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Newton Cooling Temperature and Time

Calculate newton cooling temperature and time with local equations, selectable units and supported inverse relationships.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

temperature final = 52.928698. Values use the worked example unit selections.

T(t) = Ta + (Ti−Ta)e^(−kt); k = hA/C

Worked example

Enter these known values and leave the other values blank.

Ambient temperature (T==amb==)
20 °C
Initial temperature (T==initial==)
80 °C
Cooling coefficient (k)
0.01 / sec
What's the temperature after…
1 min ?
Final temperature (T)
52.93 °C

Assumptions and limitations

  • The body is modeled as a uniform lumped temperature with fixed surroundings and constant coefficient. This exponential also models heating toward a warmer environment. Absolute temperatures must be positive.
  • Unit selectors convert known physical quantities. Leave a supported unknown blank; derived inverse branches are limited by the stated model and available captured equations.

Common questions

What does this calculation assume?

The body is modeled as a uniform lumped temperature with fixed surroundings and constant coefficient. This exponential also models heating toward a warmer environment. Absolute temperatures must be positive.

Can I solve for an input?

Where the captured model supplies an inverse, leave that quantity blank and enter the remaining known quantities. A positive square-root or principal trigonometric inverse may represent only one of multiple mathematical branches.

Which unit should I use for the worked example?

The example uses the initial metric unit selection beside each field. Change a unit using its selector to convert the same known quantity; switching a unit does not change the underlying physical value.

References

Original accessible explanations preserve the captured diagram geometry, quantities and conditional variants without external image loading. BTU-based thermal units use the International Table BTU and exact mass, time, length and temperature-interval definitions.

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