Specific heat calculator

How do I calculate the heat needed to warm something?

Q = m × c × ΔT: mass times specific heat times the temperature change. Heating 1,000 g of water from 20 °C to 100 °C takes 1,000 × 4.1813 × 80 = 334,504 J, about 335 kJ.

What is specific heat?

The energy needed to raise 1 gram of a material by 1 °C. Water’s is high — 4.18 J/(g·°C) at 25 °C — which is why it heats and cools slowly; copper’s is only 0.385.

Where do the material values come from?

Water at 25 °C from NIST, ice at 0 °C from IAPWS, and aluminum, copper, iron and lead at 25 °C from NIST-JANAF data. Air and glass are typical handbook values; choose "Custom" to enter your own.

What if the result is negative?

Then the material cools and releases that much heat — the calculator shows it as heat released.

Does it include melting or boiling?

No — changing between ice, water and steam takes extra heat (latent heat) that this formula does not count. Keep the range within one state.

How long will a kettle take to heat the water?

Divide the energy by the power. Warming 2 kg of water from 15 °C to 65 °C takes 418,130 J. A 1,500 W heater supplies 1,500 J every second, so the ideal time is 418,130 ÷ 1,500 = 279 s, about 4.6 minutes. Real kettles lose some heat to the container and the air, so expect somewhat longer.

What is the final temperature when two things are mixed?

If no heat escapes, the heat lost by the hot object equals the heat gained by the cold one, so T = (m₁c₁T₁ + m₂c₂T₂) ÷ (m₁c₁ + m₂c₂). A 100 g copper block at 100 °C dropped into 200 g of water at 20 °C ends at (38.5 × 100 + 836.3 × 20) ÷ (38.5 + 836.3) = 23.5 °C. The water barely warms because its heat capacity is so much larger.

The formula and its units

Q = m × c × ΔT, where m is the mass, c is the specific heat (the energy to warm one gram by one degree Celsius) and ΔT is the final temperature minus the starting temperature. The calculator works in grams and J/(g·°C) and converts pounds and kilograms first. A change of one degree Celsius equals a change of one kelvin, so the same c applies to ΔT in kelvins, and the temperatures can be entered in °C. The formula assumes c stays constant over the range and that the material does not change state. In reality c varies slowly with temperature, so a large range gives a small error that the table values at a single temperature cannot capture.

Worked example: a kettle and a pan

Heating 2,000 g of water from 15 °C to 65 °C: Q = 2,000 × 4.1813 × 50 = 418,130 J, which is 418.1 kJ, 99.9 food Calories (kcal) or 116.1 watt-hours. Now a 500 g aluminum pan warmed from 20 °C to 200 °C: Q = 500 × 0.897 × 180 = 80,730 J. Per degree, the same 500 g of water holds about 4.7 times as much heat as the aluminum (compare the numbers over equal ranges, ignoring that water would boil), which is why water is used to store and carry heat. In the old units, water is very close to 1 BTU per pound per °F (0.999).

Common mistakes

The most common mistake is mixing mass units: c in J/(g·°C) needs grams, not kilograms, and the calculator's mass menu does the conversion for you. A second is using Fahrenheit differences without converting; a change of 18 °F is a change of 10 °C, not 18. Third, applying the formula across a phase change: water that goes from 20 °C to steam at 120 °C needs extra heat for boiling that Q = mcΔT does not contain, and ice at −5 °C turning to water needs the heat of fusion. Finally, the result is the heat that goes into the material itself; the energy a stove or heater must supply is larger because of losses.

Sources: OpenStax University Physics, Volume 2, chapter 1 (temperature and heat; specific heat and calorimetry, Q = mcΔT); material values from NIST (water) and NIST-JANAF (metals) as noted above; unit factors (calorie = 4.184 J, BTU, pound) from NIST SP 811, Appendix B.8. Related: latent heat calculator, BTU calculator and heat loss calculator.