# What is the specific heat?

Specific heat calculator: finds the specific heat capacity from heat, mass and temperature change (c = Q ÷ mΔT), or the heat, the mass or the final temperature from Q = mcΔT.

- Page: https://www.acalculator.org/physics/specific-heat-calculator
- JSON spec: https://www.acalculator.org/physics/specific-heat-calculator.json
- Version: e3bcb16f7632

## Default answer

Example with the default inputs (Find Specific heat, Heat (Q) 39.6756246563155 BTU, Mass (m) 2.20462262184878 lb, Start temperature 67.9999999999999 °F, Final temperature 85.9999999999999 °F): The answer is c = 4186 J/(kg·°C).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| find | Find | Which value to work out from Q = m × c × ΔT. |
| Q | Heat (Q) | The heat added to the material; type a negative value for heat taken away. |
| m | Mass (m) | The mass of the material that heats or cools. |
| sub | Material | The material, which sets its specific heat (OpenStax Table 1.3, in J/(kg·°C)). |
| c | Specific heat (c) | The specific heat capacity of the material, in the unit chosen below. |
| cu | Specific heat unit | The unit of the specific heat you type. |
| t1 | Start temperature | The temperature before the heat goes in or out. |
| t2 | Final temperature | The temperature after the heat goes in or out. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| result | Answer | The value worked out, to 6 significant figures. |
| c | Specific heat (J/(kg·°C)) | The specific heat capacity in joules per kilogram per degree Celsius (or kelvin). |
| cJg | Specific heat (J/(g·°C)) | The specific heat capacity in joules per gram per degree Celsius. |
| cCal | Specific heat (cal/(g·°C)) | The specific heat capacity in calories per gram per degree Celsius. |
| cBtu | Specific heat (Btu/(lb·°F)) | The specific heat capacity in British thermal units per pound per degree Fahrenheit. |
| joules | Heat (J) | The heat in joules; negative when heat is taken away. |
| kj | Heat (kJ) | The heat in kilojoules. |
| btu | Heat (Btu) | The heat in British thermal units. |
| kg | Mass (kg) | The mass in kilograms. |
| dT | Temperature change (°C or K) | Final temperature − start temperature, in °C (the same size as kelvins). |
| dTF | Temperature change (°F) | The temperature change in degrees Fahrenheit. |
| finalC | Final temperature (°C) | The final temperature in degrees Celsius. |
| finalF | Final temperature (°F) | The final temperature in degrees Fahrenheit. |

## Method

Q = m × c × ΔT, with ΔT = final − start temperature; c = Q ÷ (m × ΔT); m = Q ÷ (c × ΔT); final = start + Q ÷ (m × c).

## Assumptions

- The material stays in one phase (no melting, freezing or boiling), and c does not change with temperature over the range.
- Table values are from OpenStax University Physics Volume 2, Table 1.3, in J/(kg·°C); a change of 1 °C is a change of 1 K.

## Worked examples

1. find = c, Q = 41,860, m = 1, t1 = 293.15, t2 = 303.15 gives c = 4,186, cCal = 1.000478, result = c = 4186 J/(kg·°C). Source: OpenStax, University Physics Volume 2, §1.4 Heat Transfer, Specific Heat, and Calorimetry (Q = mcΔT; Table 1.3), https://openstax.org/books/university-physics-volume-2/pages/1-4-heat-transfer-specific-heat-and-calorimetry (retrieved 2026-10-05).
2. find = heat, sub = aluminum, m = 0.5, t1 = 293.15, t2 = 423.15 gives joules = 58,500, kj = 58.5. Source: OpenStax, University Physics Volume 2, §1.4 Heat Transfer, Specific Heat, and Calorimetry (Q = mcΔT; Table 1.3), https://openstax.org/books/university-physics-volume-2/pages/1-4-heat-transfer-specific-heat-and-calorimetry (retrieved 2026-10-05) (c of aluminum, Table 1.3).
3. find = final, sub = water, Q = 20,930, m = 0.25, t1 = 288.15 gives dT = 20, finalC = 35. Source: OpenStax, University Physics Volume 2, §1.4 Heat Transfer, Specific Heat, and Calorimetry (Q = mcΔT; Table 1.3), https://openstax.org/books/university-physics-volume-2/pages/1-4-heat-transfer-specific-heat-and-calorimetry (retrieved 2026-10-05).
4. find = mass, sub = custom, c = 1, cu = BTU-lbF, Q = 1,055.055853, t1 = 293.15, t2 = 293.705556 gives kg = 0.453592, c = 4,186.8. Source: NIST SP 811, Appendix B.8 (1 Btu_IT = 1,055.05585262 J; 1 cal_th = 4.184 J; 1 lb = 0.45359237 kg), https://www.nist.gov/pml/special-publication-811 (retrieved 2026-10-05).

## FAQ

### How do you calculate specific heat?

Divide the heat by the mass times the temperature change: c = Q ÷ (m × ΔT). If 41,860 J warms 1 kg by 10 °C, c = 41,860 ÷ (1 × 10) = 4,186 J/(kg·°C), the value for water.

### What is the specific heat of water?

About 4,186 J/(kg·°C), or 4.186 J/(g·°C), or 1.000 cal/(g·°C), or 1.000 Btu/(lb·°F). It takes 4,186 J to warm 1 kg of liquid water by 1 °C.

### What does Q = mcΔT mean?

Q is the heat that goes in (positive) or out (negative), m is the mass, c is the specific heat of the material, and ΔT is the final temperature minus the start temperature.

### Is ΔT the same in Celsius and kelvins?

Yes. A change of 1 °C is a change of 1 K, so J/(kg·°C) and J/(kg·K) are the same unit. A change of 1 °F is 5/9 of that.

### Why does a negative heat give a lower final temperature?

A negative Q is heat taken away, so the material cools. When you find c or m, Q and ΔT must have the same sign, because c and m are always positive.

### How much heat does it take to warm an aluminum pan?

A 0.500 kg aluminum pan from 20 °C to 150 °C needs 0.500 × 900 × 130 = 58,500 J, or 58.5 kJ, with c = 900 J/(kg·°C).

### Does this work when water boils or ice melts?

No. Q = mcΔT holds only while the material stays in one phase. Melting and boiling take latent heat at a fixed temperature, which this formula does not count.

## Sources

- OpenStax, University Physics Volume 2, §1.4 Heat Transfer, Specific Heat, and Calorimetry: Q = mcΔT and Table 1.3 of specific heats, retrieved 2026-10-05. https://openstax.org/books/university-physics-volume-2/pages/1-4-heat-transfer-specific-heat-and-calorimetry
- NIST Special Publication 811 (2008), Appendix B.8: 1 Btu (IT) = 1,055.05585262 J, 1 cal (thermochemical) = 4.184 J, 1 lb = 0.45359237 kg, retrieved 2026-10-05. https://www.nist.gov/pml/special-publication-811