Enter the initial temperature, final temperature, ambient temperature, and time into the calculator to determine the cooling constant. This calculator helps in understanding the rate at which an object cools down in a given environment.

Cooling Constant Formula

The following formula is used to calculate the cooling constant (k).

k = \frac{ln\left(\frac{T_i - T_a}{T_f - T_a}\right)}{t}

Variables:

  • k is the cooling constant (1/minutes)
  • Ti is the initial temperature (°C)
  • Tf is the final temperature (°C)
  • Ta is the ambient temperature (°C)
  • t is the time (minutes)

To calculate the cooling constant, use the natural logarithm of the ratio of the temperature difference between the initial temperature and ambient temperature to the temperature difference between the final temperature and ambient temperature, divided by the time.

What is a Cooling Constant?

The cooling constant is a value that represents the rate at which an object cools down towards the ambient temperature. It is a key parameter in Newton’s law of cooling, which describes the cooling of a warmer object to the cooler temperature of the environment. The cooling constant is specific to the object and its environment and can be used to predict how long it will take for the object to reach a certain temperature.

How to Calculate Cooling Constant?

The following steps outline how to calculate the Cooling Constant.


  1. First, determine the initial temperature (Ti) of the object in degrees Celsius.
  2. Next, determine the final temperature (Tf) of the object in degrees Celsius.
  3. Next, determine the ambient temperature (Ta) of the environment in degrees Celsius.
  4. Next, determine the time (t) in minutes it took for the object to cool from the initial temperature to the final temperature.
  5. Next, gather the formula from above = k = frac{lnleft(frac{T_i – T_a}{T_f – T_a}right)}{t}.
  6. Finally, calculate the Cooling Constant (k) in 1/minutes.
  7. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Initial temperature (Ti) = 90°C

Final temperature (Tf) = 30°C

Ambient temperature (Ta) = 20°C

Time (t) = 15 minutes