Overview
Version 3.2 is the result of a systematic review of the calculation engine of version 3.1, carried out on October 27, 2026. The review compared every stored coefficient with the original publications or, where an original was not accessible, with a verbatim reproduction (Bass 1987 for the corrected US Black female radius equation, Bidmos and Brits 2025 for the Generic equations), tested the statistical model against the published figures of the reference samples, and recomputed the 40 regression scenarios of version 3.1. This page lists every change in the calculation, with the reason and the size of its effect, so that a reader of an earlier report can see what has changed and why. Nothing in version 3.2 is hidden behind a version number: the full method is on the Scientific Method page, and the grade rule is on the Reliability Grades page.
In short, version 3.2 reads the Trotter and Gleser coefficients from the scanned original tables (one corrected equation from a verbatim quotation), uses one published equation per result instead of a weighted combination of bones, computes a prediction interval with Student's t and a leverage term, replaces the percentage Accuracy Index with a reliability grade that states its reasons, shows height at death as separate lines with the published negative sign, drops the correction for time since waking, handles the tibia measurement definition explicitly, adds the Mexican series of Trotter and Gleser (1958) and a fragment module based on Steele (1970), and withholds the Thai sample until its equations can be verified against the original publication. For most inputs the estimate moves by less than 2 cm and the interval becomes somewhat wider; for inputs that relied on a placeholder or mixed coefficient of version 3.1 (fibula, ulna, and the Asian and US Black humerus and radius), the estimate moves by up to about 10 cm. The section on typical effects gives the numbers.
Coefficients by reference sample
Version 3.1 stored its coefficients under the labels European, African, Asian, Thai, and Generic. The review found that the fibula and ulna equations of version 3.1 were identical in all four population sets and both sexes (male fibula 2.40, 80.56, SEE 4.89; male ulna 3.48, 77.45, SEE 5.52; female fibula 2.68, 63.90, SEE 5.72; female ulna 3.96, 54.66, SEE 5.69), that is, they were placeholders rather than the equations of the respective samples; that the Asian and African sets mixed intercepts and slopes from different publications; and that the Thai set did not reproduce the equations of Mahakkanukrauh et al. (2011). Version 3.2 therefore rebuilt every set from the source tables. The Trotter and Gleser coefficients were read from the scanned original publications (American Journal of Physical Anthropology, volumes 10 and 16); image excerpts of each table are kept with the project. The one exception is the radius equation of US Black women, which is the corrected equation of the 1977 corrigendum as quoted verbatim by Bass (1987, p. 28). The Generic coefficients of Albanese et al. (2016) were confirmed against their reproduction in Bidmos and Brits (2025) and are unchanged.
The samples are now named after the publications: US White and US Black (Trotter and Gleser 1952) in place of European and African, and Asian male (Trotter and Gleser 1958, Mongoloid series) in place of Asian. The samples are US military samples of World War II and the Korean War and samples of the Terry Collection, from the first half and the middle of the twentieth century; the new names point to the publications that describe them. The table lists every equation of version 3.1 next to its replacement. Coefficients are slope a, intercept b in centimeters, and standard error of estimate (SEE) in centimeters; n is the sample size of the equation as published or as assigned by the program convention described on the method page.
| Sample and sex | Bone | 3.1: a, b, SEE | 3.2: a, b, SEE, n | Source of the 3.2 values | What changed |
|---|---|---|---|---|---|
| US White male (3.1: European male) | Femur | 2.38, 61.41, 3.27 | 2.38, 61.41, 3.27, 710 | Trotter and Gleser (1952), table 13, p. 495; n from table 8, p. 481 | unchanged |
| Tibia | 2.42, 81.93, 4.00 | 2.52, 78.62, 3.37, 710 | same | slope, intercept, SEE; the 3.1 values came from the 1958 series | |
| Fibula | 2.40, 80.56, 4.89 | 2.68, 71.78, 3.29, 580 | same | placeholder replaced | |
| Humerus | 2.89, 78.10, 4.57 | 3.08, 70.45, 4.05, 710 | same | slope, intercept, SEE; the 3.1 values came from the 1958 series | |
| Radius | 3.79, 79.42, 4.66 | 3.78, 79.01, 4.32, 710 | same | slope, intercept, SEE; the 3.1 values came from the 1958 series | |
| Ulna | 3.48, 77.45, 5.52 | 3.70, 74.05, 4.32, 644 | same | placeholder replaced | |
| US White female (3.1: European female) | Femur | 2.47, 54.10, 3.72 | 2.47, 54.10, 3.72, 63 | Trotter and Gleser (1952), table 13, p. 495; n from table 5, p. 478 | unchanged |
| Tibia | 2.90, 61.53, 3.66 | 2.90, 61.53, 3.66, 63 | same | unchanged | |
| Fibula | 2.68, 63.90, 5.72 | 2.93, 59.61, 3.57, 63 | same | placeholder replaced | |
| Humerus | 3.36, 57.97, 4.45 | 3.36, 57.97, 4.45, 63 | same | unchanged | |
| Radius | 4.74, 54.93, 4.24 | 4.74, 54.93, 4.24, 63 | same | unchanged | |
| Ulna | 3.96, 54.66, 5.69 | 4.27, 57.76, 4.30, 63 | same | placeholder replaced; largest single effect of the revision, see below | |
| US Black male (3.1: African male) | Femur | 2.10, 70.35, 3.91 | 2.11, 70.35, 3.94, 80 | Trotter and Gleser (1952), table 13, p. 495; n from p. 484 | slope and SEE; 3.1 mixed a 1958 slope with the 1952 intercept |
| Tibia | 2.19, 85.60, 3.70 | 2.19, 86.02, 3.78, 79 | same | intercept and SEE | |
| Fibula | 2.40, 80.56, 4.89 | 2.19, 85.65, 4.08, 68 | same | placeholder replaced | |
| Humerus | 2.88, 75.55, 4.23 | 3.26, 62.10, 4.43, 79 | same | slope, intercept, SEE | |
| Radius | 3.78, 80.41, 4.48 | 3.42, 81.56, 4.30, 74 | same | slope, intercept, SEE; the 3.1 slope was that of US White men | |
| Ulna | 3.48, 77.45, 5.52 | 3.26, 79.29, 4.42, 68 | same | placeholder replaced | |
| US Black female (3.1: African female) | Femur | 2.28, 59.76, 3.40 | 2.28, 59.76, 3.41, 177 | Trotter and Gleser (1952), table 13, p. 495; n from table 5, p. 478 | SEE |
| Tibia | 2.45, 72.84, 3.70 | 2.45, 72.65, 3.70, 177 | same | intercept | |
| Fibula | 2.68, 63.90, 5.72 | 2.49, 70.90, 3.80, 177 | same | placeholder replaced | |
| Humerus | 2.75, 66.89, 4.57 | 3.08, 64.67, 4.25, 177 | same | slope, intercept, SEE | |
| Radius | 3.67, 65.53, 4.30 | 3.67, 71.79, 4.59, 177 | Trotter and Gleser (1977) corrigendum, as quoted by Bass (1987, p. 28) | intercept and SEE; the 1952 printing contained an error corrected by the authors in 1977 | |
| Ulna | 3.96, 54.66, 5.69 | 3.31, 75.38, 4.83, 177 | Trotter and Gleser (1952), table 13 | placeholder replaced | |
| Asian male, Mongoloid series (3.1: Asian male) | Femur | 2.15, 69.89, 3.80 | 2.15, 72.57, 3.80, 60 | Trotter and Gleser (1958), table 12, p. 120; n from table 3, pp. 84 and 85 | intercept |
| Tibia | 2.39, 80.56, 3.50 | 2.39, 81.45, 3.27, 67 | same | intercept and SEE | |
| Fibula | 2.40, 80.56, 4.89 | 2.40, 80.56, 3.24, 61 | same | SEE; the placeholder slope and intercept happened to be those of this series | |
| Humerus | 2.68, 74.46, 4.30 | 2.68, 83.19, 4.25, 65 | same | intercept and SEE | |
| Radius | 3.50, 74.23, 4.24 | 3.54, 82.00, 4.60, 67 | same | slope, intercept, SEE | |
| Ulna | 3.48, 77.45, 5.52 | 3.48, 77.45, 4.66, 65 | same | SEE; as for the fibula | |
| Asian female (3.1 only) | Six bones | femur 2.45, 54.13, 3.80; tibia 2.72, 62.82, 3.50; humerus 3.08, 56.10, 4.24; radius 3.87, 55.07, 4.08; fibula 2.68, 63.90, 5.72; ulna 3.96, 54.66, 5.69 | not offered | none: Trotter and Gleser (1958) publish no female equations for the Mongoloid series | set withdrawn; no source could be identified |
| Thai (3.1 only) | Six bones, both sexes | male: femur 2.32, 65.53, 5.06; tibia 2.39, 81.45, 5.28; fibula 2.40, 80.56, 4.89; humerus 2.89, 70.64, 5.57; radius 3.54, 81.94, 5.47; ulna 3.48, 77.45, 5.52. Female: femur 2.60, 49.20, 5.21; tibia 2.72, 62.82, 5.79; fibula 2.68, 63.90, 5.72; humerus 3.36, 51.66, 5.94; radius 4.05, 57.76, 5.63; ulna 3.96, 54.66, 5.69 | listed, not available | Mahakkanukrauh et al. (2011), to be verified | set withheld: the 3.1 male femur equation was the US White male equation of 1958 (2.32, 65.53), the male tibia equation that of the Mongoloid series (2.39, 81.45), and the female tibia equation that of the Asian female set; only the standard errors 5.06, 4.89, 5.21, and 5.63 agree with the published abstract |
| Generic (Albanese et al. 2016) | Female: femur, tibia, femur and tibia | 2.37, 57.915, 3.892; 2.44, 73.985, 4.425; 1.65 and 0.89, 57.360, 3.761 | unchanged | Albanese et al. (2016) as reproduced by Bidmos and Brits (2025) | unchanged; all nine equations confirmed |
| Male | 2.50, 55.797, 4.781; 2.44, 78.999, 4.754; 1.27 and 1.31, 63.094, 4.528 | unchanged | same | unchanged | |
| Sex unknown | 2.78, 41.507, 4.624; 2.89, 59.745, 5.068; 1.83 and 1.09, 43.790, 4.453 | unchanged | same | unchanged | |
| Mexican male, Mexican series | Six bones | not offered | femur 2.44, 58.67, 2.99, 50; tibia 2.36, 80.62, 3.73, 51; fibula 2.50, 75.44, 3.52, 45; humerus 2.92, 73.94, 4.24, 58; radius 3.55, 80.71, 4.04, 56; ulna 3.56, 74.56, 4.05, 57 | Trotter and Gleser (1958), table 12, p. 120; n from table 3, p. 85 | new in 3.2 |
The two-bone equations with a common slope (femur and tibia for the 1952 samples and the Mongoloid series, femur and fibula for the Mongoloid series) are new in version 3.2 as published equations; version 3.1 did not use them but combined single-bone results (see below). The Mexican series has no two-bone equations, because the authors give none for that series (Trotter and Gleser 1958, p. 121).
Size of the effect: for a US White female ulna of 23.9 cm, version 3.1 gave 3.96 × 23.9 + 54.66 = 149.3 cm and version 3.2 gives 4.27 × 23.9 + 57.76 = 159.8 cm, a difference of 10.5 cm; this is the largest effect of any coefficient change. For an Asian male humerus of 32.8 cm the estimate rises by about 8.7 cm (intercept 74.46 to 83.19). For a US Black male radius of 24.6 cm the estimate falls by about 7.7 cm (3.78 × 24.6 + 80.41 = 173.4 cm against 3.42 × 24.6 + 81.56 = 165.7 cm). At the sample mean, the corrected US White male tibia, humerus, and radius equations differ from the 3.1 values by 0.5, 1.3, and 0.7 cm; the femur equations of the US White and US Black samples by less than 0.5 cm; the Asian male femur by 2.7 cm (intercept 69.89 to 72.57).
Tibia measurement definition
Trotter measured the tibia without the medial malleolus, which makes her lengths 10 to 12 mm shorter than the condylo-malleolar length of current standards (Buikstra and Ubelaker 1994). Applying the Trotter and Gleser tibia equation of white men to a tibia measured with the malleolus overestimates stature by about 2.5 to 3.0 cm (Jantz, Hunt, and Meadows 1995); Jantz, Meadows Jantz, and Ousley (2020) confirmed the 10 mm correction. Version 3.1 left the definition open. Version 3.2 asks how every tibia was measured and, for the US White and US Black samples, subtracts 1.0 cm from a tibia measured with the malleolus before applying the equation; the result states the entered length, the deduction, and the reason. With the femur and tibia equation of US White men, whose slope is 1.30, the deduction changes the estimate by 1.3 cm; with the single tibia equation (slope 2.52), by 2.5 cm. For the Generic sample the condylo-malleolar length is the definition of the reference sample, and no deduction is made; a tibia measured without the malleolus is used as entered with a warning and a grade of B at best. For the Mongoloid and Mexican series the tibia definition of the 1958 paper has not been established; tibia results carry a warning and are graded B at best.
One published equation instead of a weighted combination
Version 3.1 combined the single-bone estimates of all entered bones into one weighted mean, with a combined standard error that assumed a residual correlation of 0.36 between bones, applied a completeness factor, and was never allowed to fall below half of the smallest single-bone error. The review identified two problems. First, ANSI/ASB Standard 045 (2019, 4.2.5) does not allow the results of several stature estimations to be combined into one estimate unless the method itself publishes the combination. Second, the correlation of 0.36 is lower than what the published standard errors of the reference samples imply: derived from the single-bone and two-bone standard errors and the stature standard deviations of the samples, the residual correlations lie between 0.65 and 0.86 (method page, consistency check). With six bones, the 3.1 interval was narrower than a 95 percent prediction interval even at its own assumed correlation, and more so at the correlations the samples imply: in a simulation with six bones of a US White man, its coverage was about 89 percent at a true correlation of 0.36, 83 percent at 0.6, and 77 percent at 0.8.
Version 3.2 uses one published equation per result: a stored two-bone equation of the selected sample if its bones are present in a calculable condition, or a single-bone equation, whichever ranks first by reliability grade and then by total standard error. All other bones are used only for the consistency check and are listed as Cross-check only. Effect: for the six complete bones of a US White man (femur 45.6, tibia 37.2, fibula 36.6, humerus 32.8, radius 24.6, ulna 26.4 cm), version 3.1 gave 170.9 cm with an interval of 166.1 to 175.7 cm (half width 4.8 cm); version 3.2 gives 169.6 cm from the femur and tibia equation with an interval of 163.7 to 175.6 cm (half width 5.9 cm). The interval is wider because it is now the prediction interval of one published equation; the estimate moves because the tibia is reduced by 1.0 cm and the 3.1 combination gave weight to the placeholder equations.
Prediction interval
Version 3.1 computed the interval with the normal quantile and added a fixed instrument uncertainty of 0.5 cm in stature. Version 3.2 computes a prediction interval with Student's t at the degrees of freedom of the reference regression wherever a sample size is published or assigned by program convention (the Trotter and Gleser samples; for the 1958 series the sample size per equation is taken from the side counts of table 3), with a leverage term for the distance of the measured length from the reference mean; where the mean and standard deviation of the length are not stored (two-bone equations, the 1958 series, the corrected US Black female radius), the leverage is fixed at 2 standard deviations (program convention). Where no sample size is available (the Generic equations and the fragment module), the normal quantile is used and the line is labeled approximate. The measurement uncertainty is now a length uncertainty of 0.2 cm (program convention, on the order of the technical error of measurement between trained observers; Langley et al. 2018), converted to stature by the slope of the equation, so that it is larger for a radius than for a femur. Preservation enters the same way: minor surface loss adds 0.2 cm and refitted fragments add 0.5 cm of length uncertainty, in place of the multipliers 1.12 and 1.28 that version 3.1 applied to the standard error. Compared with the normal quantile, Student's t is larger by 0.2 percent for n = 710 and by 1.6 to 2.9 percent for the sample sizes of 80 down to 45 (US Black men, US White women, and the 1958 series); together with the 1/n term and the leverage convention at 2 standard deviations, the interval of these smaller samples widens by a factor of about 1.05 to 1.09, that is, by about 0.4 to 0.6 cm, while for the samples with n = 177 to 710 the effect is at most 0.2 cm; the leverage term is small for lengths near the reference mean and large for lengths outside the reference range. Example: for a US White female femur of 50.0 cm, outside the reference range of 36.6 to 49.3 cm, the leverage term is 0.125 and the half width 8.0 cm.
Consistency check
Version 3.1 compared each bone with the mean of all bones including itself, treated the bones as independent, and applied no correction for the number of comparisons; the review found that the false-alarm rate ranged from 0.2 to 35 percent depending on the number of bones and the true correlation, and that a bone in poor condition could mask a discrepancy because its wider error reduced its standardized difference. Version 3.2 compares each bone with the mean of the other bones (leave-one-out), uses the covariance of the estimates with the residual correlation derived for each sample (or the convention 0.65 where it cannot be derived), divides the 5 percent level by the number of bones (Bonferroni correction) for three or more bones, and judges discordance with the preservation terms set to zero, so that a poor condition cannot hide a disagreement. A discordance is a grade C reason for the whole result and never changes the estimate. Example from the scenarios: US White male, femur 45.6, tibia 37.2, radius 29.0 cm. Version 3.1 gave 172.2 cm with an Accuracy Index of 79; version 3.2 gives 169.6 cm from the femur and tibia equation with grade C because the bones disagree. The calculator reports that several bones disagree and warns that the radius lies outside the reference range of the sample (21.9 to 28.4 cm); the radius alone implies 188.6 cm, which points to a measurement, side, or identification error of the radius, or to commingling.
Reliability grade instead of the Accuracy Index
Version 3.1 printed an Accuracy Index, a percentage from a formula that combined the interval width, the number of bones, the condition, the consistency, the population context, and the sex assessment into one number between 32 and 92. The review documented that the index was not monotone (worsening the condition of a single bone raised the index in 2 to 4 percent of random cases, and six reconstructed bones scored 91 against 89 for three complete bones), that a bone far outside the reference range received the same score as one inside it, and that a percentage is read as a probability although no such probability exists. Version 3.2 reports the prediction interval with its half width in centimeters and a reliability grade from A to D with its reasons in plain words, from a fixed rule that cannot improve when the evidence weakens; this was tested on 1,000 random cases with 2,999 worsening steps and no violation. The Reliability Grades page gives the rule. Example: a US White male femur of 30.0 cm gave 132.8 cm with an index of 75 in version 3.1; version 3.2 gives 132.8 cm with grade D and the warning that the femur is outside the reference range of the sample, because the result rests on extrapolation.
Age at death
The Trotter and Gleser equations predict the maximum stature of early adulthood, and stature declines with age. Trotter and Gleser (1951) give 0.06 cm per year above 30 years and Galloway (1988) gives 0.16 cm per year above 45 years; both are to be subtracted. Version 3.1 contained an age term that was active only when hours since waking were entered, that was added to the estimate rather than subtracted, and whose size was 0.0048 cm per year above 50 years: at 70 years it raised the estimate by 0.1 cm, where the published adjustments lower it by 2.4 cm (Trotter and Gleser) or 4.0 cm (Galloway). Version 3.2 never changes the main estimate or its interval for the entered age at death; when an age at death is entered, it adds a separate block with Stature in early adulthood (uncorrected) followed by Height at death according to Trotter and Gleser (1951) and according to Galloway (1988), each for both ends of the age range, with the note that these values are not comparable to a height on a license or in a missing-person report (ANSI/ASB 045, 4.2.4). In the fragment module the main estimate is converted from the mean age of Steele's reference group to early adulthood (0.06 cm for each year by which that mean age exceeds 30); this conversion depends on the reference group, not on the entered age, and height at death is given according to Trotter and Gleser (1951) only. Example: US White male, femur 47.0, tibia 38.5 with malleolus, humerus 33.0 cm, age 60 to 70: stature in early adulthood 173 cm; height at death 171 cm according to Trotter and Gleser and 171 to 169 cm according to Galloway.
Correction for time since waking, removed
Version 3.1 offered a field for hours since waking and added 0.083 cm per hour, up to 14 hours, to the estimate, on the grounds that the reference statures were morning or cadaver measurements. The review rejected the correction for three reasons. A skeleton has no time of day, so there is nothing to correct. The stature definition of the reference sample already contains whatever diurnal variation the reference measurements had, and that variation is part of the published standard error (Tyrrell, Reilly, and Troup 1985 measured a mean loss of 19.3 mm over the day, 54 percent of it in the first hour after rising). And the direction was not supported: if the reference were a morning stature, a comparison with a later measurement would call for the opposite sign. The correction shifted the estimate by 0.7 cm at 8 hours and by up to 1.3 cm at 14 hours together with the age term; version 3.2 has no such field. A comparison with a reported living height should adjust the reported height for time of day, self-report, and age instead of shifting the estimate.
Fragments: the Steele module replaces the fragmentary condition
Version 3.1 accepted a bone in the condition Fragmentary estimate, multiplied the standard error by 1.55, and computed stature from the entered length as if it were a maximum length; its method page described such a length as inferred with a published fragment-to-length relationship, but neither named one nor offered one in the calculator. ANSI/ASB 045 (4.1) states that maximum length should not be estimated from fragmented bones. Version 3.2 blocks a fragmentary bone in the adult module and instead offers the module Fragment estimation (Steele 1970), which estimates stature directly from the lengths of defined segments of the femur, tibia, or humerus with the regression equations of Steele (1970), tables XLVIII to L, Terry Collection, US White and US Black, male and female. The module uses 47 of the 48 published direct equations; the first tibia equation for US Black men (constant 5.86) was excluded because it gives 96.8 cm at the segment means of its own sample, which indicates a printing error. Steele's tables XXXVI to XLVII, which estimate maximum length from segments, are not used: their single-segment slopes are identical to the correlation coefficients of the same tables, which indicates a printing error, and the two-step route from segments to maximum length to stature is excluded by the standard. Fragment estimates are graded C at best, their intervals are approximate because no sample size per equation is published, and they carry the warning that the reference individuals were born mostly in the nineteenth century. Example: US White male, femur segments 2 and 3 at the sample means (27.13 and 7.12 cm), equation 2.71 × segment 2 + 3.06 × segment 3 + 73.00 cm: 170 cm in early adulthood, approximate interval 161 to 179 cm, grade C. The scenario of version 3.1 with a fragmentary humerus of 30.1 cm, which gave 159.1 cm with an interval of 145.6 to 172.7 cm and an index of 33, is no longer calculable in the adult module.
Unknown sex
Version 3.1 averaged the male and female coefficients for unknown sex and multiplied the larger standard error by 1.25. An averaged equation describes no sample, and ANSI/ASB 045 (4.2.3) asks for a pooled equation where sex is unknown. Version 3.2 uses the pooled equations of Albanese et al. (2016) with the Generic sample; with a population sample, for which no pooled equation is published, it shows the result under both sex models together with a combined range that contains both intervals; no single estimate is given, and the grade is C at best. Example: US White, sex unknown, femur 45.6 cm. Version 3.1 gave 168.3 cm with an interval of 159.2 to 177.5 cm; version 3.2 gives 169.9 cm if male and 166.7 cm if female with a combined range of 159.1 to 176.4 cm.
Typical effect in centimeters
The 40 regression scenarios of version 3.1 were recomputed with version 3.2; the complete list with the reason for each difference is kept with the project. The following rows are taken from that list. Lengths are in centimeters, every tibia is entered as condylo-malleolar length, all bones are entered as left, and the interval is 95 percent; the 3.1 column shows the Accuracy Index, the 3.2 column the grade. Values are given to 0.1 cm for comparison; the calculator shows the estimate and the interval limits in whole centimeters.
| Inputs | Version 3.1 | Version 3.2 | Main causes |
|---|---|---|---|
| US White male: femur 47, tibia 38.5, humerus 33 | 173.9 cm, 168.5 to 179.2 cm, index 89 | 173.1 cm, 167.2 to 179.1 cm, grade A | Tibia and humerus coefficients from the 1952 table; tibia reduced by 1.0 cm; femur and tibia equation instead of a combination; t and leverage |
| US White male: six complete bones (femur 45.6, tibia 37.2, fibula 36.6, humerus 32.8, radius 24.6, ulna 26.4) | 170.9 cm, 166.1 to 175.7 cm, index 92 | 169.6 cm, 163.7 to 175.6 cm, grade A | Fibula and ulna placeholders replaced; tibia deduction; one equation instead of six combined; interval no longer narrowed by the 0.36 correlation |
| US White female: six complete bones (femur 42.1, tibia 34.3, fibula 33.8, humerus 30.1, radius 22, ulna 23.9) | 157.9 cm, 153.1 to 162.8 cm, index 92 | 158.0 cm, 150.6 to 165.4 cm, grade A | Fibula and ulna placeholders replaced; tibia reduced by 1.0 cm; the femur and tibia equation gives almost the same value as the 3.1 combination; the interval is now that of one equation |
| US Black male: six complete bones (as above) | 168.8 cm, 164.0 to 173.6 cm, index 92 | 165.1 cm, 157.8 to 172.4 cm, grade A | All six coefficients corrected (humerus, radius, fibula, ulna substantially); tibia deduction; one equation |
| US Black male: ulna 26.4, minor surface loss | 169.3 cm, 157.2 to 181.5 cm, index 50 | 165.4 cm, 156.1 to 174.6 cm, grade B | Ulna placeholder replaced; 0.2 cm length uncertainty instead of the multiplier 1.12; interval narrower because the published SEE is 4.42 cm instead of 5.52 cm |
| Asian male: six complete bones (as above) | 166.3 cm, 161.6 to 171.0 cm, index 92 | 170.5 cm, 163.9 to 177.2 cm, grade A | Intercepts corrected against table 12 of 1958; femur and fibula equation chosen; one equation |
| Asian male: humerus 12.91 in (32.8 cm), 4 hours since waking | 64 in (162.6 cm), 60.7 to 67.4 in, index 68 | 171.1 cm, 162.2 to 180.0 cm, grade B | Humerus intercept 74.46 to 83.19; time-of-day correction removed; centimeters shown first |
| US White male: femur 45.6, tibia 37.2, age 65, 8 hours since waking | 171.5 cm, 165.8 to 177.1 cm, index 83 | 169.6 cm, 163.7 to 175.6 cm, grade A; height at death shown as separate lines | Time-of-day correction removed; age no longer shifts the main line; tibia coefficients and deduction |
| US White female: femur 42.1, 12 hours since waking, age 45 | 159.1 cm, 151.7 to 166.4 cm, index 72 | 158.1 cm, 150.5 to 165.7 cm, grade B | Time-of-day correction removed; t and leverage; grade B because the total SE of 3.8 cm is above the 3.6 cm threshold |
| US White male: femur 45.6, tibia 37.2, radius 29 (discordant) | 172.2 cm, 166.4 to 178.1 cm, index 79 | 169.6 cm, 163.7 to 175.6 cm, grade C (bones disagree) | Radius not used for the estimate; the consistency check reports that several bones disagree |
| US White, sex unknown: femur 45.6 | 168.3 cm, 159.2 to 177.5 cm, index 57 | if male 169.9 cm, if female 166.7 cm, combined range 159.1 to 176.4 cm, grade C | Both sex models instead of averaged coefficients |
| Generic male: femur 45.6, tibia 37.2 | 169.7 cm, 160.9 to 178.6 cm, index 68 | 169.7 cm, 160.8 to 178.6 cm, grade B | Unchanged coefficients; the Albanese femur and tibia equation was already the main estimate; interval remains on the normal model because no sample size is published |
| US White male: femur 30 (outside the reference range) | 132.8 cm, 126.3 to 139.3 cm, index 75 | 132.8 cm, 126.1 to 139.5 cm, grade D, warning | Extrapolation now detected and graded |
| US White female: humerus 30.1, fragmentary | 159.1 cm, 145.6 to 172.7 cm, index 33 | not calculable in the adult module; use the fragment module with segment lengths | ANSI/ASB 045, 4.1 |
| Thai male: femur 44, tibia 36, humerus 36.5 | 170.1 cm, 162.8 to 177.5 cm, index 82 | sample not available in this version | Coefficients not verifiable against the original publication |
Across the 40 scenarios, estimates of the US White and Generic samples that rest on femur, tibia, or both and carried no time-of-day entry move by at most 1.3 cm; estimates that used a placeholder fibula or ulna, or the Asian or US Black humerus or radius, move by several centimeters, up to 8.4 cm for the Asian male humerus (162.67 to 171.07 cm, the inch row above); the Thai scenarios can no longer be calculated. Outside the scenarios, a single ulna can move by up to 10.5 cm (see the coefficient section). In the rows above, the half width of multi-bone results with the Trotter and Gleser samples grows by 0.6 cm for the three complete bones, by 0.3 cm for the femur and tibia row with age 65, by 1.1 to 2.6 cm for the six-bone rows, and by 0.1 cm for the discordant row, because each is now the prediction interval of one published equation; with the Generic sample the interval changes by at most 0.1 cm. The interval of a single ulna with minor surface loss becomes narrower, from a half width of 12.2 cm to 9.2 cm, because the published standard error of the corrected equation (4.42 cm) is smaller than the placeholder value (5.52 cm) and the preservation term is now a length uncertainty instead of a multiplier.
New in version 3.2
- Side. Each bone records Left, Right, or Not determined; the side is printed in the result and the report.
- Condition. Five options with defined effects: Complete; Minor surface loss, end points intact (0.2 cm); Refitted fragments, full length measurable (0.5 cm, grade C at best); Fragmentary, end point missing (not calculated); and Burned or calcined (not calculated). Reconstructed length of version 3.1 is now Refitted fragments.
- Healed fracture or deformity. A marked bone is calculated for information only and takes no part in the estimate or the consistency check.
- Tibia measurement. A required question for every tibia: with the malleolus, without the malleolus, or from the intercondylar eminence (not supported).
- Interval level. 95 or 90 percent; the level does not change the estimate, the grade, or the consistency threshold.
- Age at death as a range. From and to, 18 to 110 years, with height at death as separate lines.
- Case ID and Examiner. Optional fields of up to 80 characters that appear in the report and the JSON file only.
- Print report. A print view with the inputs as entered, every result line, the version, the date, and the build hash of the calculation files.
- JSON export. A file with all inputs, all candidate equations with coefficients, SEE, n, total SE, grade, and reasons, the chosen result, the bone-level estimates, the consistency check, the age block, warnings, notes, sources, and the stature definition of the reference sample.
- Mexican male (Trotter and Gleser 1958, Mexican series). Six single-bone equations from table 12; no two-bone equations exist for this series. Example: femur 45.6, tibia 37.5 cm with malleolus gives 170 cm, 164 to 176 cm, grade A from the femur equation (2.44 × femur + 58.67 cm, SEE 2.99 cm, n = 50); the tibia serves as a cross-check with a warning about its definition.
- Fragment estimation (Steele 1970). Direct stature equations from segment lengths of femur, tibia, and humerus, with the landmark definitions printed in the form and in the report.
- Input checking in the form. The calculator checks every field itself and names the field and the reason; lengths may carry any number of decimals.
- Results in centimeters first. With inches selected, lengths are converted using the factor 2.54 without rounding and every result line shows centimeters first, feet and inches after. The estimate and the interval limits are shown in whole centimeters and the half width to 0.1 cm; version 3.1 showed the estimate and the limits to 0.1 cm.
- Every result states its conventions and its sources. The line Program conventions lists every value that is a decision of the program rather than a published figure; Sources applied lists only the publications actually used.
No longer offered, and why
- Thai (Mahakkanukrauh et al. 2011). Listed but not selectable. The equations of version 3.1 did not reproduce the publication (see the coefficient table). At present the original paper is not freely accessible, and the secondary sources that reprint its equations contradict one another in the digits (for example, the intercept of the male tibia equation, 52.946 in one source and 52.964 in another), so the set is not released. It will be released when the equations can be read from the original tables.
- Asian female. Trotter and Gleser (1958) publish no female equations for the Mongoloid series, and no source for the 3.1 values could be identified. For female or unknown sex with Asian remains, the Generic sample is the available option; its equations come from the Terry Collection and are not an Asian reference.
- Time since waking. Removed; see above.
- Accuracy Index. Removed from the result, the report, and the JSON file; replaced by the interval and the grade. The address /accuracy-index/ is kept so that links in existing reports continue to resolve.
- Fragmentary estimate in the adult module. Replaced by the fragment module.
- Averaged coefficients for unknown sex. Replaced by both sex models or the pooled Generic equations.
How version 3.2 was checked
- Sources. With the one exception named below, every Trotter and Gleser coefficient, sample size, mean, and standard deviation was read digit by digit from the scanned original tables (1952: tables 5, 8, and 13 and page 484; 1958: tables 3 and 12); the Steele equations from tables XLVIII to L and the segment statistics from tables XXIX to XXXII of the 1970 chapter. Image excerpts of every table used are stored with the project. The US Black female radius equation was taken from the verbatim quotation of the 1977 corrigendum in Bass (1987). The Generic equations were confirmed against Bidmos and Brits (2025).
- Review. The data, the model, and the texts of version 3.1 and of the 3.2 specification were reviewed in writing from three angles: the regression coefficients against their sources, the statistical model, and forensic casework. Every finding was reproduced with an independent reimplementation of the calculation, and the results were consolidated into a written specification from which the calculator and the test reference were built.
- Independent recalculation. A reference implementation of the specification, written without access to the calculator's code, recomputed 79 test measurements: 50 for the adult module, 8 for the Mexican series, and 21 for the fragment module. All 79 cases agree with the reference: estimates, limits, and standard errors to within 0.01 cm, grades, labels, and messages exactly.
- Monotonicity. 1,000 random cases with 2,999 single worsening steps (complete to minor surface loss, minor to refitted, known sex to unknown): the grade never improved and, with an equal grade, the total standard error of the main estimate never decreased.
- Mean check of the Steele equations. Each of the 47 equations in use, evaluated at the segment means of its group, reproduces the group's mean stature to within 1.24 cm; the excluded equation misses by about 75 cm.
- Regression against version 3.1. All 40 scenarios of version 3.1 were recomputed and every difference was attributed to a listed cause.
- Pages. The content security policy of every page produced no violation in the browser; the calculator runs without external requests.
Known limits and open points
- The Thai sample (Mahakkanukrauh et al. 2011), the European Holocene equations of Ruff et al. (2012), and the line of organic correlation of Sjøvold (1990) are not included: in each case the original tables are not accessible to the project at present, and the secondary sources that reprint them disagree in the digits or omit the standard errors.
- The tibia definition of the Mongoloid and Mexican series (1958) has not been established; tibia results for these samples are graded B at best.
- For the corrected US Black female radius equation no mean and standard deviation of the corrected sample are available, so its reference range is reported as unknown.
- For the Generic equations no sample size per equation and no length distributions are published; intervals are approximate and extrapolation cannot be checked.
- Steele (1970) publishes no sample size per equation and no stature standard deviation per equation; fragment intervals are approximate, and the reference individuals were born mostly in the nineteenth century, so secular change is not accounted for.
- The length uncertainty of 0.2 cm, the preservation terms of 0.2 and 0.5 cm, the segment uncertainty of 0.3 cm, the grade threshold of 3.6 cm, the reference range rule of 2.5 standard deviations, the leverage approximation at 2 standard deviations, the sample sizes assigned to the 1958 equations and to two-bone equations, and the default residual correlation of 0.65 are program conventions. They are printed with every result.
- The age adjustment is a population average; its uncertainty is not included in the interval.
- The calculator does not compare the estimate with a reported living height and does not assess population affinity; both remain with the examiner. Stature alone is not a basis for excluding a missing person (ANSI/ASB 045, 4.2.4 and Annex A).
- The Subadult Beta module remains locked.
Recommendation for users of earlier results
A report produced with version 3.1 or earlier should be recomputed with version 3.2 from the measurements as recorded. The new report supersedes the old one; keep both in the case file, because the earlier report may already have been relied on. Where an earlier result has been passed to investigators, to a court, or to another expert, inform the recipient of the recomputed result and of the reason for any difference; the sections above can be cited for the reasons. If an earlier report quoted the Accuracy Index, the new report replaces that figure with the interval and the grade. Version 3.1 showed its version number in the result heading on screen; where a transcribed result does not state the version, ask the examiner which version was used. The recomputation matters most where the earlier result used a fibula or an ulna, the Asian, African, or Thai set, a tibia measured with the malleolus under a Trotter and Gleser equation, a correction for time since waking, an age, several bones combined, a fragmentary bone, or unknown sex. For a tibia, the recomputation requires the measurement definition; if it was not recorded, the condylo-malleolar length is the usual definition of current standards and should be confirmed from the laboratory protocol. A fragmentary bone needs the segment lengths between Steele's landmarks, which cannot be derived from an earlier entry. Results with the Thai set or with the Asian female set have no equivalent in version 3.2; the Generic sample (femur and tibia) is the alternative that does not assume a population, and any other choice of reference sample is the examiner's decision and should be justified in the new report. In the 40 recomputed scenarios, results based on a femur or on femur and tibia of the US White or Generic samples without a time-of-day entry changed by at most 1.3 cm, and their intervals became somewhat wider. This is an observation from those scenarios, not a limit for every case; a tibia measured with the malleolus alone lowers a single tibia estimate of the 1952 samples by 2.2 to 2.9 cm. Even where the estimate hardly moves, the new report should be used, because the grade, the conventions, and the sources are now stated. Version 3.2 shows the estimate and the interval limits in whole centimeters, version 3.1 to 0.1 cm, so a small difference can be rounding alone. Save the JSON file of the new calculation with the case; it contains every input and every candidate equation.
References
- Albanese, J., Tuck, A., Gomes, J., & Cardoso, H. F. V. (2016). An alternative approach for estimating stature from long bones that is not population- or group-specific. Forensic Science International, 259, 59 to 68. https://doi.org/10.1016/j.forsciint.2015.12.011
- ANSI/ASB Standard 045, First Edition (2019). Standard for stature estimation in forensic anthropology. Academy Standards Board, American Academy of Forensic Sciences.
- Bass, W. M. (1987). Human osteology: A laboratory and field manual (3rd ed.). Columbia: Missouri Archaeological Society.
- Bidmos, M. A., & Brits, D. (2025). Evaluating the accuracy of population-specific versus generic stature estimation regression equations in a South African sample. International Journal of Legal Medicine, 139, 411 to 418. https://doi.org/10.1007/s00414-024-03340-x
- Buikstra, J. E., & Ubelaker, D. H. (Eds.). (1994). Standards for data collection from human skeletal remains. Arkansas Archeological Survey Research Series No. 44. Fayetteville: Arkansas Archeological Survey.
- Galloway, A. (1988). Estimating actual height in the older individual. Journal of Forensic Sciences, 33(1), 126 to 136.
- Jantz, R. L., Hunt, D. R., & Meadows, L. (1995). The measure and mismeasure of the tibia: Implications for stature estimation. Journal of Forensic Sciences, 40(5), 758 to 761.
- Jantz, R. L., Meadows Jantz, L., & Ousley, S. D. (2020). Measuring the tibia: Trotter's error revisited. Journal of Forensic Sciences, 65(6), 2094 to 2097. https://doi.org/10.1111/1556-4029.14550
- Langley, N. R., Meadows Jantz, L., McNulty, S., Maijanen, H., Ousley, S. D., & Jantz, R. L. (2018). Error quantification of osteometric data in forensic anthropology. Forensic Science International, 287, 183 to 189. https://doi.org/10.1016/j.forsciint.2018.04.004
- Mahakkanukrauh, P., Khanpetch, P., Prasitwattanseree, S., Vichairat, K., & Case, D. T. (2011). Stature estimation from long bone lengths in a Thai population. Forensic Science International, 210(1 to 3), 279.e1 to 279.e7. https://doi.org/10.1016/j.forsciint.2011.04.025
- Ruff, C. B., Holt, B. M., Niskanen, M., Sládek, V., Berner, M., Garofalo, E., Garvin, H. M., 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. American Journal of Physical Anthropology, 148(4), 601 to 617. https://doi.org/10.1002/ajpa.22087
- Sjøvold, T. (1990). Estimation of stature from long bones utilizing the line of organic correlation. Human Evolution, 5(5), 431 to 447.
- Steele, D. G. (1970). Estimation of stature from fragments of long limb bones. In T. D. Stewart (Ed.), Personal identification in mass disasters (pp. 85 to 97). Washington, DC: Smithsonian Institution.
- Trotter, M., & Gleser, G. C. (1951). The effect of ageing on stature. American Journal of Physical Anthropology, 9(3), 311 to 324. https://doi.org/10.1002/ajpa.1330090307
- Trotter, M., & Gleser, G. C. (1952). Estimation of stature from long bones of American Whites and Negroes. American Journal of Physical Anthropology, 10(4), 463 to 514. https://doi.org/10.1002/ajpa.1330100407
- Trotter, M., & Gleser, G. C. (1958). A re-evaluation of estimation of stature based on measurements of stature taken during life and of long bones after death. American Journal of Physical Anthropology, 16(1), 79 to 123. https://doi.org/10.1002/ajpa.1330160106
- Trotter, M., & Gleser, G. C. (1977). Corrigenda to "Estimation of stature from long limb bones of American Whites and Negroes" (1952). American Journal of Physical Anthropology, 47(2), 355 to 356. https://doi.org/10.1002/ajpa.1330470216
- Tyrrell, A. R., Reilly, T., & Troup, J. D. G. (1985). Circadian variation in stature and the effects of spinal loading. Spine, 10(2), 161 to 164.