What this generator produces
This generator tabulates Newton's Law of Cooling hour by hour, so the shape of the curve is visible rather than implied by a single figure.
Seeing the whole curve is the point. The steep early section and the long flat tail explain, better than any description, why temperature estimates are more useful in the first few hours than the second day. These tools are teaching aids. They are not validated for casework, and no result from them should appear in a statement, report or investigation.
Cooling model
Before you read the table
- The same caveats apply as to the underlying equation: k is not a universal figure and the model ignores the plateau.
- The generator caps the display at 72 hours, which is well beyond the point at which the method carries useful information.
- The starting temperature must be above ambient, or there is no cooling to model.
- The table shows a model, not a measurement. Real readings scatter around any curve.
At k = 0.08 the temperature difference halves roughly every 8.7 hours. So a body starting 19°C above ambient is about 9.5°C above it after nine hours, 4.75°C after eighteen, and 2.4°C after twenty-seven. Each successive hour tells you less than the one before.
How this calculator works
The cooling equation evaluated at each whole hour:
For each hour i from 0 to the display limit:
T(i) = Ta + (T0 − Ta) × e−kiThe half-life of the temperature difference is ln(2) ÷ k, which at k = 0.08 is about 8.7 hours. That single figure describes the curve more usefully than any individual row of the table.
Worked example: 24 hours at k = 0.08
Using the default figures — 37°C starting, 18°C ambient, k of 0.08, displayed over 24 hours:
- Hour 0: 37.00°C
- Hour 6: 29.76°C — 7.2 degrees lost
- Hour 12: 25.28°C — a further 4.5
- Hour 18: 22.51°C — a further 2.8
- Hour 24: 20.79°C — a further 1.7
The first six hours account for more cooling than the following eighteen combined. By hour 24 the body is under three degrees above ambient, and an hour either way changes the reading by roughly a tenth of a degree — far less than the uncertainty in the measurement itself. That is the practical end of the method.
Common mistakes
- Reading the tail as precise. Small temperature differences carry almost no time information.
- Using a k value copied from elsewhere. It is specific to the object and conditions.
- Assuming stable ambient across a full day. Overnight temperature changes invalidate the curve.
- Expecting real measurements to sit on the line. They scatter, and the scatter matters.
- Ignoring the missing plateau. The first hours of any real curve look different from this.
Frequently asked questions
Why generate a table rather than a single figure?
Because the shape carries the lesson. A single modelled temperature invites treating the model as precise; the table makes the diminishing information content obvious at a glance. Anyone reading rows 20 to 24 and seeing changes of a tenth of a degree understands the limitation without needing it explained.
What k value should I use?
For teaching purposes, something between about 0.05 and 0.15 per hour spans plausible conditions for a clothed adult in still air through to lighter clothing with air movement. Immersion in water produces values several times higher. There is no correct answer, which is exactly why the field uses the Henssge corrective factor rather than a single constant.
How does this compare with a real cooling curve?
The general shape is right for the middle and late phases. The early phase is wrong: a real curve is flat or nearly flat for the first half hour to three hours, then falls more steeply than a single exponential predicts before settling into the tail. Plotting a real dataset against this model is a standard teaching exercise for exactly that reason.
Can I use this to estimate a time of death?
No. Reading backwards from a measured temperature to a time requires the correct k for that specific body and environment, a known starting temperature, and a stated confidence interval — none of which this provides. Casework uses validated methods with published uncertainty.
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 Regulator guidance on method validation
- 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.