Physics

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Newton's Law of Cooling Calculator.

Estimate temperature change with the ideal exponential Newton cooling model.

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01

Set your values

Results update as you type.

Temperature: 68.522453 °C

Temperature

0.000000°C
Temperature difference: 48.522453 °C

Temperature difference

0.000000°C

Results update automatically as you type.

Use Cases

Estimate cooling time for hot beverages

Use the calculator to predict how long it takes for a hot drink to cool to a desired temperature in a room with a known ambient temperature.

Example: Coffee at 90°C in a 25°C room with a time constant of 300 s: find temperature after 10 minutes.

Model temperature changes in engineering

Engineers can use this tool to approximate the thermal behavior of components or materials cooling in a controlled environment.

Example: A metal part at 200°C in a 30°C ambient with a time constant of 120 s: estimate temperature after 5 minutes.

Frequently Asked Questions

What does Newton's Law of Cooling calculator do?
This calculator estimates the temperature of an object at a given elapsed time using the ideal exponential cooling model. You input the initial temperature, ambient temperature, time constant, and elapsed time, and it computes the predicted temperature based on Newton's law of cooling.
What is the time constant in this calculator?
The time constant (in seconds) represents how quickly the object approaches the ambient temperature. A smaller time constant means faster cooling, while a larger one means slower cooling. It is a parameter of the cooling process, not a direct measurement of time.
Can this calculator be used for heating as well?
Yes, Newton's law of cooling also applies to heating when the initial temperature is lower than the ambient temperature. The calculator will estimate the temperature increase over time, following the same exponential approach to the ambient temperature.

Tips & Common Mistakes

Tips

  • Ensure the time constant matches the units of elapsed time (both in seconds) for accurate results.
  • The model assumes a constant ambient temperature and uniform object temperature; real-world conditions may vary.
  • For better accuracy, use a time constant determined experimentally for your specific object and environment.
  • Remember that this is an ideal model; it does not account for factors like convection, radiation, or phase changes.

Common Mistakes to Avoid

  • Using inconsistent units, such as minutes for elapsed time while the time constant is in seconds.
  • Assuming the time constant is the time to reach ambient temperature; it is actually the time to reach about 63.2% of the temperature difference.
  • Forgetting that the calculator uses the ideal exponential model, which may not match real-world cooling exactly.

Last updated: August 13, 2026