Created By : Vaibhavi Kumari

Reviewed By : Rajashekhar Valipishetty

Last Updated : May 17, 2023

Newton's Law of Cooling Calculator is a free tool that quickly calculates a body's temperature. This free calculator takes the temperature of the environment, the initial temperature, the cooling constant, and the time as inputs and outputs the temperature of an object in a short amount of time.

Choose Option
Initial Temperature (it)
Ambient Temperature (at)
Cooling constant (k)
What's the temperature after time (tp)

Newton's Law of Cooling

Heat exchange is governed by three primary mechanisms. Thermal conduction, convection, and radiation are the three methods. For thermal conduction and convection, Newton's law of cooling applies. An object's cooling time is determined by two factors. One of the factors is the temperature difference between an object and its surroundings. The larger the difference, the faster the cooling. The cooling coefficient, which is determined by the mechanism and the amount of heat exchanged, is the second consideration.

Newton's Law of Cooling Formula

The formula for the cooling coefficient is; k = hA/C

  • Where, k = cooling coefficient
  • h = heat transfer coefficient
  • A = area of the heat exchange
  • C = heat capacity.

According to Newton's law of cooling, the rate of change in temperature of an object is exactly proportional to the difference between its body temperature and its surroundings.

The formula for Newton's law of cooling is as follows: T = T_ambient + (T_initial - T_ambient) * e^-kt

  • Where, T = temperature of the object at the time t
  • T_ambient = surrounding temperature
  • T_initial = object temperature
  • k = cooling coefficient
  • t = time of cooling

For more concepts check out to get quick answers by using this free tool.

How to Determine an Object's Temperature?

Examine the comprehensive processes for calculating an object's temperature using Newton's Law of Cooling. To get the best results, follow these rules and recommendations.

  • Step 1: From the question, determine the ambient temperature, cooling constant, beginning temperature, and time.
  • Step 2: Find the exponential of the negative product by multiplying the cooling coefficient by the cooling duration.
  • Step 3: Take the ambient temperature and subtract it from the starting temperature.
  • Step 4: Multiply it by the result Step 2
  • Step 5: To get the temperature of the object at the time, add ambient temperature to the result.

How do I Use the Newtons Law of Cooling Calculator?

The following is the procedure how to utilise Newton's Law of Cooling Calculator

  • Step 1: Fill in the appropriate input fields with the constant temperature, core temperature, time, and beginning temperature.
  • Step 2: To get the temperature, click the "Calculate Temperature of the Object" button.
  • Step 3: Finally, in the output field, the temperature of the object over time will be displayed.

Newton's Law of Cooling Problems and Solutions

Question 1: Water is heated to 90°C for 20 min. How much would be the temperature if k = 0.56 per min and the surrounding temperature is 45°C?




Surrounding temperature T_ambient = 45°C

Water temperature T_initial = 90°C

Time t = 20 min

Cooling coefficient k = 0.56

Newton's law of cooling formula is T = T_ambient + (T_initial - T_ambient) * e^-kt

T = 45 + (90 - 45) * e^-0.56

= 45 + 45 x 0.57

= 45 + 25.65 = 70.65°C

FAQs on Newton's Law of Cooling Calculator

1. What is Newton's Cooling Law?

The rate of heat loss from a body is exactly proportional to the difference in temperature between the body and its surroundings, according to Newton's Law of cooling.

2. What are Newton's Cooling Law's Limitations?

The following are some of Newton's cooling law's limitations

  • Only radiation should be used to lose heat from a body.
  • The temperature difference between the body and its environment should be minimal.
  • During the cooling process, the temperature of the body's surrounds must remain constant.


3. What is the rate of cooling?

The cooling rate is calculated by multiplying the temperature difference between two items by the constant material.

4. What is the purpose of Newton's Law of Cooling?

The victim's time of death can be determined using Newton's Law of Cooling. It describes the cooling of a hot object to a cooler environment temperature.

5. What are factors that affect the critical cooling rate?

The critical cooling rate, or hardening ability, of steel during quenching is principally determined by three factors: (1) chemical composition, (2) chemical homogeneity, and (3) grain size.