What this calculator does
The specific heat capacity formula, Q = mcΔT, connects four quantities: the heat energy added or removed (Q), the mass of the material (m), its specific heat capacity (c), and the resulting change in temperature (ΔT). This calculator applies that formula directly, given a mass, a specific heat capacity and a temperature change, to find the heat energy involved.
Specific heat capacity itself, the c in the formula, is a property of the material: how much energy it takes to raise one kilogram of it by one degree. Water has an unusually high specific heat capacity, 4,186 J/(kg·K), which is why it takes so much energy to heat a pot of water compared with heating the same mass of metal by the same amount.
The formula
Multiply the mass by the specific heat capacity by the temperature change: Q = m × c × ΔT. The result is in joules when mass is in kilograms, specific heat capacity is in J/(kg·K), and temperature change is in kelvin or degrees Celsius (a change of 1°C equals a change of 1 K, so either unit works for ΔT). To find specific heat capacity itself rather than heat energy, rearrange the same formula: c = Q ÷ (m × ΔT).
| Term | Meaning |
|---|---|
| Q | Heat energy added or removed, in joules. |
| m | Mass of the material, in kilograms. |
| c | Specific heat capacity of the material, in joules per kilogram per kelvin. |
| ΔT | Change in temperature, in kelvin or degrees Celsius. |
The inputs explained
| Field | What to enter |
|---|---|
| Mass (kg) | The mass of the material being heated or cooled. |
| Specific heat capacity (water = 4186) (J/(kg·K)) | The specific heat capacity of the material. Water is 4,186 J/(kg·K); most metals are far lower. |
| Temperature change (°C) | The temperature change the material undergoes, as a positive number regardless of whether it is heating or cooling. |
When to use it
Working out how much energy heats a known mass of water
Water’s specific heat capacity is well known and fixed, so given a mass and a target temperature rise, the heat energy needed follows directly from the formula.
Comparing materials with different specific heat capacities
Two materials of the same mass, heated by the same temperature change, need very different amounts of energy if their specific heat capacities differ, which is the specific heat capacity equation’s main practical use.
Estimating heating time from a known power source
Once the heat energy required is known, dividing by the power of a heating element gives an estimate of how long that heating would take, ignoring losses.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Heat energy needed to warm 1 kg of water by a range of temperature changes
A fixed 1 kg mass of water, across a range of temperature changes.
| Temperature change | Heat energy required | In kilocalories |
|---|---|---|
| 5°C | 20,930 J | 5.002 kcal |
| 10°C | 41,860 J | 10.005 kcal |
| 20°C | 83,720 J | 20.010 kcal |
| 40°C | 167,440 J | 40.019 kcal |
| 60°C | 251,160 J | 60.029 kcal |
| 80°C | 334,880 J | 80.038 kcal |
Heat energy needed for the same temperature change across different materials
A fixed 1 kg mass and 20°C change, across a range of specific heat capacities.
| Specific heat capacity | Heat energy required | In watt-hours |
|---|---|---|
| 130 J/(kg·K) | 2,600 J | 0.722 Wh |
| 450 J/(kg·K) | 9,000 J | 2.500 Wh |
| 900 J/(kg·K) | 18,000 J | 5.000 Wh |
| 2050 J/(kg·K) | 41,000 J | 11.389 Wh |
| 4186 J/(kg·K) | 83,720 J | 23.256 Wh |
Questions
What is the specific heat capacity formula?
Q = mcΔT, where Q is heat energy, m is mass, c is specific heat capacity, and ΔT is the temperature change. It states that the energy needed scales directly with all three of mass, specific heat capacity and temperature change.
How do I find specific heat capacity if I already know Q, m and ΔT?
Rearrange the formula to c = Q ÷ (m × ΔT). This calculator solves the formula for Q directly; solving for c instead just means dividing the known heat energy by the mass and temperature change instead of multiplying them.
Why does water have such a high specific heat capacity?
Water’s molecular structure, particularly hydrogen bonding between molecules, means a relatively large amount of energy goes into molecular motion before the temperature rises much. That high specific heat capacity is also why large bodies of water moderate nearby climates so effectively.
Does specific heat capacity change with temperature?
In principle yes, but for most materials over ordinary temperature ranges it is close enough to constant that a single value is used without meaningfully affecting the result. Extreme temperature ranges or phase changes, such as ice turning to water, are where that assumption starts to break down.
For the physics of temperature change from thermal expansion instead of heat energy, see the thermal expansion calculator. To convert the resulting energy figure into other units, use the energy unit converter.