# Thermal Energy Calculator

URL: https://speedycalculator.com/calculators/physics/thermal-energy/
Last updated: 2026-10-30

> The thermal energy calculator finds the average kinetic energy per molecule, the rms speed and the total internal (thermal) energy of an ideal gas from its temperature, amount, molar mass and degrees of freedom.

## Inputs

- Temperature T (K, °C, °F)
- Amount n (mol)
- Molar mass M (g/mol)
- Molecule type (degrees of freedom)

## Results

- Average energy per molecule
- Average translational KE
- Total thermal energy
- RMS speed

## Formula

```
ε̄ = (f/2)·k_B·T,  U = (f/2)·n·R·T,  v_rms = √(3RT/M)
```

## Explanation

Temperature is a measure of the average kinetic energy of molecules. Each degree of freedom carries ½k_BT of energy: 3 for single atoms, 5 for diatomic molecules like N₂ and O₂ at room temperature.

### How to use the Thermal Energy Calculator

- **Temperature T**
- **Amount n (mol)**
- **Molar mass M (g/mol)**
- **Molecule type (degrees of freedom)**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the temperature, amount of gas, molar mass and choose the molecule type.

### Tips

- Use absolute temperature (K) in gas laws and efficiency formulas.
- Temperature differences are the same in K and °C.
- Heat = mass × specific heat × temperature change when no phase change occurs.
- Phase changes need latent heat at a constant temperature.

### Common mistakes to avoid

- Using °C in pV = nRT.
- Forgetting latent heat during melting or boiling.
- Confusing heat capacity (J/K) with specific heat (J/(kg·K)).

### Inputs explained

FieldWhat to enterTemperature TUnits: K, °C, °FAmount n (mol)A numberMolar mass M (g/mol)A numberMolecule type (degrees of freedom)Choose one: Monatomic (f = 3), Diatomic (f = 5), Polyatomic (f = 6)

### What each result means

- **Average energy per molecule** = [Molecule type (degrees of freedom)]÷2×1.380649[Average energy per molecule]-23×[Temperature T]
- **Average translational KE** = 1.5×1.380649[Average energy per molecule]-23×[Temperature T]÷1.602176634[Average energy per molecule]-19×1000
- **Total thermal energy** = [Molecule type (degrees of freedom)]÷2×[Amount n (mol)]×8.314462618×[Temperature T]
- **RMS speed** = sqrt(3×8.314462618×[Temperature T]÷([Molar mass M (g÷mol)]÷1000))

### Example values

How the main result changes when **Temperature T** changes and everything else stays at the example values above:

Temperature T (K)Total thermal energy (J)1503,117.92352254,676.88523006,235.8473757,794.80874509,353.770460012,471.6939

## Worked example

Inputs — Temperature T: 300 K; Amount n (mol): 1; Molar mass M (g/mol): 28.965; Molecule type (degrees of freedom): Diatomic (f = 5).

Results — Average energy per molecule = 1.0355e-20 J; Average translational KE = 38.778 meV; **Total thermal energy = 6,235.84696 J**; RMS speed = 508.27831 m/s.

## Key terms

- **Equipartition**: Equal sharing of energy among degrees of freedom.

## FAQ

**What is the equipartition theorem?**
Each quadratic degree of freedom has ½k_BT of energy on average.

**Why do diatomic molecules have 5 degrees of freedom?**
3 translational + 2 rotational (vibrations are frozen at room temperature).

**Is thermal energy the same as heat?**
No – heat is energy transferred; thermal energy is stored.

**How much thermal energy is in 1 mol of air?**
About 6.2 kJ at 300 K.

**What formula does the Thermal Energy Calculator use?**
ε̄ = (f/2)·k_B·T,  U = (f/2)·n·R·T,  v_rms = √(3RT/M).


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)
- [NIST – Fundamental physical constants](https://physics.nist.gov/cuu/Constants/)