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Newton's Law of Cooling Calculator

Newton's Law of Cooling Calculator

Use the given tool to determine the rate at which an object cools in a surrounding environment according to Newton’s Law of Cooling.

Ambient Temperature


Initial Temperature




Heat Capacity


Heat Transfer Coefficient


Temperature Check



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Using Newton’s Law of Cooling calculator, you can easily figure out how long it takes for an object to cool down from one temperature to another.

What Is Newton’s Law of Cooling?

“The rate of heat loss of a body or object is proportional to the difference between its temperature and the surrounding temperature (ambient temperature)”

In simple words, It is a scientific principle that defines the changes in the temperature of an object when it gets exposed to a surrounding medium having a different temperature.

The mechanisms of heat exchange include thermal conduction, convection, and radiation. When heat loss happens because of thermal conduction and convection then Newton’s Law of Cooling is applicable.

What Is The Formula of Newton’s Law of Cooling?

The Newton’s Law of Cooling Formula is as follows:

\( \dfrac{dT}{dt} = -k \cdot (T – T_s) \)

\( \ T(t) = -k \cdot (T – T_s) \)


  • \(\ T(t)\ is\ the\ rate\ of\ change\ of\ temperature\)
  • \(\ T_{s}\ is\ the\ Surroundings\ temperature\)

To figure out how temperature changes over time, we can further simplify it as:

\(\ T(t) =\ T_{s} + (T_{o} – T_{s})*e^{(-k*t)})\)


  • \(\ T_{o}\ is\ Initial\ Temperature\ of\ the\ Object\)
  • \(\ T_{s}\ is\ the\ Surroundings\ temperature\)
  • \(\ T\ is\ the\ Time\)
  • \(\ K\ is\ the\ Heat\ Transfer\ Coefficient\ (in W/m²K)\)

This equation enables us to determine the temperature of the body or object at any given time.

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How To Calculate Newton’s Law of Cooling?

Go through the following steps:

Determine The Ambient Temperature: It is the temperature of the air present in the object’s surroundings
Calculate The Initial Temperature: Measure the initial temperature of the object in degrees Celsius
Determine The Value of The Cooling Coefficient(k): Calculate the cooling coefficient by considering the material properties and the surface area
Measure The Final Temperature: Put the values in Newton’s law of cooling formula and get the final temperature


Find the final temperature of a body after 3 seconds using the law of cooling with the provided parameters:

  • Ambient temperature = 20 Degrees Celsius
  • Initial temperature = 3 Degrees Celsius
  • Surface area = 0.003 m²
  • Heat capacity = 4 J/K
  • Heat transfer coefficient = 1 W/(m²·K)


\(\ K = \dfrac{hA}{C}\)

\(\ K = \dfrac{1\times 0.003}{4}\)

\(\ K = \ 0.00075\)

Now put values in Newton’s law of cooling formula

\(\ T(t) =\ T_{s} + (T_{o} – T_{s})*e^{(-k*t)})\)

\(\ T(t) =\ 20 + (3 – 20)*e^{(-k*t)})\)

\(\ T(t) =\ 20 + (-17)*e^{(-1*3)})\)

\(\ T(t) =\ 20 -16.96)\)

\(\ T(t) =\ 3.038\ Degrees\ Celsius\)

Rather than dragging yourself into this long calculation, make things easier by using Newton’s law of cooling calculator and get precise results in seconds.

Limitations of Newton’s Law of Cooling:

  • The difference between the temperature of the body and its surroundings must be small
  • Loss of heat should happen via radiation
  • The surrounding temperature should remain constant during the cooling of the body or object


Why Is Newton’s Law of Cooling Important?

Newtons law of cooling is very crucial across physics, and engineering for several reasons, which are:

  • Predicting the temperature change of an object over time
  • Heat Transfer Analysis
  • Engineering Applications

What Are The Factors Affecting Newton’s Law of Cooling?

Factors that affect Newton’s Law of Cooling are:

  • Surface area
  • The difference between the temperature of your object and the surrounding
  • Heat transfer coefficient(K)

How Do You Find K in Newton’s Law of Cooling?

The constant “k” can be calculated by dividing the temperature by the time that it takes to reach the temperature difference.

\(\ k =\ \dfrac{(T_1 – T_2)}{t}\)


  • \(\ T_1 – T_2\ is\ the\ temperature\ difference\)
  • \(\ t\ is\ the\ time\ difference\ \ t=(t_1 – t_2 )\)

If you have the values of the heat transfer coefficient and the area of heat exchange, then use the following equation:

\(\ K = \dfrac{hA}{C}\)


  • K is the cooling coefficient
  • H is the Heat transfer coefficient
  • A represents the area of heat exchange
  • C is the heat capacity