Newton's Law of Cooling Calculator

Summary

Enter the initial temperature, ambient temperature, and cooling constant to get the temperature at any time plus a step-by-step table.

How it works

1. Enter the initial object temperature T₀.
2. Enter the ambient (surrounding) temperature T_amb.
3. Enter the cooling constant k (per minute or per second, matching your time unit).
4. Enter the target time t to evaluate.
5. The calculator applies T(t) = T_amb + (T₀ − T_amb)·e^(−kt) and shows the result.
6. A table lists temperatures at regular intervals from 0 to your target time.

Use cases

• Estimate how long a hot drink takes to reach a drinkable temperature.
• Predict the body temperature drop at a crime scene for forensic analysis.
• Model food cooling rates to meet food-safety guidelines.
• Verify experimental heat-transfer data against theory.
• Determine the time constant of a thermal system in engineering.
• Teach or study exponential decay in physics and calculus courses.

Frequently Asked Questions