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Physics

Calculate Specific Heat Capacity

Updated · Standard formula, shown below

Specific heat capacity 4.180 J/(g·°C)
Temperature change
10.0 °C
Result
Specific heat capacity
4,180 J/(kg·K)
Result
Heat energy added
20900 J
You entered

This calculator finds the specific heat capacity of a material from a heating measurement. Enter the heat energy added, the mass of the sample and its starting and final temperatures, and you get c in J/(g·°C) and J/(kg·K).

Formula

Q = m × c × ΔT, so c = Q ÷ (m × ΔT), with ΔT = T₂ − T₁.

  • Q: heat energy in joules (1 cal = 4.184 J, 1 BTU ≈ 1055.06 J)
  • m: mass in grams
  • ΔT: temperature change in °C, which is the same size step as a kelvin
  • c: specific heat capacity in J/(g·°C); multiply by 1000 for J/(kg·K)

Worked Example

20,900 J heats 500 g of water from 20 °C to 30 °C.

  1. ΔT = 30 − 20 = 10.0 °C
  2. c = 20,900 ÷ (500 × 10) = 20,900 ÷ 5,000 = 4.180 J/(g·°C)
  3. × 1000 = 4,180 J/(kg·K), close to the textbook value for liquid water

Limits and common mistakes

  • Heat lost to the container and the air makes a real measurement read high; insulate the sample.
  • A temperature change in °F must be multiplied by 5/9 to get °C.
  • The formula fails across a phase change (melting, boiling), where heat goes in without the temperature rising.
Formula used
in q | Heat energy added | J | 20900 | 0
in m | Mass of the sample | g | 500 | 0
in t1 | Starting temperature | °C | 20
in t2 | Final temperature | °C | 30
out c | Specific heat capacity | J/(g·°C) | q / (m * (t2 - t1)) | 3
out dt | Temperature change | °C | t2 - t1 | 1
out ck | Specific heat capacity | J/(kg·K) | c * 1000 | 0

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.