Newton's Law of Cooling Calculator

Newton's law of cooling models how an object's temperature approaches the temperature of its surroundings. It states that the rate of temperature change is proportional to the difference between the object and the ambient environment. Solving that differential relationship gives an exponential curve: final temperature equals ambient temperature plus the initial temperature difference multiplied by an exponential decay factor. The model describes cooling when the object starts hotter than its surroundings and warming when it starts colder. The cooling constant controls how quickly equilibrium is approached. It combines the effects of surface heat transfer, exposed area, thermal mass, geometry, airflow, and material properties into one empirical coefficient. A larger constant means the temperature difference decays faster. Units must match time: this calculator uses a constant per minute and elapsed time in minutes, making the exponent dimensionless. At zero elapsed time, the calculated value is exactly the initial temperature. As time becomes very large, the exponential term approaches zero and object temperature approaches ambient temperature without mathematically crossing it. The constant is usually obtained from observations rather than predicted from first principles. If one measured temperature is available at a known time, rearrange the equation to estimate the constant. Keep ambient conditions stable during that measurement. A hot drink in still air, for example, may have a different constant from the same drink beneath a fan or inside an insulated container. Changes in convection, evaporation, radiation, or contact conduction can make the effective constant vary over time. This simple lumped-capacitance model assumes the object has a nearly uniform internal temperature and the surroundings remain constant. It works best when internal conduction is fast relative to heat transfer at the surface. Thick objects with strong internal gradients, phase changes, active heating, or rapidly changing ambient conditions need a more detailed heat-transfer model. Temperature differences may be entered in Celsius because Celsius and kelvin increments have the same size. Use the result for education, process estimates, food and beverage cooling, laboratory planning, or a first check before applying a full thermal simulation.