# Black Hole Temperature Calculator (Hawking Radiation)

URL: https://speedycalculator.com/calculators/physics/black-hole-temperature/
Last updated: 2026-10-30

> The black hole temperature calculator finds the Hawking temperature, radiated power and evaporation time of a black hole from its mass.

## Inputs

- Black hole mass M (M☉, M⊕, kg, t)

## Results

- Hawking temperature
- Radiated power
- Evaporation time
- Schwarzschild radius

## Formula

```
T = ħc³ / (8πGMk_B),  P = ħc⁶ / (15360πG²M²),  t_evap = 5120πG²M³ / (ħc⁴)
```

## Explanation

Stephen Hawking showed in 1974 that black holes are not completely black: quantum effects make them glow faintly. The smaller the black hole, the hotter it is. A solar-mass black hole is colder than the cosmic microwave background, so it grows rather than evaporates.

### How to use the Black Hole Temperature Calculator

- **Black hole mass M**

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

### How it works

Enter the black hole mass.

### What each result means

- **Hawking temperature** = 1.054571817e-34×299792458^3÷(8×pi×6.6743e-11×[Black hole mass M]×1.380649e-23)
- **Radiated power** = 1.054571817e-34×299792458^6÷(15360×pi×6.6743e-11^2×[Black hole mass M]^2)
- **Evaporation time** = 5120×pi×6.6743e-11^2×[Black hole mass M]^3÷(1.054571817e-34×299792458^4)
- **Schwarzschild radius** = 2×6.6743e-11×[Black hole mass M]÷299792458^2

### Example values

How the main result changes when **Black hole mass M** changes and everything else stays at the example values above:

Black hole mass M (M☉)Hawking temperature (K)0.51.2340e-70.758.2268e-816.1701e-81.254.9361e-81.54.1134e-823.0850e-8

## Worked example

Inputs — Black hole mass M: 1 M☉.

Results — **Hawking temperature = 6.1701e-8 K**; Radiated power = 9.0076e-29 W; Evaporation time = 2.0957e67 years; Schwarzschild radius = 2.95334 km.

## Key terms

- **Hawking radiation**: Thermal radiation predicted from black holes by quantum theory.

## FAQ

**How hot is a solar-mass black hole?**
About 6 × 10⁻⁸ K – far colder than space.

**Do black holes evaporate?**
In theory, very slowly; small ones would end in a burst.

**Has Hawking radiation been observed?**
Not yet – it is far too faint for known black holes.

**Why are smaller black holes hotter?**
Temperature is inversely proportional to mass.


## Sources

- [NIST – Fundamental physical constants](https://physics.nist.gov/cuu/Constants/)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)