What this calculator works out
This calculator applies Newton's Law of Cooling: an object's temperature approaches its surroundings exponentially, at a rate proportional to the difference between them.
It returns the modelled temperature after a chosen elapsed time. It is a considerably better description of cooling than a straight line, and still an incomplete description of a human body. These tools are teaching aids. They are not validated for casework, and no result from them should appear in a statement, report or investigation.
Calculate temperature
Before you rely on the model
- The cooling constant k is specific to the object and its surroundings. It is not a universal figure and cannot be looked up for a person.
- A k of 0.08 per hour is a plausible teaching value for a clothed adult body in still air. Immersion in water gives a far larger k; heavy insulation gives a smaller one.
- The model assumes a constant ambient temperature, which few real environments provide over a full day.
- It also assumes cooling began immediately, ignoring the plateau.
The cooling rate is proportional to the temperature difference, so as the body approaches ambient the difference shrinks and cooling slows. Mathematically it never quite arrives. Practically, this is why temperature-based estimation becomes useless after a day or so — the remaining difference is too small to measure a time from.
How this calculator works
The standard exponential decay form:
T(t) = Ta + (T0 − Ta) × e−kt
Ta ambient · T0 starting temperature · k cooling constant · t hoursRearranged, the same equation solves for time: t = −ln((T − Ta) ÷ (T0 − Ta)) ÷ k. That is the direction a forensic application would use, and it is why an error in k translates directly into an error in the estimated interval.
Human bodies do not follow a single exponential. Henssge's model uses a double-exponential precisely because the plateau and the later cooling behave differently, and a single term cannot represent both.
Worked example: eight hours at k = 0.08
Using the default figures — starting at 37°C, ambient 18°C, k of 0.08, after 8 hours:
- Temperature difference at the start: 19°C
- Decay factor: e−0.64 = 0.527
- Modelled temperature: 18 + (19 × 0.527) = 28.02°C
Compare that with the linear rule of thumb, which would predict 37 − (0.83 × 8) = 30.4°C at the same point. The exponential model cools faster early and slower late, which is closer to reality — but the two differ by more than two degrees at eight hours, and in the reverse direction that is a difference of several hours in an estimated interval.
Common mistakes
- Treating k as a constant of nature. It depends on the body, clothing, surface and air movement.
- Assuming constant ambient temperature. Overnight and indoor-to-outdoor changes both break the model.
- Applying it to the first few hours. The plateau is not represented.
- Using it for a body in water. Immersion changes k by a large factor.
- Reading the output as a forensic conclusion. It is a model of a simplified object.
Frequently asked questions
Where does the cooling constant come from?
In physics teaching it is measured empirically for the object concerned. In forensic work it is not used in this form at all — the Henssge model derives an equivalent from body mass and a corrective factor covering clothing, the surrounding medium and air movement. A single k for a human body is a teaching simplification, not a measurable property.
Why does Henssge use a double exponential?
Because a body cools in two overlapping phases. The plateau reflects residual heat production and the thermal inertia of the core; the later phase is the surface-driven cooling a single exponential describes. A double-exponential model fits both, which is why it produces usable estimates in the first several hours where a single exponential does not.
Does this apply to anything other than bodies?
Yes — it is a general physical law and applies to any object cooling in a stable environment. A cup of coffee, an engine block and a building all follow the same form. This is why the equation appears in physics teaching well before anyone encounters it in a forensic context.
What happens at long intervals?
The body approaches ambient asymptotically, so temperature carries less and less information. Beyond roughly 24 to 36 hours in typical conditions, the difference between a body dead for 30 hours and one dead for 40 becomes too small to measure reliably. Other methods — entomology in particular — take over at that point.
Is what I enter stored?
No. Values are processed entirely in your browser and never transmitted or retained.
Related tools
References
- GOV.UK — forensic science regulation and standards for expert evidence
- National Institute for Health and Care Excellence — clinical guidance on temperature measurement
Sources are checked at publication and can change — how I choose and check references.