Measured Body Temperature (°C): Ambient Temperature (°C): Cooling Constant k (1/h): Estimate Interval

Forensic investigators often rely on body temperature to estimate the postmortem interval—the time that has elapsed since a person died. Shortly after death, the body begins to cool toward the surrounding environment. Although numerous factors influence this process, a simplified approach uses Newton’s Law of Cooling to approximate how long it takes for the body to reach its observed temperature. The fundamental relationship is

where represents the ambient temperature, is the normal living body temperature (around 37 °C), is a cooling constant, and is time since death in hours. Solving this expression for yields

Although many physiological variables affect how quickly a body cools—such as clothing, wind, humidity, and body mass—this calculation can provide a first-order estimate when other indicators are unavailable. The constant typically ranges from about 0.7 to 1.0 per hour in indoor settings. A value near 0.9 indicates fairly rapid cooling, while lower values correspond to slower heat loss due to insulating clothing or a warm environment.

To demonstrate how the computation works, consider an example where the measured body temperature is 28 °C, the room temperature is 20 °C, and the cooling constant is 0.9 h^-1. Plugging these values into the formula produces a postmortem interval of roughly

This indicates the person has been deceased for a handful of hours. Because real-world scenarios rarely adhere perfectly to theory, investigators compare such calculations with other clues like rigor mortis, livor mortis, and witness testimony. Nevertheless, the method provides a helpful starting point.

The table below shows estimated intervals for several measured temperatures assuming an ambient temperature of 20 °C and equal to 0.9 h^-1. These values illustrate how rapidly the postmortem interval grows as body temperature drops:

Measured Temp (°C)	Estimated Interval (h)
34	2.2
30	4.9
26	7.8

Although the numbers in the table provide a ballpark, real cases demand careful judgment. Clothing layers, body fat, and the presence of moving air can all speed or slow cooling. If a body lies on a cold surface or is exposed to rain, for instance, heat may dissipate much faster than expected. Investigators also consider whether the victim was febrile or hypothermic at death, both of which would alter the initial temperature .

Forensic science has developed standardized protocols for taking body temperatures in the field. Investigators often measure deep rectal temperature or use a probe inserted into the liver. These sites are less affected by short-term environmental fluctuations than skin temperature. To ensure accuracy, the thermometer should remain in place for at least a minute. The reading is then recorded alongside the ambient temperature, ideally measured close to the body with a similar thermometer.

When working with this calculator, remember that the constant must be chosen carefully. A value that is too high or too low can shift the estimate by hours. In general, warmer surroundings or insulating clothing reduce . Cold water immersion increases heat loss dramatically, leading to larger constants. Because these nuances are complex, the result should be viewed as an approximation, not a definitive statement of time of death.

The practice of estimating the postmortem interval has a long history. Nineteenth‑century physicians noticed that corpses cooled predictably and attempted to formalize the relationship. Modern research continues to refine mathematical models with experiments in controlled environments, using cadavers or animal analogs. Despite these advances, a single equation can never capture all the biological and environmental variables at play. Nevertheless, temperature-based estimates remain a useful component of early investigations.

In real cases, investigators also look at insect activity, chemical changes in bodily fluids, and witness statements. Each piece of evidence narrows the possible time window. The cooling calculation offered here is most reliable within the first day or so after death, before decomposition and external factors obscure temperature readings. After that point, other signs like insect colonization become more important.

Using this calculator is straightforward. Enter the measured body temperature, the ambient temperature, and the cooling constant that best matches the situation. The script computes the postmortem interval by isolating from the exponential equation. The output is displayed in hours, and a copy button appears for convenience. Because everything runs locally in your browser, no data is transmitted elsewhere.

This tool serves educational purposes and should not replace professional judgment. Experienced forensic pathologists consider many variables beyond those in a simple formula. They also account for measurement error and the inevitable uncertainty in real-world observations. Still, practicing with a straightforward model helps students grasp how body temperature trends reflect the passage of time.

As you experiment with different parameter values, note how sensitive the estimate is to the cooling constant and ambient temperature. A slight change in can shift the interval by an hour or more. This variability underscores why investigators gather as much context as possible before settling on a timeline.