How this calculator works
A hot drink loses heat to the room through its surface, and the rate depends on how much hotter the drink is than the room. That gives Newton's law of cooling: the temperature difference shrinks exponentially, so the first ten degrees come off quickly and the last ten take a long time. The time constant is the mass times the specific heat capacity of the water, divided by the heat transfer coefficient and the exposed area. A tall narrow mug has less surface for its volume than a wide shallow one, so it holds heat longer. Adding cold water is a different problem: the mixture settles at a temperature between the two, weighted by the masses, which is the mixing equation. The cooling model assumes the drink is well mixed and at one temperature, which is a fair approximation for a stirred cup but not for a large pot with a lid.
Formula
cooling: time = (mass x specific heat capacity / (h x area)) x ln((initial - room) / (target - room)). For water the specific heat capacity is 4186 J/(kg K) and one litre weighs 1 kg. mixing: cold volume = drink volume x (initial - target) / (target - cold). final volume = drink volume + cold volume.
Worked example
A 250 mL mug of tea at 95 C in a 20 C room, with 250 cm2 of surface and a coefficient of 15 W/(m2 K), has a time constant of 0.25 x 4186 / (15 x 0.025) = 2791 seconds. To reach 60 C, the time is 2791 x ln(75 / 40) = 2791 x 0.6286 = 1754 seconds, or about 29 minutes. Adding water instead: 250 mL at 95 C brought down to 60 C with 5 C water needs 250 x (95 - 60) / (60 - 5) = 159 mL of cold water, giving a final volume of 409 mL.
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Frequently asked questions
Why does the last part of cooling take so long?
The rate of heat loss is proportional to the temperature difference between the drink and the room. As the drink approaches room temperature the difference shrinks, so it loses heat more and more slowly and never quite arrives. Most of the drop happens in the first few minutes.
How accurate is the waiting time?
Treat it as a guide, not a promise. The heat transfer coefficient depends on the shape of the cup, whether there is a lid, the air movement and evaporation, and those change the time by a large factor. The default suits an open mug in still air; a lid roughly halves the loss and a fan can double it.
Can I put the drink in the fridge or freezer?
The model covers a drink left in the room. A fridge adds moving cold air and a much larger temperature difference, so the real time is shorter than the figure here. A sealed container is safer: a glass with a wide mouth can crack in a freezer.
Does adding ice water taste different from waiting?
Yes. Adding water dilutes the drink and makes it weaker as well as cooler, which matters for tea, coffee, soup and stock. Waiting keeps the strength and loses a little water to evaporation instead.