Specific Heat Calculator

Specific heat capacity is the energy needed to warm one kilogram of a substance by one degree. This calculator solves Q = mcΔT for whichever quantity you need: the heat to warm or cool something, the temperature change a given amount of heat produces, the mass that can be heated, or the specific heat of an unknown material from a measurement. Choose from 31 common materials or enter your own value in J/(kg·K), cal/(g·°C) or BTU/(lb·°F).

The mixing mode handles the classic calorimetry problem: two objects at different temperatures placed in contact, such as a hot metal block dropped into water, and finds the temperature where they meet. Results show joules, kilojoules, kilocalories, kilowatt-hours and BTU, plus how long a 1 kW heater would take.

Q = mcΔT

Mixing: Tf = (m₁c₁T₁ + m₂c₂T₂) ÷ (m₁c₁ + m₂c₂)

Q is the heat added in joules, m the mass in kilograms, c the specific heat in J/(kg·K) and ΔT the change in temperature. A change of 1 K equals a change of 1 °C, so either can be used for ΔT, while a change of 1 °F is 5/9 of that. A negative ΔT or Q means the object is cooling and giving off heat. The mixing formula comes from setting the heat lost by the hotter object equal to the heat gained by the colder one. Both formulas assume no phase change: melting ice or boiling water needs latent heat in addition.

Boiling water for tea. Heating 1 kg of water from 20 °C to 100 °C takes 334.7 kJ, about 0.093 kWh. A 2 kW kettle with no losses would need 2.79 minutes.

An aluminum pan. 10 kJ into a 0.5 kg aluminum pan raises it by 22.3 °C. The same energy would warm 0.5 kg of water by only 4.78 °C.

Identifying a metal. If 3.85 kJ warms a 100 g sample by 100 °C, its specific heat is 385 J/(kg·K), which matches copper.

Hot copper in water. A 200 g copper block at 100 °C dropped into 500 g of water at 20 °C ends at 22.84 °C. The water barely warms because its heat capacity is about 27 times larger.

A swimming pool. Raising 50 m³ of water by 5 °C takes 291 kWh, which is why pool heaters are sized in tens of kilowatts.

Water stores about 4.2 kJ per kilogram per degree, roughly ten times as much as iron and more than almost any other common substance, because hydrogen bonds between molecules absorb energy that would otherwise raise the temperature. This is why coastal climates are mild, why oceans moderate the planet's temperature, and why water is used in car radiators, home heating loops and industrial cooling. It is also why a pot of water takes much longer to heat than the metal pot holding it, and why your body, which is mostly water, holds a steady temperature.

At a melting or boiling point, added heat changes the state rather than the temperature. Melting ice takes 334 kJ/kg and boiling water takes 2,257 kJ/kg, far more than warming it: boiling away 1 kg of water already at 100 °C takes about seven times the energy needed to bring it from 20 °C to 100 °C. For a problem that crosses a phase change, calculate each stage separately, warming the solid, melting it, warming the liquid and so on, and add the energies. Ice and steam have their own specific heats, both listed above.