Specific Heat Calculator

About the Specific Heat Calculator

Put a pan of water and a metal spoon on the same stove and the spoon gets hot far faster. The reason is specific heat capacity: the energy needed to raise the temperature of one kilogram of a substance by one degree. Water needs a lot of energy to warm up; metals need much less. Specific heat explains why kettles take minutes to boil, why coastal climates are mild and why car engines use water for cooling.

This specific heat calculator uses Q = mcΔT to find the heat energy needed to change a material's temperature, or works backwards to the temperature change, the mass or the specific heat capacity. It includes typical values for water, ice, steam, aluminium, copper, iron, steel, glass, concrete, air and olive oil, or you can enter your own. It shows the energy in joules, kilojoules, kilowatt-hours and kilocalories, and how long a 2 kW heater would take to supply it.

How to Use the Specific Heat Calculator

Choose Find heat, Find temperature change, Find mass or Find specific heat.

Choose the material, or enter a custom specific heat in J/kg·K.

Enter the known values: mass, starting and final temperatures, or heat energy.

Use a negative heat energy for heat removed, when something cools.

The Formula

  Q = m × c × ΔT

  Q  = heat energy (J)
  m  = mass (kg)
  c  = specific heat capacity (J/kg·K)
  ΔT = temperature change (°C or K — the same size of degree)

  ΔT = Q ÷ (m c)      m = Q ÷ (c ΔT)      c = Q ÷ (m ΔT)

Step-by-Step Examples

Heating a litre of water from 20 °C to 100 °C.

  Q = 1 × 4,184 × 80 = 334,720 J = 334.72 kJ ≈ 0.093 kWh
  2 kW kettle: 334,720 ÷ 2,000 = 167.4 s

Warming 2 kg of aluminium by 50 °C.

  Q = 2 × 897 × 50 = 89,700 J = 89.7 kJ

Heating 0.5 kg of copper with 10 kJ.

  ΔT = 10,000 ÷ (0.5 × 385) = 51.948 °C

Typical Specific Heat Capacities

  Substance     J/kg·K        Substance     J/kg·K
  water         4,184         concrete      880
  ice           2,100         glass         840
  steam         2,010         aluminium     897
  olive oil     1,970         iron          449
  air           1,005         steel         490
                              copper        385

Values vary a little with temperature and composition.

Why Water Is Special

Water has one of the highest specific heats of any common substance, about 4,184 J/kg·K — more than ten times that of copper and nearly five times that of aluminium. It takes a great deal of energy to warm, and gives it back slowly as it cools. That makes water an excellent coolant in car engines and power stations, and a good way to store heat in central heating systems and hot water tanks. On a global scale, the oceans absorb enormous amounts of heat in summer and release it in winter, which is why places near the sea have smaller temperature swings than places far inland.

Heat, Temperature and Energy

Heat and temperature are different things. Temperature measures how hot something is — the average energy of its particles. Heat is energy transferred because of a temperature difference. A bath of warm water holds far more heat energy than a cup of boiling water, even though the cup is hotter, because the bath has so much more mass. Specific heat links the two: the same amount of heat raises the temperature of a small mass or a low-capacity material much more than a large mass or a high-capacity one.

Changes of State

The formula Q = mcΔT applies only while the substance stays in one state. When ice melts or water boils, energy goes into breaking the bonds between molecules rather than raising the temperature — the latent heat. Melting ice needs about 334 kJ per kilogram, and boiling water about 2,260 kJ per kilogram, far more than the 419 kJ needed to heat that water from 0 to 100 °C. To heat ice at −10 °C into steam, you would add the heat for each stage separately: warming the ice, melting it, warming the water, boiling it and warming the steam.

Energy Costs of Heating

Because one kilowatt-hour is 3.6 million joules, heating a litre of water from 20 °C to boiling uses about 0.093 kWh — more in practice, because kettles lose some heat to the air and the kettle itself. Filling a kettle only with the water you need is one of the simplest ways to save energy at home. Heating a 150-litre hot water tank by 45 °C needs about 7.8 kWh.

Measuring Specific Heat

Specific heat capacity is measured with a calorimeter. In a simple school experiment, an electric heater of known power warms a block of metal while its temperature is recorded; the energy supplied, power multiplied by time, divided by the mass and the temperature rise gives the specific heat. Heat lost to the surroundings makes the measured value a little too high, so blocks are wrapped in insulation. In the method of mixtures, a hot object is dropped into cold water and the final temperature reveals its specific heat.

Understanding Your Result

The headline is the heat, temperature change, mass or specific heat you asked for.

The energy line gives the heat in J, kJ, kWh and kcal.

The values line restates the mass, material, specific heat and temperature change.

The heating time line shows how long a 2 kW heater would take, ignoring losses.

When Should You Use This Calculator?

Use it for physics and chemistry homework on heat.

Use it to estimate the energy and cost of heating water.

Use it to compare how quickly different materials warm up.

Common Mistakes

Using grams with J/kg·K. Convert grams to kilograms; the calculator does it for you.

Ignoring changes of state. Melting and boiling need latent heat.

Confusing heat and temperature. Heat is energy; temperature is how hot something is.

Forgetting heat losses. Real heating takes more energy than the ideal figure.