Time of Death Calculator

Algor Mortis and Time Since Death Estimation

Estimating the postmortem interval (PMI)—the time elapsed between biological death and discovery of the body—is a cornerstone of forensic pathology. Among the classical triad of postmortem changes (algor mortis, rigor mortis, and livor mortis), algor mortis (the progressive cooling of the body) provides the most objective, quantifiable mathematical basis for early PMI determination (typically within the first 24 to 36 hours).

The Henssge Nomogram Method

Early forensic medicine relied on simplistic linear cooling rules (such as the Glaister formula assuming body cooling of 1.5°F per hour). However, actual body cooling is non-linear: it begins with an initial temperature plateau (where core temperature remains relatively stable while peripheral tissues cool), followed by an accelerated exponential drop, and finally an asymptotic leveling as the body approaches ambient temperature.

Professor Claus Henssge formulated a double-exponential thermodynamic model that accurately simulates this cooling curve while accounting for body mass, ambient temperature, and external insulation factors.

Mathematical Formulation

The Henssge equation models the temperature quotient ($Q$) over time ($t$, in hours):

$$Q = \frac{T_r - T_a}{T_0 - T_a}$$

Where:

• $T_r$ is the measured core (rectal) body temperature.
• $T_a$ is the ambient environmental temperature at the scene.
• $T_0$ is the body temperature at the time of death (standard assumption is 37.2°C / 99.0°F).

For ambient temperatures $\le 23^\circ\text{C}$, the relation is:

$$Q(t) = 1.25 \cdot e^{k \cdot t} - 0.25 \cdot e^{5 \cdot k \cdot t}$$

For warm ambient temperatures $> 23^\circ\text{C}$, the relation shifts to:

$$Q(t) = 1.11 \cdot e^{k \cdot t} - 0.11 \cdot e^{10 \cdot k \cdot t}$$

The cooling coefficient $k$ is calculated from the effective body mass ($m_c$, in kilograms):

$$k = -1.2815 \cdot m_c^{-0.625} + 0.0284$$

Correction Factors for Clothing and Environment

Body weight is multiplied by a correction factor ($cf$) based on thermal insulation:

• Naked, still dry air: 1.0 (baseline standard)
• 1 to 2 thin layers of clothing: 1.1
• Standard 2 to 3 layers of clothing: 1.3
• Heavy / winter garments: 1.8
• Thick duvet or blanket covering: 2.4
• Submerged in water: 0.35 to 0.7 (accelerates heat transfer significantly)

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