Time of Death Calculator (Henssge body-cooling equation, educational)

Understanding the time of death calculator (Henssge, educational) — concept and principle

This calculator estimates the time since death from rectal temperature, ambient temperature and body weight using Henssge's body-cooling nomogram equation. It is an educational tool for students of forensic medicine and crime-fiction readers, not a forensic determination.

How it is calculated

Q = (T_rectal − T_ambient) ÷ (T_death − T_ambient)

For ambient ≤ 23.2 °C: Q = 1.25 × e^(B·t) − 0.25 × e^(5·B·t)

For ambient > 23.2 °C: Q = 1.11 × e^(B·t) − 0.11 × e^(10·B·t)

B = −1.2815 × (corrective factor × body weight)^(−0.625) + 0.0284

The time t (hours) is found numerically; the narrowest 95% range is about ±2.8 hours.

• T_death is usually taken as 37.2 °C; the corrective factor (1.0 = naked, dry, still air) adjusts for clothing, covers and wetness.

The principle

After death the body cools towards the room temperature, but not in a simple exponential way: at first there is a plateau, because heat must travel from the core to the surface, then cooling speeds up and finally slows as the temperatures converge. Henssge's double-exponential model reproduces this S-shaped curve. Heavier or better-insulated bodies cool more slowly, which B captures.

Worked example

Default inputs: rectal 30 °C, ambient 18 °C, weight 75 kg, factor 1.0, T_death 37.2 °C, measured at 06:30.

1. Q = (30 − 18) ÷ (37.2 − 18) = 12 ÷ 19.2 = 0.625.
2. B = −1.2815 × 75^(−0.625) + 0.0284 ≈ −0.0579.
3. Solving 1.25e^(Bt) − 0.25e^(5Bt) = 0.625 gives 11 h 45 min.
4. 95% range 8 h 57 min to 14 h 33 min; estimated time of death 18:45 the day before.

How to read the result

The estimate assumes constant surroundings, a normal temperature at death and correct body weight. Fever, hypothermia, changing room temperature, sunlight, water or moving the body make the real uncertainty much larger. In practice forensic experts combine temperature with other signs.

Common mistakes

• Using the wrong corrective factor for clothing or covers.
• Measuring ambient temperature far from the body.
• Treating the central estimate as exact.

Frequently asked questions

Why is there a temperature plateau after death?

Heat has to move from the core to the skin before the core starts cooling noticeably.

What is the corrective factor?

A multiplier on body weight that accounts for clothing, covers and environment.

How accurate is the method?

Under ideal conditions the 95% range is about ±2.8 hours; real cases are often less certain.

Sources: Henssge C, "Death time estimation in case work. I. The rectal temperature time of death nomogram", Forensic Sci Int 1988;38(3–4):209–236