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Schwarzschild Black Hole Hawking Temperature

Relate mass and theoretical Hawking temperature for an ideal nonrotating, uncharged black hole, with inverse mass solving and fourteen mass unit choices.

Formula & worked example
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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

For the retained approximate solar-mass scale of 1.989 ×10³⁰ kg, the modeled Hawking temperature is about 6.17 ×10⁻⁸ K. Doubling mass halves the temperature.

T_H = ℏ c³/(8π G M k_B) = h c³/(16π² G M k_B), with ℏ = h/(2π).

Worked example

Enter these known values and leave the other values blank.

Black hole mass: 1 Suns

Theoretical Hawking temperature: 6.168e-8 K

Assumptions and limitations

This is the semiclassical Hawking temperature of an ideal Schwarzschild black hole: nonrotating and uncharged, with the radiation temperature referenced to a distant observer. It is not the temperature of surrounding gas or an accretion disk.
The calculation assumes an isolated asymptotically flat model and does not include rotation, charge, a cosmological background, environmental heating or evaporation over time.
Mass and absolute temperature must be positive. Celsius and Fahrenheit are converted through their absolute-zero offsets; zero kelvin and values below it are rejected. A negative Celsius value can still be a valid positive absolute temperature.
The constants h = 6.62607015 ×10⁻³⁴ J·s, c = 299792458 m/s and k_B = 1.380649 ×10⁻²³ J/K are exact SI definitions. G = 6.67430 ×10⁻¹¹ m³/(kg·s²) is the 2022 CODATA measured central value, with uncertainty 0.00015 ×10⁻¹¹; displayed digits do not remove that uncertainty.
The retained Earth and Sun mass units are approximate input scales: 5.9722 ×10²⁴ kg and 1.989 ×10³⁰ kg respectively. They are not exact defining constants or new astronomical measurements. Choose kilograms when using a specific mass estimate.
The u conversion uses the 2022 CODATA measured atomic mass constant 1.66053906892 ×10⁻²⁷ kg. That unit is retained for conversion completeness; it does not imply that atomic-sized black holes satisfy this approximation.
Near or below the Planck mass, about 2.18 ×10⁻⁸ kg, this semiclassical relation is not a reliable physical prediction. Any returned number in that range is a formal extrapolation of the stated equation, not an established black-hole temperature.
For stellar masses the predicted temperature is extremely small. Use kelvin and retain the unrounded value when solving backward; a rounded Celsius or Fahrenheit display can be indistinguishable from absolute zero.

Common questions

Is Hawking temperature the temperature of matter falling into a black hole?

No. This model concerns theoretical thermal radiation associated with the horizon. It does not calculate the often much hotter gas or disk outside the black hole.

What happens when the black hole mass doubles?

Under the same Schwarzschild assumptions, its theoretical Hawking temperature halves. The mass-temperature product is fixed by the constants in this model.

Why can the Celsius result look like absolute zero?

A stellar-mass result is only a few tens of nanokelvins. Rounding after subtracting 273.15 can hide that small positive value. Select kelvin for a meaningful display or inverse input.

References

Use exact SI h, c and k_B, mathematical pi and the NIST 2022 CODATA central G throughout both Schwarzschild mass/temperature relationships, replacing the captured 3.14 and older rounded hbar/G values. Use the 2022 CODATA measured atomic mass constant for u and sign-based positive mass/absolute-temperature predicates. Preserve the two disclosed approximate Earth/Sun mass scales, other mass factors and Celsius/Fahrenheit affine conversions.

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