Last updated: 2026-07-13

Calorimetry and the q = mcΔT equation

Calorimetry measures heat by watching temperature change. When heat flows into or out of a substance without changing its state, the amount of heat is tied to how much the substance is, what it is made of, and how far its temperature moves. That relationship is the specific-heat equation:

Specific heat c is the heat needed to raise one gram of a substance by one degree. Multiplying it by the mass and by the temperature change gives the total heat exchanged. Because the four quantities are locked together, knowing any three fixes the fourth, and the equation rearranges to solve for whichever one you need:

The sign of q

The temperature change carries the sign. When a substance warms, ΔT is positive and so is q — the substance gained energy. When it cools, ΔT and q are both negative — energy left the substance. In an ideal calorimeter the heat lost by a hot object equals the heat gained by everything around it, so the two heats are equal in size and opposite in sign and add up to zero. That bookkeeping is what lets calorimetry pin down an unknown specific heat or an unknown final temperature.

Why water is the reference

Liquid water has a specific heat of about 4.18 J/(g·°C), which is unusually large. Written other ways that is 4184 J/(kg·K) or 1 calorie per gram per degree — the calorie was originally defined from exactly this. The high value means water soaks up a lot of energy for a modest temperature rise, which is why it moderates climate, cools engines, and stores heat in hot-water systems. Ice sits near 2.09 J/(g·°C) and steam near 2.01 J/(g·°C), while metals are far lower: copper is about 0.385 J/(g·°C) and iron about 0.449 J/(g·°C). A small metal object therefore heats and cools much faster than the same mass of water.

Worked example

How much heat is needed to warm 100 g of water from 20 °C to 45 °C?

The temperature change is ΔT = 45 − 20 = 25 °C, and water's specific heat is 4.18 J/(g·°C):

So about 10.45 kJ, or roughly 2497 calories, is required. Cooling the same water back down would release the same amount of heat, with q carrying a negative sign.

Keeping units consistent

The equation works in any coherent set of units, as long as they cancel. Grams with J/(g·°C) and a Celsius change give joules; kilograms with J/(kg·K) and a kelvin change also give joules. A one-degree change is the same size on the Celsius and Kelvin scales, so a temperature change never needs converting between the two — only absolute temperatures do. This calculator tracks the unit bookkeeping for you and can also report the heat in kilojoules, calories, or kilocalories.

Related calculators

When a reaction's heat is measured in a coffee-cup calorimeter and you want the enthalpy per mole, use the Calorimetry Enthalpy Calculator. To explore how specific heat relates energy and temperature for a fixed sample, see the Specific Heat Calculator. For heat exchanged during a phase change — melting or boiling, where temperature holds steady — use the Latent Heat Calculator instead, since q = mcΔT applies only while the substance stays in one state.