Newton's Law of Cooling describes how an object's temperature changes over time as it reaches thermal equilibrium with its surroundings. The formula T(t) = T_env + (T_initial − T_env) × e−kt predicts temperature at any time t. Enter the initial and ambient temperatures, cooling constant k, and elapsed time to compute the result.
Cooling Calculator
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Formula Reference
How to Use the Newton's Law of Cooling Calculator
Newton's Law of Cooling predicts how an object's temperature changes over time in a surrounding medium. The calculator supports two modes: computing temperature at a given time, or finding the cooling constant k from two known temperature readings.
Step 1: Select Mode
Choose "Compute T(t)" to find temperature at a specific time, or "Find k from 2 points" if you have two temperature measurements and want to determine the cooling rate.
Step 2: Enter Temperatures
Enter the initial temperature (T₀) and the ambient (environment) temperature (T_env). Toggle between Celsius and Fahrenheit using the switch. For example, a cup of coffee starting at 90°C cooling in a 20°C room.
Step 3: Enter k and Time
Enter the cooling constant k (units: 1/minute) and elapsed time. If k is unknown, use the "Find k" mode with two temperature-time pairs. Typical k values: 0.02-0.1/min for beverages, 0.001-0.01/min for large objects.
Example Calculation
Coffee at 90°C cools in a 20°C room with k = 0.05/min. After 10 minutes: T(10) = 20 + (90 − 20) × e^(−0.5) = 20 + 70 × 0.607 = 62.5°C. The half-cooling time = ln(2)/0.05 = 13.9 minutes.
Unit Toggle
Switch between Celsius and Fahrenheit — the calculator automatically converts all temperatures to Celsius internally, then displays results in your chosen unit. The cooling constant k remains the same regardless of temperature scale.
Frequently Asked Questions
What is Newton's Law of Cooling?
Newton's Law of Cooling states that the rate of heat loss of an object is proportional to the temperature difference between the object and its surroundings. The formula is T(t) = T_env + (T_initial - T_env) × e^(-kt), where k is the cooling constant and t is time.
What does the cooling constant k represent?
The cooling constant k determines how quickly the object cools. A larger k means faster cooling. It depends on the material's thermal properties, surface area, and the medium surrounding it. Typical values range from 0.01 to 0.5 per minute for common objects.
How do I find k from two temperature measurements?
If you know the temperature at two different times, use k = -ln((T2 - T_env)/(T1 - T_env)) / (t2 - t1), where T1 and T2 are temperatures at times t1 and t2. This calculator can compute k from two measurements.
Is this calculator free to use?
Yes, completely free with no signup required. All calculations run locally in your browser.
What is half-cooling time?
Half-cooling time is the time for an object to reach halfway between its current temperature and the ambient temperature. It equals ln(2)/k. For example, if k = 0.1/min, the half-cooling time is about 6.93 minutes.