Algor Mortis: Estimating Time of Death from Body Cooling

Death Scene Conditions

Ambient temperature T_a 18°C

Body mass 75 kg

Insulation (Henssge Q-factor)

Simulation Clock

Playback speed 60×

Readout

Elapsed (true PMI)

0h 00m

Core (rectal) temp

37.2°C

Cooling constant B

– /h

Ambient T_a

18°C

No reading taken yet — press Take rectal reading to estimate the PMI from the current core temperature, the way a medical examiner backs out time-of-death in the field.

How it works

Deep body (core) temperature drops from ~37.2°C toward ambient in a curve that starts flat (a metabolic/circulatory "plateau"), then falls fastest, then flattens again as it nears T_a. Real forensic pathology models this with Henssge's double-exponential formula, the basis of the nomogram used in death investigations worldwide:

Tr(t) = Ta + (37.2−Ta)·[1.25·e^(−Bt) − 0.25·e^(−5Bt)]
B = 1.2815 / (Q · m^−0.625) − 0.0284

t = hours since death, m = body mass (kg), Q = a correction factor for insulation and environment (≈1.0 nude in still air; lower in water, which conducts heat away faster; higher under clothing/bedding, which traps it).

T_a / mass / Q — change the cooling physics; watch B and the cooling curve respond.
Take rectal reading — samples the current core temperature (±0.2°C sensor noise, matching real thermometer precision) and numerically inverts the formula for the elapsed time — exactly the calculation behind the Henssge nomogram.
The instanced "tissue" grid on the body is illustrative: peripheral tissue loses heat faster than the core, which is why the rectum — insulated and well-perfused until late — is the standard measurement site.

Because Tr(t) is monotonically decreasing, the inversion is unique and solved here by bisection — the same numerical idea used in real PMI-estimation software, though real casework also weighs body position, wind, and clothing far more heterogeneously than this model.

t = 0h 00m

37.2°C (core at death) Ambient T_a

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