Hawking evaporation physics for Schwarzschild black holes
This Schwarzschild black hole evaporation calculator examines the striking prediction that an isolated black hole is not completely dark. In Hawking's semiclassical description, quantum fields around the event horizon produce a faint thermal emission known as Hawking radiation. As energy escapes, the hole loses mass; it becomes hotter as it shrinks and, in the idealized theory, ultimately evaporates.
Enter a mass in solar masses to obtain linked estimates of Hawking temperature, evaporation time, Schwarzschild radius, radiated power, and Bekenstein-Hawking entropy. Every output comes from the same mass, but their responses differ: temperature rises as mass falls, radius is proportional to mass, Hawking power rises rapidly for lighter holes, and lifetime is proportional to the cube of mass. This cubic dependence leaves stellar and supermassive black holes with lifetimes far beyond ordinary cosmic timescales in the isolated textbook model.
Read these values as order-of-magnitude theoretical estimates, not as forecasts for every object in the sky. A black hole in a galaxy may accrete gas, absorb ambient radiation, merge with another compact object, or rotate. This calculator addresses the narrower question of which temperature, radius, power, entropy, and Hawking lifetime follow when an isolated, uncharged, non-rotating Schwarzschild black hole is assigned a mass.
How to use the Schwarzschild black hole evaporation calculator
This Hawking evaporation calculator requires one physical input: black-hole mass in solar masses (M☉). A value of 1 represents one solar mass, 10 represents ten solar masses, and 0.1 represents one tenth of a solar mass. Very small positive values can be used to explore hypothetical low-mass regimes. After you click Compute Properties, the page converts the mass to kilograms and applies the semiclassical Schwarzschild relations in SI units.
The result area reports several aspects of Hawking evaporation. Evaporation time is the idealized lifetime in years. Hawking temperature is the effective thermal temperature for the black hole. Schwarzschild radius is the event-horizon radius of a non-rotating hole. Hawking power is the simplified radiated power in watts, while Bekenstein-Hawking entropy is expressed in Boltzmann-constant units, a dimensionless convention used in black-hole thermodynamics.
To see the mass dependence of Hawking evaporation, compare entries separated by a factor of 10. Increasing mass tenfold makes temperature ten times lower, radius ten times larger, power 100 times lower, and the evaporation time about 1,000 times longer. The especially strong lifetime change follows directly from its M3 dependence.
The Copy Result button appears after a successful calculation and copies a compact summary of the Hawking lifetime, temperature, radius, and power. It is useful for comparing several mass choices without manually transcribing scientific notation.
The black hole evaporation formulas used here apply to an isolated, uncharged, non-rotating Schwarzschild black hole with mass M. Hawking temperature is inversely proportional to that mass: lower-mass holes are hotter, while higher-mass holes are colder.
T = ħc³ / (8π G M kB)
The idealized Hawking evaporation lifetime is the other central relation. Its dependence on the cube of mass explains why even a solar-mass black hole persists for an extraordinarily long time in the isolated approximation.
t ≈ 5120π G² M³ / (ħ c⁴)
The mass also determines the Schwarzschild radius, rs = 2GM/c², the simplified Hawking power, which varies as 1/M², and entropy in Boltzmann-constant units, which varies as M². Together these relations describe the calculator's pattern: a lighter hole is smaller, hotter, more powerful in Hawking radiation, and shorter-lived; a heavier hole is larger, colder, dimmer, and much longer-lived.
SI constants and mass units in the Hawking lifetime calculation
This Schwarzschild black hole calculator evaluates the relations with SI constants. The gravitational constant is G = 6.67430×10−11 m3 kg−1 s−2, the speed of light is c = 299,792,458 m/s, the reduced Planck constant is ħ = 1.054571817×10−34 J·s, the Boltzmann constant is kB = 1.380649×10−23 J/K, and one solar mass is 1.98847×1030 kg. Mass is entered in solar masses, evaluated internally in kilograms, and the calculated lifetime is converted from seconds to years.
The displayed equations are deliberately the clean baseline formulas. More detailed treatments can account for greybody factors, the particle species available at high temperature, and physics near the final stages of evaporation. Those refinements are outside this calculator's intended isolated Schwarzschild model.
Interpreting Hawking lifetime and black hole property results
Interpret the Hawking evaporation results as a connected set rather than unrelated values. At astrophysical masses, the computed temperature is extremely low. For a one-solar-mass black hole it is around 10−8 K, far below the roughly 2.7 K cosmic microwave background. Consequently, a real black hole in the present universe is not described completely by a simple one-way evaporation countdown.
The evaporation lifetime is often the most eye-catching output. Since it scales as mass cubed, it grows extraordinarily quickly with mass. Stellar-mass and supermassive holes are therefore effectively permanent on human, geological, and usual cosmological timescales within this idealized model. A sufficiently smaller hypothetical hole would instead be hotter, emit more Hawking power, and have a far shorter lifetime. The radius and power values provide useful context for that transition between regimes.
The entropy output is less familiar but physically important. Bekenstein-Hawking entropy connects horizon area with thermodynamics and represents an enormous number of possible microscopic states. It should not be read like a household temperature or energy-use value; it shows that the black hole has a thermodynamic description as well as a gravitational one.
Worked example: Hawking evaporation of a one-solar-mass black hole
This Schwarzschild evaporation example uses a mass of 1, or one solar mass. The calculator converts it to approximately 1.988×1030 kg. Its Hawking temperature is roughly 10−8 K, only tens of nanokelvin; its evaporation lifetime is about 1067 years; and its Schwarzschild radius is on the order of a few kilometers. These scales illustrate why Hawking emission is mainly a theoretical concern for stellar black holes.
Reducing the example mass by a factor of 10 reduces the radius by 10, raises temperature by 10, and shortens lifetime by 1,000. Repeated reductions shift the same equations into a hypothetical low-mass regime with hotter, more powerful, and briefer evaporation behavior. The calculator does not alter its model between those entries; only the mass changes.
The multiple outputs make the physical meaning of evaporation easier to inspect. Radius gives the horizon scale, temperature describes the thermal character of Hawking radiation, power indicates the simplified emission rate, and entropy connects the horizon to black-hole thermodynamics.
Relative Hawking scaling for selected Schwarzschild masses
| Mass (in M☉) |
Relative temperature |
Relative lifetime |
| 10 |
~0.1× the 1 M☉ temperature |
~1000× the 1 M☉ lifetime |
| 1 |
1× baseline |
1× baseline |
| 0.1 |
~10× hotter |
~0.001× the lifetime |
| 10−12 |
~1012× hotter |
~10−36× the lifetime |
Limits of isolated Schwarzschild Hawking evaporation estimates
These Hawking evaporation estimates intentionally use clean semiclassical Schwarzschild relations. That makes them useful for understanding the basic mass dependencies, but it does not make them a complete model for every observed black hole. Several assumptions determine how literally the values can be applied.
- Schwarzschild assumption: the relations describe a non-rotating, uncharged black hole. Astrophysical black holes can spin, which changes their detailed thermodynamics and emission.
- Isolation assumption: the lifetime assumes no accretion, mergers, or meaningful absorption of surrounding radiation. In realistic environments, growth can dominate Hawking mass loss.
- Semiclassical regime: Hawking radiation treats quantum fields on a classical spacetime background. Near the Planck scale, that approximation may no longer hold and the final outcome of evaporation is uncertain.
- Idealized emission spectrum: the lifetime constant omits detailed greybody factors and changes in available particle species at very high temperatures.
- Order-of-magnitude use: the outputs are baseline theoretical scaling estimates, not precision predictions for a black hole embedded in a particular astrophysical environment.
For Hawking-radiation intuition, these simplifications keep the most important dependencies clear. Modeling a particular real black hole would require additional environmental and relativistic details, so this calculator is best treated as a focused starting point for the isolated Schwarzschild case.
Schwarzschild black hole evaporation questions
Which Schwarzschild black-hole properties does this calculator estimate?
Enter a mass in solar masses. The calculator converts that mass to kilograms and uses idealized semiclassical Schwarzschild relations to estimate Hawking temperature, evaporation lifetime, Schwarzschild radius, Hawking radiation power, and Bekenstein-Hawking entropy.
Why does a lower-mass black hole have a shorter Hawking lifetime?
For an isolated Schwarzschild black hole, Hawking temperature is inversely proportional to mass, while the evaporation lifetime is proportional to mass cubed. A smaller hole is therefore hotter and loses mass much more quickly in this idealized model.
Do these Hawking evaporation estimates describe real astrophysical black holes exactly?
No. The results assume an isolated, non-rotating, uncharged Schwarzschild black hole. Actual black holes may accrete matter, absorb ambient radiation, spin, or merge, so these outputs are best used as baseline semiclassical estimates rather than literal environmental forecasts.
Enter a black hole mass in solar masses to estimate evaporation time, temperature, Schwarzschild radius, power, and entropy.