Physics

Newton's Law of Cooling Calculator

Find the temperature of a cooling object over time.

Initial temperature (°C)

Ambient temperature (°C)

Cooling constant (1/min)

Time

Calculated Output

Temperature (°C) 62.457

Formula: T = T_env + (T₀ − T_env)·e^(−k·t)

Step-by-Step Breakdown

1. Values used:

2. Initial temperature = 90 °C

3. Ambient temperature = 20 °C

4. Cooling constant = 0.05 1/min

5. Time = 10

7. Temperature = 62.457°C

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The math behind it

T = T_env + (T₀ − T_env)·e^(−k·t). It cools fastest when the temperature gap is largest.

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

Does it ever fully reach room temperature?

Only asymptotically — it gets arbitrarily close.