Black Hole Evaporation Time Calculator
Introduction
Black holes are often described as cosmic objects that swallow everything and never give anything back. That classical picture is useful, but it is not the whole story. When quantum field theory is applied near the event horizon, a black hole is predicted to emit a faint thermal glow now called Hawking radiation. In the semiclassical model, that radiation carries energy away. Because energy and mass are related, the black hole slowly loses mass, becomes hotter, and eventually evaporates.
This calculator turns that big idea into numbers you can inspect. Enter a mass in solar masses, and the page estimates the black hole's Hawking temperature, evaporation time, Schwarzschild radius, radiated power, and Bekenstein-Hawking entropy. Those quantities are connected, but they do not all scale in the same way. Temperature rises when mass falls, radius grows linearly with mass, power increases strongly as the hole gets lighter, and lifetime depends on the cube of mass. That last point is the reason astrophysical black holes live for absurdly long times in the idealized model.
The outputs are best read as order-of-magnitude physical estimates. They are not forecasts for a real black hole sitting inside a galaxy, feeding from gas, or absorbing ambient radiation. Instead, they answer a cleaner theoretical question: if you take an isolated Schwarzschild black hole with a given mass and apply the standard Hawking formulas, what temperature and lifetime do you get?
How to use
Start with the black hole mass input. The field expects a positive number measured in solar masses (M☉), so a value of 1 means one Sun's mass, 10 means ten solar masses, and 0.1 means one tenth of a solar mass. After you click Compute Properties, the calculator converts your value into kilograms and evaluates the standard semiclassical Schwarzschild formulas.
The result table reports several quantities. Evaporation time is the estimated lifetime in years under the isolated-black-hole assumption. Hawking temperature is the effective thermal temperature seen by a distant observer. Schwarzschild radius is the radius of the event horizon for a non-rotating black hole. Hawking power is the simplified radiated power in watts, and Bekenstein-Hawking entropy is shown in units of Boltzmann's constant, which is a common way to express black-hole entropy.
If you want intuition rather than a one-off calculation, try comparing masses that differ by a factor of 10. Increasing the mass by ten makes the temperature ten times smaller, but it makes the lifetime about one thousand times longer. That dramatic cubic sensitivity is the reason a tiny shift in mass means very little for radius yet an enormous amount for the final evaporation timescale.
Formula
The core temperature formula for a non-rotating, uncharged Schwarzschild black hole of mass M is shown below. The important physical message is that temperature is inversely proportional to mass: lighter black holes are hotter, while heavier black holes are colder.
T = ħc³ / (8π G M kB)
The standard idealized evaporation time used in many introductory discussions is
t ≈ 5120π G² M³ / (ħ c⁴)
Those equations explain most of the behavior you will see in the calculator. If mass is cut in half, the temperature doubles. If mass is cut by a factor of 10, the lifetime falls by a factor of 1000. The page also computes the Schwarzschild radius rs = 2GM/c², a simplified Hawking power that scales like 1/M², and entropy that scales like M² in the chosen convention. Together, the outputs show how strongly different black-hole properties respond to mass.
Constants and units
This calculator uses standard 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 taken as 1.98847×1030 kg. The input is in solar masses, the formulas run in SI units, and the final lifetime is converted to years for readability.
How to interpret the result table
The temperature result is usually tiny for black holes with astrophysical masses. A one-solar-mass black hole has a Hawking temperature far below the cosmic microwave background temperature of about 2.7 K. That means such a black hole is not hotter than its environment today. In realistic surroundings it would absorb more background radiation than it emits, so the formal evaporation clock is not the whole environmental story.
The lifetime output is the number most people come to this calculator to see. It is extraordinarily sensitive to mass because of the cubic dependence. A stellar-mass black hole lasts vastly longer than the current age of the universe in the idealized model. By contrast, a sufficiently tiny hypothetical black hole would be much hotter and would radiate away its mass much faster. The radius and power outputs help bridge the intuition: a small radius does not just mean a compact object, it also means a hotter and more rapidly radiating one in the Hawking picture.
Entropy is included because black-hole thermodynamics is one of the deepest links between gravity, quantum theory, and information. The entropy value here is not meant to be emotionally intuitive in the way that temperature or radius can be. Instead, it reminds you that a black hole behaves like a thermodynamic system with an enormous number of accessible microscopic states under the standard interpretation.
Example
Suppose you enter 1 for the mass, meaning one solar mass. Internally the calculator uses approximately 1.988×1030 kg. The Hawking temperature comes out at roughly 10−8 K, which is only tens of nanokelvin. The evaporation time is about 1067 years, and the Schwarzschild radius is on the order of a few kilometers. Those numbers are a good reality check: ordinary stellar black holes are far too cold and far too long-lived for Hawking evaporation to matter observationally today.
Now imagine reducing the mass by many orders of magnitude. The radius would shrink in direct proportion, but the temperature would climb sharply and the lifetime would crash even faster. That is why discussions of black-hole evaporation often focus on hypothetical primordial black holes rather than stellar remnants. The same formulas are being used, but once the mass becomes tiny, the outputs move into a completely different physical regime.
| 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 |
Limitations
This calculator uses the cleanest and most commonly quoted semiclassical formulas, so it is accurate in the sense of reproducing the textbook Schwarzschild estimates. But that is not the same thing as describing every real black hole in every environment. Several assumptions matter when you interpret the result.
- Schwarzschild assumption: the formulas apply to a non-rotating, uncharged black hole. Real astrophysical black holes can spin, and spin changes the detailed thermodynamics and emission behavior.
- Isolation assumption: the lifetime estimate assumes no accretion, no mergers, and no substantial absorption of surrounding radiation. In galaxies and stellar systems, growth can easily dominate evaporation.
- Semiclassical regime: Hawking radiation is derived using quantum fields on a classical spacetime background. Near the Planck scale, the approximation may fail, so the true end state of evaporation is still uncertain.
- Idealized emission spectrum: the simplified lifetime constant ignores detailed greybody factors and changes in the number of particle species that can be emitted at high temperatures.
- Order-of-magnitude interpretation: the results are best read as theoretical scaling estimates, not as precise predictions for an observed black hole embedded in a realistic astrophysical environment.
If your goal is conceptual understanding, these assumptions are usually acceptable. If your goal is high-precision modeling of an actual object, they are not sufficient on their own. That difference is exactly why a simple calculator is still useful: it makes the baseline physics clear before additional complications are layered on top.
Optional mini-game: Hawking Tuner
This arcade mini-game does not change the calculator math. It turns the same mass–temperature–lifetime relationship into a fast timing challenge: hold to radiate mass away, release to let accretion win, and line the black hole up with each target band before the scan ring arrives.