How to use the calculator

Select Module. Choose Adult estimation for skeletonized or defleshed adult remains with confirmed skeletal maturity. Adult regression formulas do not apply to growing individuals. Subadult Beta exists as a scientific boundary marker until the full nonlinear models are implemented.
Select Reference population. Choose the population reference that matches your biological profile assessment. If population affinity is uncertain, select Generic or uncertain. Generic models add a documented uncertainty penalty to the Accuracy Index.
Set Sex assessment. Choose Male or Female when sex has been established from the biological profile. Use Unknown or disputed when it has not. Sex-pooled models carry a wider regression error.
Select Unit. Centimeters or inches, matching your laboratory records. Internally the engine works in centimeters.
Select Interval display. Use 95 percent for forensic reporting. A wider interval is scientifically more honest than a narrower one for the same data set.
Optional: Time since waking. Living stature decreases through the day as the intervertebral discs lose hydration under gravitational load (Tyrrell, Reilly, & Troup, 1985; White & Panjabi, 1990). The reference regressions are calibrated against morning living stature or cadaver length, so an afternoon reference comparison can introduce a small bias. Selecting hours since waking applies a transparent diurnal correction.
Optional: Estimated age. Vertebral height loss accelerates above approximately 50 years (Cline, Meadors, Cole, Boyles, & Lukens, 1989). Antrometric adds a small additional correction proportional to the age above the threshold.
Enter bone measurements. Click Add Bone for each measurable adult long bone. Select the bone, enter the measured length in your selected unit, and choose the honest measurement condition. Do not claim Complete bone if the specimen is fragmentary.
Click Calculate. The result shows the combined stature estimate, model interval at the selected level, the per-bone breakdown, the consistency diagnosis (including a named most-discordant bone if present), the diurnal correction applied (if any), and the Accuracy Index.

Abstract

Antrometric V3.1 is a transparent computational instrument for adult stature estimation from osteometric input. Each estimate is built from cited population- and sex-specific linear regression equations, condition-adjusted standard errors, an instrument uncertainty term propagated in quadrature, robust inverse-variance combination across multiple bones, and an explicit model interval. An optional diurnal and age correction reconciles the morning and cadaver baselines used by classical reference studies with afternoon living-stature comparisons. The output is a point estimate, a prediction interval, a per-bone breakdown, a consistency diagnosis, and a separate Accuracy Index that is a precision and confidence summary, not an identification probability.

Scope and intended use

The adult calculator implements the established mathematical method for stature estimation from complete or sufficiently reconstructable adult limb bones. It is intended for skeletonized or defleshed adult remains where at least one long bone can be measured with osteometric integrity. The Scientific Working Group for Forensic Anthropology (SWGANTH, n.d.) and the OSAC subcommittees that succeeded it emphasize that regression-based stature must be reported with a clearly labeled prediction interval and that point estimates without intervals or naive averages of multiple equations are scientifically inappropriate. Antrometric is structured around those expectations.

The instrument does not perform identification. A stature interval is one input to a biological profile, alongside sex, ancestry assessment, age-at-death, and individuating features. Antrometric therefore separates the estimate, the interval, the model family, and the precision score in the result. None of these is a probability of identity.

Osteometric input definitions

The adult module accepts measurements of the femur, tibia, fibula, humerus, radius, and ulna. Maximum length definitions follow Trotter and Gleser (1952, 1958) where applicable, with population-specific protocols documented in the source references. The user must select the actual measurement condition for each bone:

Complete bone. No reconstruction was required. Standard error is the source SEE.
Minor surface loss. Cortical erosion or articular damage that does not compromise the maximum length. SEE is widened by a small condition multiplier.
Reconstructed length. The bone was assembled from fragments and the maximum length was estimated. SEE is widened proportionally.
Fragmentary estimate. The maximum length was inferred from a partial bone using a published fragment-to-length relationship. SEE is widened the most. Such measurements should be flagged in the case report.

The calculator does not validate whether the laboratory protocol used to measure the bone matches the protocol of the source equation. That responsibility remains with the analyst. A femur measured oblique-to-board cannot be substituted for a Trotter-protocol maximum femoral length without acknowledging the introduced bias.

Univariate adult regression model

For each entered bone, the engine applies a univariate linear regression equation when a coefficient set exists for the selected reference scenario:

{\hat{S}}_{i} = α_{i} \cdot L_{i} + β_{i}

Univariate adult long-bone regression. L_i is in centimeters.

For example, the current V3.1 data include European male femur S = 2.38 · L + 61.41 with SEE 3.27 cm, European male tibia S = 2.42 · L + 81.93 with SEE 4.00 cm, Thai male femur S = 2.32 · L + 65.53 with SEE 5.06 cm, and Thai male tibia S = 2.39 · L + 81.45 with SEE 5.28 cm. The exact coefficients used in the calculator are visible in science-data.js.

Measurement condition adjustment

The published SEE assumes the measurement condition used in the source model. V3.1 widens the SEE for preservation condition and then adds the instrument uncertainty floor in quadrature:

{SEE}_{i}^{tot} = \sqrt{{({SEE}_{i} \cdot q_{i})}^{2} + σ_{M}^{2}}

Quality multipliers q_i are 1.00 (Complete), 1.12 (Minor surface loss), 1.28 (Reconstructed), and 1.55 (Fragmentary). Default instrument 1σ is 0.5 cm.

Instrument uncertainty in quadrature

Even a complete bone measured by a trained osteologist on an osteometric board is not measured perfectly. ISO 5725-2 distinguishes trueness from precision; here the precision floor is the repeatability of the measurement act. Field calibration of osteometric boards and replicate-observer studies place the typical 1σ instrument repeatability for adult long bones on the order of 0.5 cm. Antrometric propagates this floor in quadrature with the regression SEE so the final per-bone error reflects both the regression model and the measurement act:

{SEE}_{i}^{tot} = \sqrt{{({SEE}_{i}^{*})}^{2} + σ_{M}^{2}}

Default instrument 1σ is 0.5 cm. The value is documented in science-data.js.

Worked example. A European male femur at 47.0 cm gives 2.38 · 47.0 + 61.41 = 173.27 cm. With source SEE 3.27 cm, complete condition, and σ_M = 0.5 cm, total SEE is √(3.27² + 0.5²) = 3.31 cm. If the same bone were fragmentary, total SEE would be √((3.27 · 1.55)² + 0.5²) = 5.09 cm.

Multi-bone combination

Multiple bones from the same skeleton can improve precision when they are mathematically and biologically consistent. They never justify a naive average. Bones from one individual are anatomically correlated, and equations from the same historical reference tradition are not perfectly independent. Antrometric uses robust inverse-variance weighting with a residual factor:

w_{i} = \frac{r_{i}}{{({SEE}_{i}^{tot})}^{2}}

Robust weighting reduces the influence of a discordant bone without hiding it.

{\hat{S}}_{combined} = \frac{\underset{i}{Σ} w_{i} {\hat{S}}_{i}}{\underset{i}{Σ} w_{i}}

Weighted combined estimate.

The combined SEE is the larger of two values: the weighted naive SEE adjusted by a correlation factor sqrt(1 + (n - 1) · 0.36) and a completeness factor, or 50 percent of the smallest single-bone total SEE. This is conservative by design and prevents correlated bones from producing an implausibly narrow interval.

Consistency diagnostics and named outlier

For every multi-bone calculation Antrometric computes the standardized residual of each bone with respect to the combined estimate:

z_{i} = \frac{| {\hat{S}}_{i} - {\hat{S}}_{combined} |}{{SEE}_{i}^{tot}}

Standardized residual per bone.

Residuals at or below 1.65 are labeled high consistency. Above 1.65 the label becomes moderate consistency. Above 2.65 the label becomes possible outlier, the Accuracy Index receives an 8 point consistency penalty, and the most discordant bone is named in the result panel.

Diurnal and age correction

Living stature is not constant during a day. Intervertebral discs lose water under axial load and the spine can shorten over waking hours. V3.1 treats this only as an optional comparison aid, not as an individualized diagnosis.

When hours since waking are selected, Antrometric adds back the estimated decrement. If age above 50 is also selected, a small attenuated age term is added. Two terms are combined:

Δ h = 0.083 \cdot \min (h, 14) + 0.012 \cdot \max (0, age - 50) \cdot 0.4

Diurnal and age correction. Hours since waking are capped at 14.

The 0.083 cm per hour term integrates a waking-day stature loss of approximately 1.0 to 1.2 cm over a typical 12 to 14 hour day, consistent with controlled disc-compression studies (Tyrrell, Reilly, & Troup, 1985). The 0.012 cm per year age slope above 50 years is a conservative scaling of vertebral height loss reported by Cline, Meadors, Cole, Boyles, and Lukens (1989) and the longitudinal stature literature. The 0.4 attenuation reflects that part of the age-related loss is structural and is therefore already implicit in older reference samples.

The correction is opt-in. With hours since waking left at the default value, the engine applies Δh = 0. The age field alone does not trigger a correction unless hours since waking are also selected.

Prediction interval handling

Antrometric reports 90 percent and 95 percent model intervals at the user's choice. The current V3.1 implementation uses the combined SEE and normal multipliers:

{PI}_{level} = {\hat{S}}_{combined} + Δ h \pm z_{level} \cdot {SEE}_{combined}

z_90 = 1.645, z_95 = 1.96. The interface calls this a model interval because many source equations provide SEE values rather than full case-specific prediction interval specifications.

Worked example: complete European male skeleton

Inputs: European reference, Male, centimeters, 95 percent interval, time since waking 8 hours, age 35.

Femur, complete, 47.0 cm.
Tibia, complete, 38.5 cm.
Humerus, complete, 33.0 cm.

Per-bone estimates from the current V3.1 data: femur 2.38 · 47.0 + 61.41 = 173.27 cm, tibia 2.42 · 38.5 + 81.93 = 175.10 cm, humerus 2.89 · 33.0 + 78.10 = 173.47 cm. Per-bone total SEE with σ_M = 0.5 cm: 3.31, 4.03, and 4.60 cm respectively. The robust combined estimate is 173.88 cm. Diurnal correction with 8 waking hours and age 35 is Δh = 0.083 · 8 = 0.66 cm. Final point estimate is 174.54 cm, displayed as 174.5 cm. With combined SEE 2.73 cm, the 95 percent model interval is approximately 169.2 to 179.9 cm.

The consistency check returns standardized residuals well below 1.65 for every bone, so the consistency label is high consistency and no bone is named as an outlier. The Accuracy Index is in the high range, consistent with three complete bones, a known sex, a known population, and concordant per-bone estimates.

Worked example: discordant bone in a Thai male

Inputs: Thai reference, Male, centimeters, 95 percent interval, no diurnal correction.

Femur, complete, 45.0 cm.
Tibia, reconstructed, 40.0 cm.

Per-bone estimates from the current V3.1 data: femur 2.32 · 45.0 + 65.53 = 169.93 cm with total SEE 5.08 cm. Tibia reconstructed: 2.39 · 40.0 + 81.45 = 177.05 cm with total SEE 6.78 cm. The combined estimate is 172.49 cm, combined SEE is 4.58 cm, and the 95 percent interval is approximately 163.5 to 181.5 cm. The standardized residuals remain below 1.65, so the consistency label is high consistency.

If the tibia were entered at 25.0 cm in the same scenario, it would imply 141.20 cm while the femur implies 169.93 cm. The tibia would sit 3.28 standardized residuals from the combined estimate. V3.1 would label this as possible outlier, name the tibia as the most discordant bone, and lower the Accuracy Index.

Population-specific and generic models

Population-specific adult equations remain preferred when sex, population affinity, measurement protocol, and temporal context are defensible (Trotter & Gleser, 1952, 1958; Mahakkanukrauh, Khanpetch, Prasitwattanseree, Vichairat, & Troy Case, 2011). When ancestry assignment is uncertain or contested, generic non-group-specific equations are useful and explicitly designed for that scenario (Albanese, Tuck, Gomes, & Cardoso, 2016). Bidmos and Brits (2025) independently evaluated those equations on a South African sample and reported that they perform usefully but can underestimate measured living stature in some contexts. Antrometric therefore lets the user pick the population family and applies a transparent uncertainty penalty when Generic or uncertain is selected, rather than hiding the choice in the model.

Subadult boundary

Subadult stature estimation is scientifically separate. Growth changes the relationship between long-bone measurements and stature in ways that do not match adult linear regression assumptions (Smith & Buschang, 1994). Recent work supports linear and nonlinear, age-aware approaches with usable prediction intervals (Chu & Stull, 2025). Antrometric therefore does not apply adult formulas to juvenile remains. The Subadult Beta module is a documented placeholder until a vetted subadult engine with citable prediction intervals is implemented.

Limitations

Antrometric is a computational assistant, not a forensic identification tool.
The accuracy of any estimate depends on the quality of the laboratory measurement, the appropriateness of the chosen reference population, and the integrity of the bone.
Diurnal and age corrections are population-level approximations. Individual variation in disc compression and vertebral aging is real and is not captured by a simple linear term.
Generic equations are useful when ancestry is uncertain, but they are not a substitute for a defensible biological profile.
The Subadult module is intentionally locked.

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, 59-68. https://doi.org/10.1016/j.forsciint.2015.12.011
Bidmos, M., & 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, 411-418. https://doi.org/10.1007/s00414-024-03340-x
Chu, E. Y., & Stull, K. E. (2025). An investigation of the relationship between long bone measurements and stature: Implications for estimating skeletal stature in subadults. International Journal of Legal Medicine, 139, 441-453. https://doi.org/10.1007/s00414-024-03336-7
Cline, M. G., Meadors, A. K., Cole, T. M., Boyles, J. R., & Lukens, A. (1989). Decline of height with age in adults in a general population sample: Estimating maximum height and distinguishing birth cohort effects from actual loss of stature with aging. Human Biology, 61, 415-425.
Konigsberg, L. W., Hens, S. M., Jantz, L. M., & Jungers, W. L. (1998). Stature estimation and calibration: Bayesian and maximum likelihood perspectives in physical anthropology. Yearbook of Physical Anthropology, 41, 65-92.
Mahakkanukrauh, P., Khanpetch, P., Prasitwattanseree, S., Vichairat, K., & Troy Case, D. (2011). Stature estimation from long bone lengths in a Thai population. Forensic Science International, 210(1-3), 279.e1-279.e7. https://doi.org/10.1016/j.forsciint.2011.04.025
Scientific Working Group for Forensic Anthropology. (n.d.). Stature estimation and Statistical methods. National Institute of Standards and Technology.
Sjovold, T. (1990). Estimation of stature from long bones utilizing the line of organic correlation. Human Evolution, 5, 431-447.
Smith, S. L., & Buschang, P. H. (1994). Variation in longitudinal diaphyseal long bone growth in children three to ten years of age. American Journal of Human Biology, 6, 651-668.
Trotter, M., & Gleser, G. C. (1952). Estimation of stature from long bones of American Whites and Negroes. American Journal of Physical Anthropology, 10, 463-514. 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, 79-123. https://doi.org/10.1002/ajpa.1330160106
Tyrrell, A. R., Reilly, T., & Troup, J. D. (1985). Circadian variation in stature and the effects of spinal loading. Spine, 10, 161-164.
White, A. A., & Panjabi, M. M. (1990). Clinical biomechanics of the spine (2nd ed.). J. B. Lippincott.

How Antrometric works.