the calipers oriented parallel to the diaphysis" and the MLD is measured "on the plantar side of the head," (De Groote and Humphrey 2011:626-627)
Sources:

This page uses sources from De Groote and Humphrey (2011).

Left Elements
Right Elements
Element Pairs

MNI #1: Maximum (L, R):
MNI #2: L + R - P:
MNI #3: (L + R) / 2
MLNI: (L + 1)(R + 1) / (P + 1)) - 1

Sources:

This page uses sources from Adams and Konigsberg (2004).

Anthropomotron (Mobile/Web) version 2.1.1

Introduction
Welcome to Anthropomotron! I made this website/app to consolidate many of the anthropometric tools used in biological anthropology. This app wouldn't have been possible without the work of the many researchers cited on the Sources page. In adding their contributions to this app, there is the chance that I have made an error in programming. If you're using this app for a matter of serious importance it is a good idea to confirm the calculation with the original source, especially if the estimate is wildly off or too good to be true.

General Instructions
Choose the measurement you want to measure from the main screen (ie. stature, body mass, or MNI). Generally, move from the top of the page downward filling in values and choosing options as they appear. The estimate should automatically be calculated near the bottom of the page.

Change Log

2.1.1 2015 update

General

iOS 9 optimized
Minor typography fixes

Stature

Adult Long Bone Measurements
New formulae!
Sjøvold (1990) has probably the first formulae that combined both sexes and ancestries.
Lee et al. (2014) has formulae for lower limb bones and femur fragments in a modern Korean population.

Change Log

2.1 stature and fixes

General

iOS 8 optimized
Fixed typography of Info section
Long menu labels are no longer truncated on iOS

Stature

Adult Long Bone Measurements
Section renamed from Adult Long Bone Length, due to the inclusion of Bidmos (2008) formulae (see below).
Reference Sample menu organized by geographical region of the sample. This is where they died, not their ancestry, which is another matter.

New formulae!
Pearson (1899) is the first use of linear regression to produce equations to estimate stature from long bone length. These formulae are included here for the historically curious
Olivier (1976) section now has all of the formulae given in the original article.
Bidmos (2008) is notable for providing formulae for femur fragments.

Fixed bug in Trotter and Gleser (1952…) 2-limb confidence intervals
Fixed behavior where choosing a reference sample moves the screen down

2.0 Stature Update & More!

General

You can now copy the result to paste it in a different app (note: I believe this is functionally equivalent to having a built-in notepad function and far easier to program)
Placement of text in output boxes made more visually appealing.
Graphics have been iOS7-ified to remove most shadows and gradients
Content background darkened and text whitened for clarity
Animations added when some menu items change
Interface should be especially improved in Firefox from before
Whited out select menu bug in Windows Chrome fixed

Stature

New subheadings added!
Calculate juvenile stature estimation using formulae by Ruff (2007) and Robbins Schug et al. (2013)
Calculate stature from all of the skeletal elements that contribute to stature (Fully 1956; Raxter et al., 2006, 2007)!
Adult stature estimation is now in its own subheading
About/Info page renamed to "Stature Info" and reorganized to consolidate instructions and data tables under subheadings
New adult long bone length reference samples!
Raxter et al. (2008) is an ancient Egyptian sample. Auerbach and Ruff (2010) has ancient Native North Americans, and Pomeroy and Stock (2012) provides equations for ancient Andeans
Tibia-based formulae from Trotter and Gleser (1958) have been changed to the (1952) version where available or removed since the methodology of measuring the tibiae is disputed
Wrong formulae listed for under Sciulli and Giesen (1993) for estimating female stature. Calculations were not affected
Stature Info page now lists sample sizes used to generate the equations
Jumping menu bug in adult long bone length section when using Firefox fixed

Body Mass

Missing data table for the first metatarsal technique added
About/Info page renamed to "Body Mass Info" and reorganized to consolidate instructions and data tables under subheadings

MNI

About/Info page renamed to "MNI Info"

1.5.1 Bug Fixes

Body Mass

Fixed bug in which pounds were not converted correctly from kilograms in certain cases.
Typos untypoed.

1.5 Additions to Body Mass Estimation

Femoral Head

Removed "prehistoric adjustment," which has been deprecated as a useful calculation
New technique dubbed Auerbach and Ruff (2004) added. This averages the results of three other estimations (by Ruff et al. 1991, Grine et al. 1992, and McHenry 1992).
New technique Ruff et al. (2012) added, combined with the technique for calculating confidence intervals found in Ruff (2007).

Juvenile Femoral Head

New technique: Robbins Schug et al. (2013)

Juvenile Femoral Distal Metatarsal

New technique: Robbins Schug et al. (2013)

Bi-Iliac Breadth and Sections

Ruff et al. (2005) updated formulae replaced Ruff (1991) formulae.

New estimator! Both Robbins and colleagues's technique (2010) and Robbins Schug and colleagues' (2013) use the second moment of area of the femoral shaft to estimate body mass in juveniles. Input J, Imax and Imin, or a combination of cortical diameter, medullary diameter and cortical thickness to get an estimate.

First Metatarsal

New estimator by De Groote and Humphrey (2011) added. This one uses measurements from the first metatarsal (behind your big toe).

1.0.1 Fixed crash on startup in Android version

1.0 Initial Release

Acknowledgements
Besides the researchers whose work is used by this app, several others had a role in the development of Anthropomotron. Meg Halley introduced me to JQT, which started this whole thing. Derek Brillon and Shilo Bender were my Android beta testers. Bob Benfer provided valuable advice on all issues anthropological for over a decade and counting. Various researchers have offered me invaluable suggestions and support and I thank them all for seeing the potential in this project. Anthropomotron was made using Xcode, JQT, PhoneGap, Dreamweaver, and Eclipse.

By Keith Chan, Chantastisoft, 2012 - 2015.
I hope you find this app useful, interesting, and entertaining. Let me know if you have any comments, issues, suggestions, or umbrages at: chekeichan@gmail.com

Adams BJ, Konigsberg LW. 2004. Estimation of the most likely number of individuals from commingled human skeletal remains. Am J Phys Anthropol. 125:138-151.

Auerbach BM, Ruff CB. 2004. Human body mass estimation: A comparison of "morphometric" and "mechanical" methods. Am J Phys Anthropol. 125:331-342.

Auerbach BM, Ruff CB. 2010. Stature estimation formulae for indigenous North American populations. Am J Phys Anthropol. 141:190-207.

del Angel A, Cisneros HB. 2004. Technical note: Modification of regression equatiions used to estimate stature in Mesoamerican skeletal remains. Am J Phys Anthropol. 125:264-265.

Bidmos MA. 2008. Stature reconstruction using fragmentary femora in South Africans of European descent. J Forensic Sci. 53:1044-1048.

Fully G. 1956. Une nouvelle méthode de détermination de la taille. Ann Med Legale. 35:266-273.

Genovés S. 1967. Proportionality of the long bones and their relation to stature among Mesoamericans. Am J Phys Anthropol. 26:67-78.

Grine FE, Jungers WL, Tobias PV, Pearson OM. 1995. Fossil Homo femur from Berg Aukas, northern Namibia. Am J Phys Anthropol. 97:151-85.

De Groote I, Humphrey LT. 2011. Body mass and stature estimation based on the first metatarsal in humans. Am J Phys Anthropol. 144:625-32.

Jantz RJ, Hunt DR, Meadows L. 1995. The measure and mismeasure of the tibia: Implications for stature estimation. J Forensic Sci. 40:758-761.

Lee, J., Kim, Y. S., Lee, U., Park, D., Jeong, Y., Lee, N. S., . . . Han, S. (2014). Stature estimation from partial measurements and maximum length of lower limb bones in koreans. Australian Journal of Forensic Sciences, 46(3), 330-338.

McHenry HM. 1992. Body size and proportions in early Hominids. Am J Phys Anthropol. 87:407-431.

Olivier G. 1976. The stature of Australopithecines. J Hum Evol. 5:529-534.

Ousley S. 1995. Should we estimate biological or forensic stature? J Forensic Sci. 40:768-773.

Pearson K. 1899. IV. Mathematical contributions to the theory of evolution.- --V. On the reconstruction of stature in prehistoric races. Philos T R Soc Lond. 192:167-244.

Pomeroy E, Stock JT. 2012. Estimation of stature and body mass from the skeleton among coastal and mid-altitude Andean populations. Am J Phys Anthropol. 147:264-79.

Raxter MH, Auerbach BM, Ruff CB. 2006. Revision of the Fully technique for estimating statures. Am J Phys Anthropol. 130:374-84.

Raxter MH, Ruff CB, Auerbach BM. 2007. Technical note: revised Fully stature estimation technique. Am J Phys Anthropol. 133:817-818.

Raxter MH, Ruff CB, Azab A, Erfan M, Soliman M, El-Sawaf A. 2008. Stature estimation in ancient Egyptians: a new technique based on anatomical reconstruction of stature. Am J Phys Anthropol. 136:147-155.

Robbins G, Sciulli PW, Blatt SH. 2010. Estimating body mass in subadult human skeletons. Am J Phys Anthropol. 143:146-50.

Robbins Schug G, Gupta S, Cowgill LW, Sciulli PW, Blatt SH. 2013. Panel regression formulas for estimating stature and body mass from immature human skeletons: a statistical approach without reference to specific age estimates. J Archaeol Sci. 40:3076-3086.

Ruff C. 2007. Body size prediction from juvenile skeletal remains. Am J Phys Anthropol. 133:698-716.

Ruff CB, Holt BM, Niskanen M, Sladék V, Berner M, Garofalo E, Garvin HM, Hora M, Maijanen H, Niinimäki S, Salo K, Schuplerová E, Tompkins D. 2012. Stature and body mass estimation from skeletal remains in the European Holocene. Am J Phys Anthropol. 148:601-17.

Ruff CB, Niskanen M, Junno J, Jamison P. 2005. Body mass prediction from stature and bi-iliac breadth in two high latitude populations, with application to earlier higher latitude humans. J Hum Evol. 48:381-392.

Ruff CB, Scott WW, Liu AY. 1991. Articular and diaphyseal remodeling of the proximal femur with changes in body mass in adults. Am J Phys Anthropol. 86:397-413.

Ruff CB, Trinkaus E, Holliday TW. 1997. Body mass and encephalization in Pleistocene Homo. Nature. 387:173-176.

Sciulli PW, Giesen MJ. 1993. Brief communication: an update on stature estimation in prehistoric Native Americans of Ohio. Am J Phys Anthropol. 92:395-399.

Sjøvold, T. (1990). Estimation of stature from long bones utilizing the line of organic correlation. Human Evolution, 5(5), 431-447.

Trotter M, Gleser GC. 1952. Estimation of stature from long bones of American Whites and Negroes. Am J Phys Anthropol. 10:463-514.

Trotter M, Gleser GC. 1958. A re-evaluation of estimation of stature based on measurements of stature taken during life and of long bones after death. Am J Phys Anthropol. 16:79-123.

Trotter M, Gleser GC. 1977. Corrigenda to "estimation of stature from long limb bones of American Whites and Negroes," American Journal Physical Anthropology (1952). Am J Phys Anthropol. 47:355-356.

Estimation of stature from long bone measurements or multiple skeletal measurements is one of the core tools in forensic anthropology. Choose one of the techniques from the Method menu. Instructions and underlying formulae for each section is below. The instructions and equations used to estimate body mass are in the following subheadings. (You may have to rotate your device to portrait mode to fully see certain tables):

Juvenile Limb Bone Length

Procedure for Estimating Stature Using Juvenile Long Bone Length:

Choose a comparative Reference Sample.
Choose the Sex of the individual (options may change depending on the sample).
Choose the most likely Ancestry of the individual
Choose the Long Bone or bones you want to use to estimate stature. The spaces beneath this menu will change to reflect your selection.
Fill in the measurements where indicated. Measurements are in centimeters.
The estimated stature based on the criteria you chose will be displayed under Estimated Stature.

Juvenile Stature from Femur Length Equations and Values
Ruff (2007)
Age (years)	Equation (Diaphyseal Length)	n	Mean	SD	SEE2
1	0.303(Fe) + 32.6	20	132.4	5.0	2.89
2	0.294(Fe) + 35.7	20	166.7	7.1	4.41
3	0.310(Fe) + 34.1	20	192.8	8.6	3.61
4	0.295(Fe) + 29.5	20	216.0	10.8	4.00
5	0.311(Fe) + 34.1	20	237.1	11.9	4.84
6	0.287(Fe) + 40.5	20	258.4	15.2	4.41
7	0.294(Fe) + 39.1	20	278.5	16.4	4.84
8	0.284(Fe) + 42.8	20	296.6	17.4	5.29
9	0.308(Fe) + 35.6	20	315.8	18.2	7.84
10	0.292(Fe) + 40.6	20	332.6	20.7	8.41
11	0.306(Fe) + 36.3	20	349.4	22.2	9.00
12	0.320(Fe) + 31.4	20	366.9	19.9	10.24
	Equation (Total Length)
11	0.279(Fe) + 36.4	20	383.7	24.5	7.29
12	0.290(Fe) + 31.8	20	404.0	24.9	9.00
13	0.288(Fe) + 33.0	20	424.2	25.6	10.24
14	0.294(Fe) + 31.5	20	441.9	23.4	9.61
15	0.269(Fe) + 43.8	20	455.1	24.1	9.61
16	0.270(Fe) + 43.9	20	462.6	25.9	11.56
17	0.286(Fe) + 37.4	20	466.4	26.6	10.89

Robbins Schug et al. (2013)
0.5 to 11.5	0.3221(Fe) + 31.0390	440	--	--	--

Juvenile Stature from Tibia Length Equations and Values
Ruff (2007)
Age (years)	Equation (Diaphyseal Length)	n	Mean	SD	SEE2
1	0.353(Ti) + 35.4	20	105.7	4.9	2.25
2	0.380(Ti) + 33.5	20	134.8	6.5	2.56
3	0.342(Ti) + 39.9	20	157.7	8.5	2.56
4	0.327(Ti) + 43.7	20	176.7	10.1	3.61
5	0.322(Ti) + 45.3	20	194.3	11.8	4.00
6	0.330(Ti) + 44.9	20	211.7	13.3	4.41
7	0.325(Ti) + 46.8	20	228.7	14.8	4.84
8	0.304(Ti) + 52.9	20	244.2	16.6	4.00
9	0.324(Ti) + 48.9	20	259.3	18.1	4.41
10	0.321(Ti) + 50.1	20	273.7	19.8	4.41
11	0.331(Ti) + 47.3	20	288.6	21.1	4.84
12	0.333(Ti) + 47.9	20	304.1	20.4	6.76
	Equation (Total Length)
11	0.296(Ti) + 47.3	20	324.2	23.6	5.29
12	0.309(Ti) + 43.3	20	342.2	24.0	5.76
13	0.321(Ti) + 40.1	20	358.3	23.0	10.24
14	0.307(Ti) + 46.8	20	372.4	21.8	12.25
15	0.273(Ti) + 61.6	20	382.2	22.8	12.96
16	0.274(Ti) + 62.7	20	387.3	24.9	13.69
17	0.281(Ti) + 61.5	20	390.0	26.3	14.44

Juvenile Stature from Femur and Tibia Lengths Equations and Values
Ruff (2007)
Age (years)	Equation (Diaphyseal Lengths)	n	Mean*	SD**	SEE2
1	0.175(Fe + Ti) + 31.1	20	238.1	5.0	2.56
2	0.185(Fe + Ti) + 29.0	20	301.5	6.8	2.89
3	0.174(Fe + Ti) + 33.0	20	350.5	8.6	2.56
4	0.163(Fe + Ti) + 37.7	20	392.7	10.5	3.24
5	0.168(Fe + Ti) + 35.5	20	431.4	11.9	3.24
6	0.160(Fe + Ti) + 39.5	20	470.1	14.3	3.61
7	0.162(Fe + Ti) + 38.6	20	507.2	15.6	3.61
8	0.153(Fe + Ti) + 44.3	20	540.8	17.0	3.61
9	0.165(Fe + Ti) + 38.0	20	575.1	18.2	4.84
10	0.160(Fe + Ti) + 40.8	20	606.3	20.3	4.84
11	0.165(Fe + Ti) + 38.2	20	638.0	21.7	5.29
12	0.148(Fe + Ti) + 38.7	20	671.0	20.2	6.25
	Equation (Total Lengths)
11	0.155(Fe + Ti) + 33.6	20	707.9	24.1	4.84
12	0.158(Fe + Ti) + 31.3	20	746.2	24.5	5.76
13	0.159(Fe + Ti) + 32.1	20	782.5	24.3	7.84
14	0.145(Fe + Ti) + 44.8	20	814.3	22.6	7.84
15	0.143(Fe + Ti) + 47.0	20	837.3	23.5	8.41
16	0.149(Fe + Ti) + 43.4	20	849.9	25.4	10.24
17	0.148(Fe + Ti) + 38.7	20	853.4	26.5	9.61
Calculated as the sum of the tibia and femur means. *Calculated by converting the tibia and femur SD to variances, adding them, and taking the square root of the result.

Juvenile Stature from Humerus Length Equations and Values
Ruff (2007)
Age (years)	Equation (Diaphyseal Length)	n	Mean	SD	SEE2
1	Omitted by Ruff (p > 0.10)	20	100.5	5.0	--
2	0.437(Hu) + 30.0	20	125.0	5.3	3.24
3	0.393(Hu) + 38.1	20	141.9	6.7	4.00
4	0.407(Hu) + 37.7	20	156.9	8.0	4.00
5	0.394(Hu) + 40.6	20	170.5	9.0	5.76
6	0.422(Hu) + 36.8	20	185.1	9.8	6.76
7	0.445(Hu) + 33.2	20	197.5	10.2	7.84
8	0.439(Hu) + 35.3	20	209.0	10.3	9.61
9	0.448(Hu) + 34.3	20	220.3	11.1	14.44
10	0.442(Hu) + 35.6	20	231.1	13.0	12.25
11	0.475(Hu) + 28.6	20	239.8	11.2	14.44
12	0.433(Hu) + 39.3	20	248.8	12.5	15.21
	Equation (Total Length)
11	0.465(Hu) + 21.6	20	261.0	14.7	13.69
12	0.420(Hu) + 34.3	20	273.3	16.4	16.00
13	0.397(Hu) + 41.6	20	286.2	18.0	13.69
14	0.381(Hu) + 47.7	20	298.5	17.6	11.56
15	0.368(Hu) + 52.1	20	309.2	16.6	14.44
16	0.371(Hu) + 51.6	20	315.8	17.7	17.64
17	0.396(Hu) + 44.3	20	319.7	17.9	19.36

Juvenile Stature from Radius Length Equations and Values
Ruff (2007)
Age (years)	Equation (Diaphyseal Length)	n	Mean	SD	SEE2
1	0.386(Ra) + 42.7	20	77.8	3.3	3.61
2	0.509(Ra) + 36.9	20	93.9	4.2	4.00
3	0.514(Ra) + 39.0	20	106.7	5.0	4.41
4	0.526(Ra) + 39.3	20	118.1	5.8	4.84
5	0.548(Ra) + 37.6	20	128.4	6.4	5.76
6	0.570(Ra) + 36.0	20	138.1	7.3	6.25
7	0.574(Ra) + 36.4	20	147.4	8.1	6.76
8	0.546(Ra) + 41.7	20	156.3	9.0	5.76
9	0.565(Ra) + 39.9	20	164.4	9.8	8.41
10	0.575(Ra) + 38.3	20	173.0	10.7	7.29
11	0.570(Ra) + 39.7	20	181.6	11.7	9.61
12	0.547(Ra) + 44.6	20	191.0	11.9	9.00
	Equation (Total Length)
11	0.513(Ra) + 43.4	20	194.8	13.1	9.00
12	0.532(Ra) + 40.2	20	205.0	13.6	9.00
13	0.507(Ra) + 45.8	20	216.1	14.5	10.89
14	0.483(Ra) + 51.8	20	226.6	13.8	12.25
15	0.455(Ra) + 59.3	20	234.8	13.7	13.69
16	0.463(Ra) + 57.9	20	239.6	14.4	16.00
17	0.465(Ra) + 58.6	20	241.9	15.5	17.64

Juvenile Stature from Humerus and Radius Lengths Equations and Values
Ruff (2007)
Age (years)	Equation (Diaphyseal Lengths)	n	Mean*	SD**	SEE2
1	0.131(Hu + Ra) + 49.4	20	178.3	4.2	4.41
2	0.264(Hu + Ra) + 26.9	20	218.9	4.8	2.89
3	0.235(Hu + Ra) + 35.5	20	248.6	5.9	3.61
4	0.236(Hu + Ra) + 36.6	20	2750	7.0	4.00
5	0.236(Hu + Ra) + 37.4	20	298.9	7.8	5.76
6	0.254(Hu + Ra) + 32.6	20	323.2	8.6	5.29
7	0.261(Hu + Ra) + 31.1	20	344.9	9.2	6.25
8	0.255(Hu + Ra) + 33.8	20	365.3	9.7	6.76
9	0.260(Hu + Ra) + 32.8	20	384.7	10.5	10.89
10	0.259(Hu + Ra) + 33.0	20	404.1	11.9	8.41
11	0.252(Hu + Ra) + 36.7	20	421.4	11.5	10.89
12	0.213(Hu + Ra) + 54.5	20	439.8	12.2	14.44
	Equation (Total Lengths)
11	0.131(Hu + Ra) + 49.4	20	455.8	13.9	9.61
12	0.254(Hu + Ra) + 27.4	20	478.3	15.1	11.56
13	0.243(Hu + Ra) + 32.8	20	502.3	16.3	10.89
14	0.230(Hu + Ra) + 39.9	20	525.1	15.8	10.24
15	0.222(Hu + Ra) + 44.5	20	544.0	15.2	11.56
16	0.218(Hu + Ra) + 47.5	20	555.4	16.1	14.44
17	0.219(Hu + Ra) + 47.2	20	561.6	16.7	15.21
Calculated as the sum of the humerus and radius means. *Calculated by converting the humerus and radius SD to variances, adding them, and taking the square root of the result.

Diaphyseal Length to Total Length Conversion (Used for Diaphyseal Length and Age >12)
(Total Length) = (Diaphyseal Length) * (Limb Conversion Factor)
Limb	Limb Conversion Factor
Femur	1.097
Tibia	1.125
Humerus	1.079
Radius	1.072

Adult Limb Bone Length

Procedure for Estimating Stature Using Adult Long Bone Measurements:

Choose a comparative Reference Sample.
Choose the Sex of the individual (options may change depending on the sample).
Choose the most likely Ancestry of the individual
Choose the Long Bone or bones you want to use to estimate stature. The spaces beneath this menu will change to reflect your selection.
Fill in the measurements where indicated. Measurements are in centimeters.
The estimated stature based on the criteria you chose will be displayed under Estimated Stature.

Additional Options:

The methods based on the Trotter and Gleser and Ousley samples also produce ranges of estimated statures based on long bone length. For the Trotter and Gleser equations, you can choose among one to three sizes of the interval. Consult the original sources for what these intervals mean (and don't mean!). Ruff et al. (2012) has enough information for confidence intervals for a single estimate to be made in most cases. You can choose from among several levels of confidence.
Trotter and Gleser also provided a means of adjusting the estimated stature based if an individual is over thirty years of age. Enter the Age in the given input field. Raxter et al. (2008) allow this adjustment to their equations as well. Note that Ousley (1995:770) claims this correction is arbitrary.

Pearson (1899)
Female
Long Bone(s)	Formula	n
Femur	(1.945)(Fe) + 72.844	50
Tibia	(2.352)(Ti) + 74.774	50
Humerus	(2.754)(Hu) + 71.475	50
Radius	(3.343)(Ra) + 81.224	50
Femur, Tibia, Humerus, and Radius	(0.782)(Fe) + (1.120)(Ti) + (1.059)(Hu) - (0.711)(Ra) + 67.469	50
Femur and Tibia (Type 1)	(1.117)(Fe) + (1.125)(Ti) + 69.561	50
Femur and Tibia (Type 2)	(1.126)(Fe + Ti) + 69.154	50
Femur and Humerus	(1.339)(Fe) + (1.027)(Hu) + 67.435	50
Humerus and Radius (Type 1)	(2.582)(Hu) + (0.281)(Ra) + 70.542	50
Humerus and Radius (Type 2)	(1.628)(Hu + Ra) + 69.911	50

Male
Femur	(1.880)(Fe) + 81.306	50
Tibia	(2.376)(Ti) + 78.664	50
Humerus	(2.894)(Hu) + 70.641	50
Radius	(3.271)(Ra) + 85.925	50
Femur, Tibia, Humerus, and Radius	(0.913)(Fe) + (0.600)(Ti) + (1.225)(Hu) - (0.187)(Ra) + 67.049	50
Femur and Tibia (Type 1)	(1.220)(Fe) + (1.080)(Ti) + 71.443	50
Femur and Tibia (Type 2)	(1.159)(Fe + Ti) + 71.272	50
Femur and Humerus	(1.030)(Fe) + (1.557)(Hu) + 68.397	50
Humerus and Radius (Type 1)	(2.769)(Hu) + (0.195)(Ra) + 69.788	50
Humerus and Radius (Type 2)	(1.730)(Hu + Ra) + 66.855	50

Trotter and Gleser (1952, 1958, 1977)
Female - African
Long Bone(s)	Formula	n	Standard Error
Femur	(2.28)(Fe) + 59.76	177	3.41
Tibia	(2.45)(Ti) + 72.65*	177	3.70
Fibula	(2.49)(Fi) + 70.90	177	3.80
Humerus	(3.08)(Hu) + 64.67	177	4.25
Radius	(3.67)(Ra) + 71.79**	177	4.59
Ulna	(3.31)(Ul) + 75.38	177	4.83
Femur, Tibia, Humerus, and Radius	(1.46)(Fe) + (0.86)(Ti) + (0.44)(Hu) - (0.20)(Ra) + 56.33*	177	3.22
Femur and Tibia (Type 1)	(1.53)(Fe) + (0.96)(Ti) + 58.54*	177	3.23
Femur and Tibia (Type 2)	(1.26)(Fe + Ti) + 59.72*	177	3.28
Tibia and Humerus	(1.79)(Ti) + (1.08)(Hu) + 62.80*	177	3.58

Female - European
Femur	(2.47)(Fe) + 54.10	63	3.72
Tibia	(2.90)(Ti) + 61.53*	63	3.66
Fibula	(2.93)(Fi) + 59.61	63	3.57
Humerus	(3.36)(Hu) + 57.97	63	4.45
Radius	(4.74)(Ra) + 54.93	63	4.24
Ulna	(4.27)(Ul) + 57.76	63	4.30
Femur, Tibia, and Humerus	(1.17)(Fe) + (1.15)(Ti) + (0.68)(Hu) + 50.12*	63	3.51
Femur and Tibia (Type 1)	(1.48)(Fe) + (1.28)(Ti) + 53.07 *	63	3.55
Femur and Tibia (Type 2)	(1.39)(Fe + Ti) + 53.20*	63	3.55
Tibia and Humerus	(1.95)(Ti) + (1.35)(Hu)*	63	3.67

Male - African
Femur	(2.10)(Fe) + 72.22	343, 338	3.91
Tibia	(2.19)(Ti) +86.02*	85	3.78
Fibula	(2.34)(Fi) + 80.07	301, 306	4.02
Humerus	(2.88)(Hu) + 75.48	378, 385	4.23
Radius	(3.32)(Ra) + 85.43	361, 364	4.57
Ulna	(3.20)(Ul) + 82.77	368, 348	4.74
Femur and Tibia	(1.15)(Fe+Ti) + 71.04*	--	3.53
Femur and Fibula	(1.20)(Fe+Fi) + 67.77	--	3.63
Humerus and Ulna	(1.65)(Hu+Ul ) +70.67	--	4.23
Humerus and Radius	(1.66)(Hu+Ra) + 73.08	--	4.18

Male - European
Femur	(2.32)(Fe) + 65.53	2327, 2345	3.41
Tibia	(2.52)(Ti ) +78.62*	1115	3.37
Fibula	(2.60)(Fi) + 75.50	2207, 2217	3.86
Humerus	(2.89)(Hu) + 78.10	2817, 2817	4.57
Radius	3.79)(Ra) + 79.42	2673, 2641	4.66
Ulna	(3.76)(Ul) + 75.55	2638, 2652	4.72
Femur and Tibia	(1.30)(Fe+Ti) + 63.29*	--	2.99
Femur and Fibula	(1.31)(Fe+Fi) + 63.05	--	3.62
Humerus and Ulna	(1.78)(Hu+Ul) + 66.98	--	4.37
Humerus and Radius	(1.82)(Hu+Ra) + 67.97	--	4.31

Male - Asian
Femur	(2.15)(Fe) + 72.57	67, 60	3.80
Fibula	(2.40)(Fi) + 80.56	61, 62	3.24
Humerus	(2.68)(Hu) + 83.19	65, 74	4.25
Radius	(3.54)(Ra) + 82.00	68, 67	4.60
Ulna	(3.48)(Ul) + 77.45	65, 65	4.66
Femur and Fibula	(1.22)(Fe+Fi ) + 70.24	--	3.18
Humerus and Ulna	(1.68)(Hu+Ul) + 71.18	--	4.14
Humerus and Radius	(1.67)(Hu+Ra) + 74.83	--	4.16

Male - Mexican
Femur	(2.44)(Fe) + 58.67	50, 57	2.99
Fibula	(2.50)(Fi) + 75.44	52, 45	3.52
Humerus	(2.92)(Hu) + 73.94	58, 63	4.24
Radius	(3.55)(Ra) + 80.71	56, 58	4.04
Ulna	(3.56)(Ul) + 74.56	57, 57	4.05

*Equations from Trotter and Gleser (1952). Jantz et al. (1995) concluded that the tibia was measured without the medial malleoulus. These researchers could not conclusively reconstruct how the tibae were measured for the Trotter and Gleser (1958) tibia equations, so they have been deprecated in the literature.
**Equation corrected in Trotter and Gleser (1977).

Olivier (1976)
Long Bones	Formula	n	Standard Deviation of the Estimate
Femur	(1.74)(Fe) + 84.5	91	3.87
Tibia	(1.85)(Ti) + 88.8	91	3.82
Humerus	(2.66)(Hu) + 73.0	91	3.87
Radius	(2.96)(Ra) + 84.5	91	3.90
Ulna	(2.93)(Ul) + 79.8	91	3.90
Femur, Tibia, and Humerus	(0.996)(Fe+Ti+Hu) + 48.8	91	2.63
Femur and Tibia	(1.31)(Fe+Ti) + 55.3	91	2.79

Sjøvold (1990)
Long Bone(s)	Formula	n (Samples)*	SEE**
Caucasians
Femur (Maximum)	(2.63)(Fe) + 49.96	6706 (11)	4.52
Femur (Bicondylar)	(3.10)(Fe) + 28.82	2308 (13)	3.85
Tibia (Maximum)	(3.02)(Ti) + 58.94	3993 (9)	4.11
Tibia (Physiological)***	(5.10)(Ti) - 22.78	3643 (10)	4.69
Fibula (Maximum)	(3.78)(Fi) + 30.15	4190 (13)	4.06
Humerus (Maximum)	(4.74)(Hu) + 15.26	8577 (23)	4.94
Radius (Maximum)	(4.03)(Ra) + 69.96	4625 (10)	4.98
Radius (Physiological)	(4.67)(Ra) + 55.18	3492 (9)	5.49
Ulna (Maximum)	(4.65)(Ul) + 47.96	4994 (13)	4.96

Combined Ethnic Groups
Femur (Maximum)	(2.71)(Fe) + 45.86	8247 (25)	4.49
Femur (Bicondylar)	(3.01)(Fe) + 32.52	3232 (22)	3.96
Tibia (Maximum)	(3.29)(Ti) + 47.34	5580 (24)	4.15
Tibia (Physiological)***	(3.67)(Ti) - 29.50	4151 (17)	4.57
Fibula (Maximum)	(3.59)(Fi) + 36.31	5526 (26)	4.10
Humerus (Maximum)	(4.62)(Hu) + 19.00	10573 (44)	4.89
Radius (Maximum)	(3.78)(Ra) + 74.70	6396 (27)	5.01
Radius (Physiological)	(4.80)(Ra) + 51.15	3785 (14)	5.40
Ulna (Maximum)	(4.61)(Ul) + 46.83	6793 (33)	4.97

* Equations are the weighted lines of organic correlation of the mean values of a number of samples.
** Standard error of the estimate calculated from the weighed residual variance of the samples.
*** Sjøvold notes the low r for this equation (< 0.6), possibly related to the lack of consensus in taking this measurement (see Trotter and Gleser [1958] and Jantz et al. [1995]).

Sciulli and Giesen (1993)
Female
Long Bone(s)	Formula	n	Standard Error
Femur	(2.336)(Fe) + 44.253	76	2.54

Male
Femur	(2.443)(Fe) + 42.805	95	2.66
Tibia	(2.680)(Ti) + 50.721	95	2.74

Ousley (1995)
Female - African
Long Bone(s)	Formula (mm to inches)	n	90% Prediction Interval
Femur	(0.11640)(Fe) + 11.98	18	2.4

Female - European
Femur	(0.11869)(Fe) + 12.43	48	2.4
Tibia	(0.11168)(Ti) + 24.65	43	3.0
Humerus	(0.11827)(Hu) + 28.30	45	3.1
Radius	(0.18467)(Ra) + 22.42	38	3.4
Ulna	(0.13353)(Ul) + 31.99	40	3.1
Femur and Tibia	(0.06163)(Fe + Ti) + 15.43	42	2.4
Femur and Fibula	(0.06524)(Fe + Fi) + 12.94	38	2.3

Male - African
Femur	(0.08388)(Fe) + 28.57	17	4.0
Tibia	(0.10521)(Ti) + 26.26	19	3.8
Humerus	(0.07824)(Hu) + 43.19	20	4.4
Ulna	(0.16997)(Ul) + 21.20	14	3.3

Male - European
Femur	(0.10560)(Fe) + 19.39	69	2.8
Tibia	(0.10140)(Ti) + 30.38	67	2.8
Humerus	(0.12740)(Hu) + 26.79	66	3.3
Radius	(0.16398)(Ra) + 28.35	59	3.3
Ulna	(0.15890)(Ul) + 26.91	62	3.1
Femur and Tibia	(0.05566)(Fe + Ti) + 21.64	62	2.5
Femur and Fibula	(0.05552)(Fe + Fi) + 22.00	54	2.6

del Angel and Cisneros (2004)
Female
Long Bone(s)	Formula	n
Femur	(2.588)(Fe) + 47.25	29
Tibia	(2.720)(Ti) + 61.29	29
Fibula	(2.988)(Fi) + 54.55	29
Humerus	(4.160)(Hu) + 32.35	29
Radius	(3.926)(Ra) + 66.88	29
Ulna	(3.991)(Ul) + 58.72	29

Male
Femur	(2.262)(Fe) + 63.89	69
Tibia	(1.958)(Ti) + 91.26	69
Fibula	(1.919)(Fi) + 94.09	69
Humerus	(2.505)(Hu) + 83.52	69
Radius	(2.668)(Ra) + 98.22	69
Ulna	(2.615)(Ul) + 94.80	69

Bidmos (2008)
Femur Measurement(s)	Formula	n	SEE
Female
Bicondylar Breadth	(1.26)(BCB) + 56.96	50	3.95
Lateral Condyle Length	(1.42)(LCL) + 61.88	50	3.93
Lateral Condyle Length and Epicondylar Breadth	(1.21)(LCL) + (0.38)(EpB) + 61.08	44	3.78
Bicondylar Breadth and Epicondylar Breadth	(0.67)(BCB) + (0.79)(EpB) + 52.00	50	3.71
Bicondylar Breadth, Lateral Condyle Length, and Epicondylar Breadth	(0.37)(BCB) + (1.03)(LCL) + (0.17)(EpB) + 47.07	44	3.78
Bicondylar Breadth, Vertical Neck Diameter, Lateral Condyle Length and Epicondylar Breadth	(0.40)(BCB) - (0.21)(VND) + (1.07)(LCL) + (0.23)(EpB) + 45.43	44	3.81

Male
Lateral Condyle Length	(1.31)(LCL) + 72.32	50	5.31
Upper Epicondyle Length	(0.82)(UEpL) + 75.64	50	5.31
Upper Epicondyle Length and Lateral Condyle Length	(0.50)(UEpL) + (0.80)(LCL) + 55.63	50	4.89
Upper Epicondyle Length, Vertical Neck Diameter, Lateral Condyle Length, and Epicondylar Breadth	(0.83)(UEpL) + (0.58)(VND) + (0.58)(LCL) - (0.22)(EpB) + 63.68	48	4.81
Upper Epicondyle Length, Vertical Neck Diameter, and Lateral Condyle Length	(0.49)(UEpL) + (0.54)(VND) + (0.53)(LCL) + 55.93	49	4.80
Upper Epicondyle Length, Vertical Neck Diameter, Lateral Condyle Length, Bicondylar Breadth, and Epicondylar Breadth	(0.55)(UEpL) + (0.56)(VND) + (0.41)(LCL) + (0.41)(BCB) - (0.49)(EpB) + 61.07	48	4.80

Raxter (2008)
Long Bone(s)	Formula	n	SEE
Female
Femur (Maximum)	(2.340)(Fe) + 56.99	37	2.517
Femur (Bicondylar)	(2.341)(Fe) + 57.63	37	2.511
Tibia (Maximum)	(2.699)(Ti) + 61.08	37	1.921
Tibia (Lateral Condyle)	(2.340)(Ti) + 61.89	37	1.893
Humerus (Maximum)	(2.827)(Hu) + 70.94	30	2.732
Radius (Maximum)	(2.509)(Ra) + 96.73	28	4.047
Femur (Maximum) and Tibia (Maximum)	(1.313)(Fe + Ti) + 54.36	37	1.968
Femur (Maximum) and Tibia (Lateral Condyle)	(1.312)(Fe + Ti) + 55.27	37	1.961
Humerus (Maximum) and Radius (Maximum)	(1.291)(Hu + Ra) + 86.41	24	3.247

Male
Femur (Maximum)	(2.257)(Fe) + 63.93	63	3.218
Femur (Bicondylar)	(2.253)(Fe) + 64.76	63	3.226
Tibia (Maximum)	(2.554)(Ti) + 69.21	63	3.002
Tibia (Lateral Condyle)	(2.552)(Ti) + 70.18	63	3.060
Humerus (Maximum)	(2.594)(Hu) + 83.85	51	4.218
Radius (Maximum)	(2.641)(Ra) + 100.91	48	3.731
Femur (Maximum) and Tibia (Maximum)	(1.282)(Fe + Ti) + 59.35	63	2.851
Femur (Maximum) and Tibia (Lateral Condyle)	(1.276)(Fe + Ti) + 60.64	63	2.900
Humerus (Maximum) and Radius (Maximum)	(1.456)(Hu + Ra) + 83.76	41	3.353

Auerbach and Ruff (2010)
Long Bone(s)	Formula*	n	SEE2
Female - Arctic
Femur (Bicondylar)	(2.13)(Fe) + 64.82	117	2.99
Tibia	(2.31)(Ti) + 74.71	117	3.01
Femur (Bicondylar) and Tibia	(1.17)(Fe) + (1.20)(Ti) + 64.00	117	2.82

Female - Temperate
Femur (Bicondylar)	(2.67)(Fe) + 44.80	245	2.58
Tibia	(2.96)(Ti) + 52.30	245	2.90
Femur (Bicondylar) and Tibia	(1.76)(Fe) + (1.17)(Ti) + 41.75	245	2.40

Female - Great Plains
Femur (Bicondylar)	(2.44)(Fe) + 55.85	70	2.58
Tibia	(2.59)(Ti) + 65.10	70	2.97
Femur (Bicondylar) and Tibia	(1.68)(Fe) + (1.04)(Ti) + 50.55	70	2.41

Male - Arctic
Femur (Bicondylar)	(2.25)(Fe) + 62.73	157	2.90
Tibia	(2.55)(Ti) + 69.51	157	2.99
Femur (Bicondylar) and Tibia	(1.28)(Fe) + (1.26)(Ti) + 59.86	157	2.62

Male - Temperate
Femur (Bicondylar)	(2.54)(Fe) + 52.85	287	2.55
Tibia	(3.02)(Ti) + 51.66	287	2.81
Femur (Bicondylar) and Tibia	(1.60)(Fe) + (1.26)(Ti) + 47.11	287	2.35

Male - Great Plains
Femur (Bicondylar)	(2.69)(Fe) + 46.56	91	2.05
Tibia	(2.78)(Ti) + 60.76	191	2.77
Femur (Bicondylar) and Tibia	(1.17)(Fe) + (1.20)(Ti) + 64.00	91	1.94

*Estimator is in millimeters in published formulae. Centimeters are used here.

Pomeroy and Stock (2012)
Long Bone(s)	Formula	n	SEE
Female
Femur (Maximum)	(2.593)(Fe) + 48.340	70	2.295
Femur (Bicondylar)	(2.600)(Fe) + 49.147	70	2.231
Tibia (Maximum)	(2.863)(Ti) + 55.493	70	1.963
Tibia (Lateral Condyle)	(2.800)(Ti) + 57.748	70	2.052
Humerus (Maximum)	(3.155)(Hu) + 61.228	69	2.975
Radius (Maximum)	(3.717)(Ra) + 69.331	69	3.012
Ulna (Maximum)	(3.762)(Ul) + 61.525	68	2.987
Femur (Bicondylar) and Tibia (Maximum)	(1.443)(Fe + Ti) + 45.955	70	1.927
Femur (Bicondylar) and Tibia (Lateral Condyle)	(1.134)(Fe) + (1.637)(Ti)+ 51.947	70	1.992
Femur (Maximum) and Tibia (Maximum)	(0.945)(Fe) + (1.943)(Ti) + 48.248	70	1.844
Humerus (Maximum) and Radius (Maximum)	(1.798)(Hu) + (1.995)(Ra) + 56.175	68	2.722

Male
Femur (Maximum)	(2.738)(Fe) + 44.803	52	2.627
Femur (Bicondylar)	(2.705)(Fe) + 47.207	52	2.581
Tibia (Maximum)	(2.995)(Ti) + 52.179	52	3.644
Tibia (Lateral Condyle)	(2.997)(Ti) + 53.354	52	2.524
Humerus (Maximum)	(3.483)(Hu) + 53.771	52	2.391
Radius (Maximum)	(4.184)(Ra) + 59.305	52	2.290
Ulna (Maximum)	(4.212)(Ul) + 51.273	52	2.289
Femur (Bicondylar) and Tibia (Maximum)	(1.483)(Fe + Ti) + 44.938	52	3.522
Femur (Bicondylar) and Tibia (Lateral Condyle)	(1.293)(Fe) + (1.643)(Ti)+ 44.453	52	3.467
Femur (Maximum) and Tibia (Maximum)	(1.404)(Fe) + (1.643)(Ti) + 41.814	52	3.615
Humerus (Maximum) and Radius (Maximum)	(1.934)(Hu) + (2.453)(Ra) + 42.088	52	3.214

Ruff et al. (2012)
Long Bone(s)	Formula	n	Mean	SD	SEE2
Female - All European
Femur	(2.69)(Fe) + 46.56	233	41.80	2.18	8.53
Humerus	(3.38)(Hu) + 54.60	228	29.95	1.72	15.52
Radius	(4.20)(Ra) + 63.08	216	22.12	1.40	16.73

Female - Northern European
Tibia	(2.924)(Ti) + 56.94	146	--*	--*	10.24
Femur and Tibia	(1.42)(Fe + Ti) + 48.59	300	--*	--*	6.76

Female - Southern European
Tibia	(3.05)(Ti) + 46.68	87	--*	--*	8.41
Femur and Tibia	(1.42)(Fe + Ti) + 48.59	87	--*	--*	6.76

Male - All European
Femur	(2.72)(Fe) + 42.85	268	45.20	2.73	10.30
Humerus	(3.83)(Hu) + 41.42	265	32.53	1.92	18.84
Radius	(4.85)(Ra) + 47.46	257	24.45	1.53	20.52

Male - Northern European
Tibia	(3.09)(Ti) + 52.04	154	--*	--*	12.46
Femur and Tibia	(1.49)(Fe + Ti) +43.55	154	--*	--*	8.59

Male - Southern European
Tibia	(2.78)(Ti) + 60.76	114	--*	--*	9.30
Femur and Tibia	(1.40)(Fe + Ti) + 49.68	114	--*	--*	7.51

Combined - All European
Femur	(2.77)(Fe) + 40.50	501	43.62**	2.49**	9.73
Humerus	(3.72)(Hu) + 44.86	493	31.34**	1.83**	17.89
Radius	(4.46)(Ra) + 46.94	473	23.39**	1.47**	18.66

Combined - Northern European
Tibia	(3.13)(Ti) +50.11	300	--*	--*	11.97
Femur and Tibia	(1.49)(Fe+Ti) +43.53	300	--*	--*	7.84

Combined - Southern European
Tibia	(3.02)(Ti) + 51.39	201	--*	--*	9.86
Femur and Tibia	(1.48)(Fe + Ti) + 43.00	201	--*	--*	8.24

Mean and SD not presented by region in Ruff et al. (2012). *Mean calculated here by calculating a weighed mean from both sexes. SD calculated by converting male and female SD to variances, calculating a weighed mean of the variances, and taking the square root of the result.

Lee et al. (2014)
Long Bone(s)	Formula (mm to mm)	n	SE
Female
Femur: Maximum	(2.521)(Fe) + 542.413	50	45.6
Femur: VDHF	(18.318)(VDHF) + 766.130	50	51.4
Femur: IFLM	(3.219)(IFLM) + 579.238	50	44.6
Femur: IFGP	(2.747)(IFGP) + 567.539	50	48.0
Femur: EBF	(8.793)(EBF) + 879.540	50	54.6
Femur: IFLM and EBF	(2.544)(IFLM) + (5.461)(EBF) + 368.075	50	41.6
Tibia: Maximum	(2.939)(Ti) + 593.325	50	48.0
Fibula: Maximum	(3.019)(Fi) + 585.330	50	48.6

Male
Femur: Maximum	(2.883)(Fe) + 427.728	55	29.1
Femur: VDHF	(13.095)(VDHF) + 1054.524	55	32.9
Femur: IFLM	(2.933)(IFLM) + 729.295	55	36.2
Femur: IFGP	(2.836)(IFGP) + 587.393	55	54.4
Femur: EBF	(7.569)(EBF) + 1035.797	55	46.6
Femur: IFGP and EBF	(2.543)(IFGP) + (3.418)(EBF) + 413.642	55	44.9
Tibia: Maximum	(2.618)(Ti) + 758.742	55	55.5
Fibula: Maximum	(2.430)(Fi) + 837.503	55	37.3

Combined
Femur: Maximum	(3.232)(Fe) + 266.667	105	42.0
Femur: VDHF	(20.758)(VDHF) + 675.610	105	49.6
Femur: IFLM	(4.031)(IFLM) + 354.175	105	50.8
Femur: IFGP	(3.620)(IFGP) + 270.105	105	56.3
Femur: EBF	(11.707)(EBF) + 671.548	105	51.8
Femur: IFGP and EBF	(2.553)(IFGP) + (5.708)(EBF) + 204.615	105	50.4
Tibia: Maximum	(3.545)(Ti) + 416.001	105	58.3
Fibula: Maximum	(3.404)(Fi) + 481.114	105	44.4

Anatomical (Full Body) Method

Instructions for measuring the height of each element is taken directly from Raxter et al. (2006, p. 382-383), which includes some illustrations.
Element	Measurement Instructions
Cranial Height	"The maximum length between bregma (at the confluence of the coronal and sagittal sutures) and basion (at the anteroinferior margin of the foramen magnum, between the occipital condyles)"
Second Cervical Vertebra (C2) Height	"The most superior point of the odontoid process (dens) to the most inferior point of the anterioinferior rim of the vertebral body."
C3 to C7	"The maximum height of the vertebral body, measured in its anterior third, medial to the superiorly curving edges of the centrum."
First to Twelfth Thoracic Vertebra (T1 to T12) Height	"The maximum height of the vertebral body, anterior to the rib articular facets and pedicles."
First Lumbar Vertebra (L1) Height	"The maximum height of the vertebral body, anterior to the pedicles, not including any swelling of the centrum due to the pedicles."
First Sacral Vertebra (S1) Height	"The maximum height between the anterior-superior rim of the body (i.e., the sacral promontory) and its point of fusion/articulation with the second sacral vertebra. This most commonly occurs in the midline. Measure with the calipers parallel to the anterior surface of S1."
Femur Lengths (Physiological)	"Place the condyles on the stationary end of the osteometric board, flat against the horizontal plane. Set the mobile end against the most superior aspect of the femoral head, parallel to the stationary end. Measure at maximum length."
Tibia Lengths	"Place the medial malleolus on the stationary end of the osteometric board, with the shaft of the tibia parallel to the long axis of the board. Set the mobile end against the most superior aspect of the lateral condyle of the tibia, parallel to the stationary end. We recommend that a trackless osteometric board be used to take this measure, to allow the freedom of the mobile end's placement."
Talus and Calcaneus Heights	"Articulate the talus and the calcaneus, using the right hand for the left tarsals and vice versa. Use one hand to stabilize the articulation, point the distal articulations away from your palm, with a thumb holding the bones together superior to the peroneal tubercle (where the talus and calcaneus meet), an index finger on the opposite side lateral to the trochlea of the talus, and a middle finger in the sustentacular sulcus. Place the trochlea against the stable end of the osteometric board, with both lateral and medial edges of the trochlea contacting the board. Position the trochlea of the talus so that the stable end of the board forms a tangent to the midpoint of the trochlear surface. Place the mobile end of the osteometric board against the most inferior point of the calcaneal tuber, parallel to the stable end."

Method	Process
Fully (1956)	Add the above elements together to obtain the skeletal height. For paired elements, if both elements are present, the mean is calculated. Otherwise, the single element is used. An adjustment is added to the sum depending on its value. n = 102.
	Sum of Elements	Adjustment
	≤ 153.5	+10cm
	Between 153.5 and 165.4	+10.5cm
	≥ 165.4	+11.5cm

Raxter et al. (2006, 2007)	Add the above elements together to obtain the skeletal height. For paired elements, if both elements are present, the mean is calculated. Otherwise, the single element is used. Then calculate the final estimate either with an age adjustment (more accurate) or without the adjustment (less accurate). n = 119.
	Age Factor?	Equation
	Yes	1.009 (SH) - 0.0426(Age) + 12.1
	No	0.996(SH) +11.7

Abbreviations

Abbreviation Guide
Variable	Abbreviation
General Formulae
Femur	Fe
Tibia	Ti
Fibula	Fi
Humerus	Hu
Radius	Ra
Ulna	Ul

Bidmos (2008)
Bicondylar Length	BCB
Epicondylar Breadth	EpB
Lateral Condylar Length	LCL
Upper Epicondylar Length	UEpL
Vertical Neck Diameter	VND

Lee et al. (2014)
VDHF	Vertical diameter of the femur head
IFLM	Distance from the most proximal point of the intercondylar fossa to the midpoint of the lesser trochanter
IFGP	Distance from the most proximal point of the intercondylar fossa to the most proximal point of the greater trochanter
EBF	Epicondylar breadth of the femur

Anatomical (Full Body) Method
Skeletal Height	SH

Several elements, or combinations of elements, can be used to estimate the body mass of an individual. The stability of the femoral head against response to external forces allow it to be a useful predictor of body mass (Ruff 1991). The bi-iliac breadth of the pelvis was also found to be correlated with body mass (Ruff et al., 1997). The previous version of Anthropomotron used formulae from Ruff et al. (1997). This version uses updated forumulae from Ruff et al. (2005). Ruff (2007) also provides various methods of estimating body mass for juveniles. Robbins and colleagues (2010) and Robbins Schug and colleagues (2013) created forumulae to estimate mass using the polar second moment of area of the femoral shaft (J) and made new ways to estimate body mass using the width of the distal femoral metaphysis and femoral head diameter. Use the Method menu to choose among the available types of body mass estimation. The instructions and equations used to estimate body mass are in the following subheadings. (you may have to rotate your device to see certain tables):

Femoral Head

Procedure for Estimating Body Mass Femoral Head Diameter:

Choose the Sex of the individual.
Choose the Reference Sample.
Enter the Diameter of the femoral head in millimeters. The estimated body mass will be calculated automatically.

Femoral Head Equations
Method	n	Equation
Ruff et al. (1991)
Male	41	(0.9)((2.741)(FH) - 54.9)
Female	39	(0.9)((2.426)(FH) - 35.1)
Combined Sex	80	(0.9)((2.160)(FH) - 24.8)
McHenry (1992)	59	(2.239)(FH) - 39.9
Grine et al. (1995)	10*	(2.268)(FH) - 36.5
Auerbach et al. (2004)		This formula averages the results of Ruff et al. (1991), McHenry (1992), and Grine et al. (1995) for combined sex samples.
Ruff et al. (2012)
Male	624	(2.80)(FH) - 66.7
Female	521	(2.18)(FH) - 35.81
Combined Sex	1145	(2.30)(FH) - 41.72

*Sex-specific population means.

Stature and Bi-Iliac Breadth
Procedure for Using Stature and Bi-Iliac Breadth:
1. Choose the Sex of the individual.
2. Under Bi-Iliac Breadth Type, choose whether you are entering the living or skeletal bi-iliac breadth.
3. Enter the Bi-Iliac Breadth Measurement in centimeters.
4. Enter the Stature in centimeters. The estimated body mass will be calculated automatically.
Stature and Bi-Iliac Breadth Equations (Ruff et al. 2005)

Method n Equation
Male 32 (0.422)(Stature) + (3.126)(BB) - 92.9
Female 26 (0.504)(Stature) + (1.804)(BB) - 72.6
Bi-Iliac Breath (BB) (1.17)(SBB) - 3

Femoral Metaphyis Breadth

Procedure for Using Juvenile Femoral Metaphysis Breadth:

Choose from two Techniques. Ruff (2007) requires an estimated age while Robbins Schug (2013) uses panel regression to remove that added step. The Robbins Schug et a. (2013) technique works on individuals from 6 months to 12.5 years of age.
Enter the femoral metaphysis Breadth measurement in centimeters.
Choose whether you want the breadth to be Log-Transformed. Ruff (2007) recommends log-transforming the datum to produce an estimate with a slightly smaller error. Anthropomotron will automatically correct for detransformation bias using the quasimaximum likelihood estimator as Ruff suggested.
Enter the Age in years (1 to 13 for a transformed datum or 1 to 12 for a non-transformed datum).
The estimated body mass will be calculated automatically when all of the data has been entered.

Femoral Metaphysis Breadth Equations and Values (Ruff 2007)
Age	Equation	Log- Transformed Equation	Log- Transformed Mass Correction Factor	n	Mean	SD	SEE2	SEE2 (Log- Transformed)
1	0.188(FM) + 2.6	0.751 * ln(FM) - 0.45	1.003	20	34.3	6.76	0.423	0.410
2	0.268(FM) + 0.2	0.994 * ln(FM) - 1.28	1.001	20	42.5	6.76	0.656	0.314
3	0.257(FM) + 1.5	0.899 * ln(FM) - 0.86	1.002	20	47.1	5.76	0.828	0.423
4	0.328(FM) - 0.7	1.048 * ln(FM) - 1.35	1.002	19	49.4	6.76	1.166	1.040
5	0.367(FM) - 1.6	1.096 * ln(FM) - 1.47	1.002	19	51.3	6.76	1.166	1.188
6	0.367(FM) - 0.4	1.034 * ln(FM) - 1.16	1.002	18	53.7	6.76	1.742	1.742
7	0.419(FM) - 1.6	1.095 * ln(FM) - 1.33	1.003	18	55.7	7.84	1.904	2.045
8	0.414(FM) + 0.5	1.010 * ln(FM) - 0.90	1.004	18	57.5	9.61	5.198	5.382
9	0.694(FM) - 12.8	1.524 * ln(FM) - 2.89	1.010	20	59.9	9.00	19.714	17.057
10	0.992(FM) - 29.5	1.939 * ln(FM) - 4.55	1.012	20	61.9	8.41	28.730	25.200
11	0.938(FM) - 23.9	1.690 * ln(FM) - 3.46	1.016	20	63.8	8.41	46.786	41.603
12	1.351(FM) - 49.6	2.263 * ln(FM) - 5.82	1.015	20	66.0	6.76	54.464	48.581
13	--	1.766 * ln(FM) - 3.67	1.019	20	57.9	9.00	--	76.388

Femoral Metaphysis Breadth Equations and Values (Robbins Schug et al. 2013)
Equation				n
ln(Body Mass) = 13.0615 - 7.3338 * ln(FH) + 1.2058 * ln (FH)2				432

Juvenile Femoral Head Breadth

Procedure for Using Juvenile Femoral Head Breadth:

Choose from two Techniques. Ruff (2007) requires an estimated age while Robbins Schug (2013) uses panel regression to remove that added step. Both techniques work on individuals from 7 to 17 years of age.
Enter the femoral metaphysis Breadth measurement in centimeters.
For the Ruff (2007) technique, choose whether you want the breadth to be Log-Transformed. Ruff (2007) recommends log-transforming the datum to produce an estimate with a slightly smaller error. Anthropomotron will automatically correct for detransformation bias using the quasimaximum likelihood estimator as Ruff suggested.
For the Ruff (2007) technique, enter the Age in years (7 to 17).
The estimated body mass will be calculated automatically when all of the data has been entered.

Juvenile Femoral Head Breadth Equations and Values (Ruff 2007)
Age	Equation	Log- Transformed Equation	Log- Transformed Mass Correction Factor	n	Mean	SD	SEE2	SEE2 (Log- Transformed)
7	0.495(FH) + 8.0	0.650(FH) + 0.92	1.002	18	27.9	7.29	1.823	1.988
8	0.606(FH) + 6.1	0.749(FH) + 0.64	1.003	18	30.1	7.84	3.842	4.040
9	1.155(FH) - 8.7	1.286(FH) - 1.12	1.006	20	324	8.41	12.390	10.498
10	1.279(FH) - 12.2	1.374(FH) - 1.41	1.009	20	34.5	8.41	22.373	19.536
11	1.626(FH) - 23.0	1.582(FH) - 2.11	1.011	20	36.2	8.41	31.472	27.878
12	1.850(FH) - 31.3	1.725(FH) - 2.62	1.009	20	38.3	9.61	31.923	28.196
13	1.830(FH) - 29.4	1.656(FH) - 2.35	1.014	20	40.4	9.61	61.466	54.908
14	1.438(FH) - 10.3	1.226(FH) - 0.68	1.011	20	41.8	8.41	60.063	55.354
15	NA	NA		20	43.6	6.25	NA	NA
16	NA	0.842(FH) + 0.88	1.009	20	44.5	7.84	NA	36.361
17	1.750(FH) - 17.2	1.327(FH) - 0.94	1.006	20	45.0	7.84	53.876	49.140

Juvenile Femoral Head Breadth Equations and Values (Robbins Schug et al. 2013)
Equation				n
ln(Body Mass) = 11.5770 - 6.2969 * ln(FH) + 1.1297 * ln (FH)2				378

Mid-Teen Long Bone Length and Bi-Iliac Breadth

Procedure for Using Mid-Teen Long Bone Length and Bi-Iliac Breadth:

Choose the estimated Sex of the individual.
Choose the estimated Age of the individual.
Use the Bi-Iliac Breadth Type menu to choose whether the following datum is skeletal or living bi-iliac breadth.
Enter the value for Bi-Iliac Breadth Measurement in millimeters.
Choose the appropriate Long Bone.
Enter the Long Bone Length in millimeters.
Once all of the data have been chosen, the estimated body mass will automatically be calculated

Mid-Teen Long Bone Length and Bi-Iliac Breadth (Ruff 2007)
	Female Age (n = 10)
Long Bone	15	16	17
Humerus	0.350(BB) + 0.133(LB) - 84.1	0.390(BB) + 0.104(LB) - 88.0	0.308(BB) + 0.209(LB) - 91.3
Radius	0.343(BB) + 0.143(LB) -74.4	0.375(BB) + 0.135(LB) - 82.7	0.246(BB) + 0.270(LB) - 73.1
Femur	0.342(BB) + 0.063(LB) - 69.3	0.374(BB) + 0.055(LB) - 75.8	0.338(BB) + 0.051(LB) - 64.6
Tibia	0.355(BB) + 0.024(LB) - 53.8	0.374(BB) + 0.042(LB) - 66.6	0.370(BB) - 0.005(LB) - 48.7

Mid-Teen Long Bone Length and Bi-Iliac Breadth(Ruff 2007)
	Male Age (n = 10)
Long Bone	15	16	17
Humerus	0.289(BB) + 0.137(LB) - 66.5	0.394(BB) + 0.216(LB) - 119.4	0.308(BB) + 0.209(LB) - 91.3
Radius	0.265(BB) + 0.174(LB) - 59.1	0.353(BB) + 0.292(LB) - 110.4	0.246(BB) + 0.270(LB) - 73.1
Femur	0.286(BB) + 0.102(LB) - 70.2	0.404(BB) + 0.168(LB) - 132.2	0.296(BB) + 0.153(LB) - 92.8
Tibia	0.282(BB) + 0.137(LB) - 75.4	0.374(BB) + 0.186(LB) - 118.6	0.234(BB) + 0.164(LB) - 68.0

Juvenile Femoral Second Moment of Area

Procedure for Using the Juvenile Polar Second Moment of Area (J):

Choose from two Techniques. Robbins et al. (2010) requires an estimated age while Robbins Schug (2013) uses panel regression to remove that added step. The Robbins Schug et a. (2013) technique works on individuals from 6 months to 12.5 years of age.
Choose the Input Type. Both techniques calculate body mass using J, however you can enter the external diameter and either the cortical thickness or medullary diameter of the femoral diaphysis to have J calculated for you.
Use the Bi-Iliac Breadth Type menu to choose whether the following datum is skeletal or living bi-iliac breadth.
Enter the the necessary data according to the input type.
If using the Robbins et al. (2010) technique, enter the age in years (between 0 and 17).
Once all of the data have been chosen, the estimated body mass will automatically be calculated.

Juvenile Femoral Second Moments of Area Equations (Robbins et al. 2010)
Age	Equation Using J	n
0	0.003(J) + 3.8	15
1	0.002(J) + 7.1	20
2	0.002(J) + 8.1	20
3	0.001(J) + 10.5	20
4	0.001(J) + 11.4	19
5	0.001(J) + 12.8	19
6	0.001(J) + 14.2	18
7	0.001(J) + 15.8	18
8	0.001(J) + 16.0	18
9	0.001(J) + 17.1	20
10	0.001(J) + 16.3	20
11	0.001(J) + 18.4	20
12	0.001(J) + 19.2	20
13	0.001(J) + 21.1	20
14	0.001(J) + 30.4	20
15	0.001(J) + 36.6	20
16	0.000(J) + 45.8	20
17	0.000(J) + 46.2	20

Juvenile Femoral Second Moments of Area Equation (Robbins Schug et al. 2013)
Equation		n
ln(Body Mass) = 2.0683 - 0.3126 * ln(J) + 0.0477 * ln (J)2		432

Equations for Calculating J
J = (π/32) * (TD4 - (TD - CD)4)
J = (π/32) * (TD4 - MD4)
J = Imax + Imin

First Metatarsal
Procedure for Estimating Body Mass Using the First Metatarsal:
1. Choose the Input Type (whether the estimated is calculated from the proximal dorsoplantar diameter alone or with the distal mediolateral diameter).
2. Enter the measurement(s).
3. Choose the Prediction Interval (optional).
4. The estimated body mass will be calculated automatically.
First Metatarsal Equations
Method Equation n SEE
DPP Only 3.553(DPP) - 37.167 87 4.251
DPP and MLD 2.900(DPP) + 0.911(MLD) - 38.450 87 4.144

Abbreviations

Guide to Abbreviations
Variable	Abbreviation
Femoral Head A-P Diameter	FH
Femoral Metaphysis Breadth	FM
Body Mass	None
Stature	None
Living Bi-Iliac Breadth	BB
Skeletal Bi-Iliac Breadth	SBB
External Diameter	TD
Cortical Diameter	CD
Medullary Diameter	MD
Maximum Moment of Area	Imax
Perpendicular Moment of Area	Imin
Second Moments of Area	J
Proximal Dorsoplantar Diameter	DPP
Distal Mediolateral Diameter	MLD

MNI (Minumim Number of Individuals) and MLNI (Most Likely Number of Individuals) techniques are used to estimate the number of individuals that constitute a skeletal collection. These methods are taken from Adams and Konigsberg (2004). L represents the bone elements from the left side, R represents the right, and P is the number of confirmed bone pairs found.

Adams and Konigsberg (2004) suggest that the MLNI should be used as a less biased alternative to standard NMI techniques. The original article advocates the calculation of highest density regions (HDR) to provide an estimated confidence interval. Unfortunately the calculation of HDRs is beyond the scope of this program. Visit http://konig.la.utk.edu/MLNI.html for the author's own automation of the MLNI.

Procedure:

Enter the Number of Left Elements of a bone.
Enter the Number of Right Elements of the same type of bone.
Enter the Number of Element Pairs of the same type of bone.
The four calculations will be presented in the region below.

If nothing is entered, the value will be calculated as zero.

Maximum (L,R): The greater number of a certain bone element on the left or right side.

L + R - P: The number of confirmed pairs subtracted from the number of unpaired bones on each side.

(L + R) /2: The average number of right and left elements.

(L + 1)(R + 1) / (P + 1)) - 1: The MLNI adapts an estimator called the Lincoln Index (Chapman, 1951; Adams and Konigsberg, 2004). Only the integer of the solution is kept.

Stature and Bi-Iliac Breadth Equations (Ruff et al. 2005)

Method	n	Equation
Male	32	(0.422)(Stature) + (3.126)(BB) - 92.9
Female	26	(0.504)(Stature) + (1.804)(BB) - 72.6
Bi-Iliac Breath (BB)		(1.17)(SBB) - 3

First Metatarsal Equations
Method	Equation	n	SEE
DPP Only	3.553(DPP) - 37.167	87	4.251
DPP and MLD	2.900(DPP) + 0.911(MLD) - 38.450	87	4.144

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