How this calculator works
- Step 1ChangeΔT = end − startNegative when cooling.
- Step 2Substancec × mHeat per degree for this amount.
- Step 3Heatq = c m ΔTIn joules, then kJ, kcal and kWh.
Specific heat is how much energy it takes to warm one gram of a substance by one degree. Water’s is high, which is why it heats slowly and holds warmth.
Multiply by the mass and the temperature change for the total heat. A negative answer means heat was given out.
Worked example: OpenStax Example 5.1
- q
c × m × ΔT
- ΔT85 − 2164 °C
- c × m4.184 × 8003,347.2 J/°C
- Heat absorbed3,347.2 × 642,14,220.8 J
OpenStax rounds this to 2.1 × 10⁵ J, or 210 kJ.
Read the result
Heating a 50 L geyser from 20 to 45 °C takes 1.453 kWh, about 43.6 min with a 2,000 W element if no heat is lost.
- Water4.184 J/g·°CSlow to heat, slow to cool.
- Iron0.449 J/g·°CHeats about nine times faster per gram.
Assumptions and limits
- One phaseNo melting, freezing or boiling in the range.
- Constant cSpecific heat changes slightly with temperature.
- No lossesHeater time ignores heat lost to the room.
- °C or KA change of 1 °C equals 1 K.
Related energy tools
Heat energy and electrical energy are the same quantity in different units.
To see what a heater’s kilowatt-hours cost, use the electricity calculator. The BTU calculator converts heating and cooling power, and the ideal gas law calculator relates temperature to pressure.
Common mistakes
Mistake: Using kilograms with c in J/g·°C.
Instead: Enter grams, or multiply kg by 1,000.
Mistake: Including boiling or melting.
Instead: Add latent heat separately for a phase change.
Checking the method
A separate script adds up the heat in hundredth-of-a-degree steps in exact fractions and reproduces OpenStax Example 5.1.
Read how we test our calculators, or browse more maths calculators.