Newton's Law of Cooling Calculator

Newton's law of cooling describes how an object approaches the surrounding temperature.

How the Math Works

Newton's Law of Cooling describes how an object's temperature changes as it loses heat to its surrounding environment. The formula T = T_env + (T0 - T_env) * e^(-k*t) calculates the temperature (T) at any given time (t) by accounting for the environmental temperature (T_env), the object's initial temperature (T0), and the cooling constant (k) which depends on the material and surface properties. The exponential term e^(-k*t) represents the natural decay of the temperature difference over time, approaching equilibrium with the environment as time increases.

Practical Applications

To apply this calculator, input the ambient temperature of the surroundings, the object's starting temperature, and determine the cooling constant either from experimental data or typical values for the material. For example, when cooling metal in air, you might measure temperature at two time points to calculate k. This calculation is essential in engineering for designing cooling systems, in food safety for determining when hot food reaches safe storage temperatures, and in forensic science for estimating time of death based on body temperature decay.

Day-to-Day Use

Understanding cooling rates helps in everyday cooking scenarios - knowing how long to let hot soup cool to a safe temperature, or determining the optimal time to put recently baked goods aside for storage. It's also useful for troubleshooting household issues like why electronics overheat, or for outdoor activities where metal objects left in the sun become dangerously hot. Coffee lovers use these principles to calculate the perfect waiting time before their drink cools to an enjoyable sipping temperature, and parents can estimate how long to wait before handling a hot cup from the dishwasher.

Worked example

90 °C coffee in 20 °C room, k 0.05/min, 10 min → about 62.5 °C.

FAQ