How to Use Newton’s Law of Cooling Calculator
- Pick the variable to solve for — T(t), t, k, T₀, or T_env.
- Enter the four known values with consistent units.
- Read the answer in the result panel.
Formula & Theory - Newton’s Law of Cooling Calculator
dT/dt = − k · ( T − T_env )
Integrated form:
T(t) = T_env + ( T₀ − T_env ) · exp(−k · t)
Inverse for t:
t = − ln[(T(t) − T_env) / (T₀ − T_env)] / k
Inverse for k:
k = − ln[(T(t) − T_env) / (T₀ − T_env)] / t| Symbol | Meaning |
|---|---|
| T(t) | Temperature at time t |
| T₀ | Initial temperature |
| T_env | Ambient temperature |
| k | Cooling constant (1/time) |
| t | Elapsed time |
Assumptions and Limits
- Lumped-capacitance: object has uniform internal temperature (small Biot number).
- Constant T_env and constant k over the interval.
- Convection dominates; radiation is negligible.
Use Cases for Newton’s Law of Cooling Calculator
- Forensics — Estimate time of death from body temperature decay.
- Food safety — Predict cooling time of cooked food to safe storage.
- Engineering — Quick check of quench or warm-up curves.
The Newton’s Law of Cooling Calculator rearranges the exponential model for any unknown.