Black Hole Evaporation Time Calculator
Introduction to black hole evaporation and Hawking lifetime
This black hole evaporation calculator is built around one of the most surprising predictions in modern physics: an isolated black hole is not perfectly black. In the semiclassical picture developed by Stephen Hawking, quantum fields near the event horizon make the hole emit a faint thermal spectrum now called Hawking radiation. That radiation carries energy away, so the black hole gradually loses mass, becomes hotter as it shrinks, and in the idealized theory eventually evaporates.
The calculator turns that abstract idea into concrete estimates 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 outputs are linked by the same mass input, but they do not all respond in the same way. Temperature rises when mass falls, radius grows linearly with mass, power increases sharply as the hole gets lighter, and lifetime depends on the cube of mass. That cubic dependence is the reason stellar and supermassive black holes survive for timescales that are fantastically longer than the current age of the universe in the clean textbook model.
The results are best read as order-of-magnitude theoretical estimates, not as forecasts for every real object in the sky. A black hole in a galaxy can accrete gas, absorb surrounding radiation, merge with other compact objects, or spin rapidly. This calculator instead answers a simpler and more focused question: if you take an isolated, non-rotating, uncharged Schwarzschild black hole with a given mass and apply the standard Hawking formulas, what temperature, radius, power, entropy, and evaporation lifetime follow from that assumption set?
How to use the black hole evaporation time calculator
This black hole evaporation time calculator starts with a single physical input: the mass of the black hole in solar masses (M☉). A value of 1 means one Sun's mass, 10 means ten solar masses, 0.1 means one tenth of a solar mass, and very small positive values let you explore hypothetical low-mass or primordial-black-hole-style regimes. After you click Compute Properties, the calculator converts that mass into kilograms and evaluates the standard semiclassical Schwarzschild formulas in SI units.
The result area then reports several related quantities. Evaporation time is the idealized lifetime in years. Hawking temperature is the effective thermal temperature measured by a distant observer. Schwarzschild radius is the event-horizon radius 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 standard dimensionless convention in black-hole thermodynamics.
If you want intuition instead of a single answer, compare masses that differ by a factor of 10. Multiplying mass by 10 makes the temperature 10 times smaller, the radius 10 times larger, the power 100 times smaller, and the evaporation time about 1000 times longer. That contrast is the central lesson of the calculator: a modest change in mass barely changes some outputs, but it completely transforms the lifetime because the lifetime scales with M3.
The Copy Result button appears after a successful calculation and copies a compact summary of the main outputs. That makes it easy to compare several masses in notes, assignments, or discussions without retyping the scientific-notation results by hand.
Formula for Hawking temperature, lifetime, radius, power, and entropy
The black hole evaporation formulas in this calculator assume an isolated, non-rotating, uncharged Schwarzschild black hole of mass M. The first key relation is the Hawking temperature. Its main physical message is simple and important: the temperature is inversely proportional to mass, so lighter black holes are hotter and heavier black holes are colder.
T = ħc³ / (8π G M kB)
The second headline relation is the idealized evaporation time. In this approximation, the lifetime grows with the cube of mass, which is why even a one-solar-mass black hole outlives ordinary cosmic timescales by an overwhelming margin.
t ≈ 5120π G² M³ / (ħ c⁴)
The same input mass also feeds the familiar Schwarzschild radius relation rs = 2GM/c², a simplified Hawking power that scales like 1/M², and an entropy expression that scales like M² when written in Boltzmann-constant units. Put together, those scaling rules explain the whole result table. A lighter black hole is smaller, hotter, more luminous in Hawking radiation, and much shorter-lived. A heavier one is larger, colder, dimmer, and vastly longer-lived.
Constants and units in the black hole calculation
This black hole calculator uses standard SI constants throughout the computation. 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. You enter mass in solar masses for convenience, the formulas run in SI units internally, and the lifetime is converted to years because the raw value in seconds is too large to read comfortably for most astrophysical masses.
One subtle point is worth emphasizing. The formulas shown here are the standard clean versions often quoted in textbooks and introductory discussions, but some advanced treatments include greybody factors, changing particle species at very high temperatures, or corrections relevant near the final stages of evaporation. This calculator deliberately keeps the baseline formulas visible so that the main scaling relationships remain easy to understand.
How to interpret the black hole evaporation result table
This black hole evaporation result table makes the most sense when you read the outputs together rather than as isolated numbers. For ordinary astrophysical masses, the temperature is extremely small. A one-solar-mass black hole has a Hawking temperature around 10−8 K, which is far below the roughly 2.7 K temperature of the cosmic microwave background. In today's universe, such a black hole is not hotter than its environment, so a literal real-world evaporation countdown is not the full story.
The lifetime output is usually the headline result. Because the lifetime scales as mass cubed, it becomes enormous very quickly as mass increases. That means a stellar-mass or supermassive black hole is effectively immortal on human, geological, and even standard cosmological timescales in the idealized model. By contrast, a much smaller hypothetical black hole would be hotter, more radiative, and drastically shorter-lived. The radius and power outputs help bridge the intuition: a tiny radius is not just a geometric curiosity, but a clue that the hole sits in the high-temperature, high-power part of the Hawking picture.
The entropy result is less intuitive in everyday terms, yet it is one of the deepest pieces of the calculation. Black-hole entropy ties horizon area to thermodynamics and hints at a huge number of microscopic states. You do not need to interpret the entropy number as a household-style temperature reading or energy bill. Its value is mainly conceptual: it shows that the black hole behaves like a thermodynamic system, not just a one-way gravitational sink.
Worked example: a 1-solar-mass Schwarzschild black hole
This black hole evaporation example starts with a mass of 1, meaning one solar mass. Internally the calculator converts that to 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 results immediately tell you why Hawking evaporation is a theoretical rather than observationally urgent effect for stellar black holes.
Now compare that baseline with a smaller mass. If you drop the mass by a factor of 10, the radius drops by a factor of 10, the temperature rises by a factor of 10, and the lifetime falls by a factor of 1000. If you push the mass down by many more orders of magnitude, the change becomes dramatic. The same equations are still being evaluated, but the physical regime shifts from cold, long-lived astrophysical holes to hot, short-lived hypothetical ones that are more relevant to discussions of primordial black holes or very early universe scenarios.
The worked example also shows why the calculator reports multiple outputs instead of only the lifetime. The radius tells you about the horizon scale, the temperature shows the quantum-thermal side of the story, the power shows how quickly energy is being emitted in the simplified model, and the entropy connects the calculation to black-hole thermodynamics. Reading those values together gives you a fuller picture of what “evaporation” means physically.
| 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 of semiclassical black hole evaporation estimates
These black hole evaporation estimates are intentionally based on the clean semiclassical Schwarzschild formulas, which makes them excellent for learning the baseline physics but imperfect for modeling every real black hole. The numbers are accurate in the sense that they reproduce the standard textbook relations, yet several assumptions matter when you decide how literally to apply the outputs.
- 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, star-forming regions, and binary systems, growth processes can easily dominate evaporation.
- Semiclassical regime: Hawking radiation is derived using quantum fields on a classical spacetime background. Near the Planck scale, that approximation may fail, so the true end state of evaporation remains uncertain.
- Idealized emission spectrum: the simplified lifetime constant ignores detailed greybody factors and changes in the number of particle species available for emission at very high temperatures.
- Order-of-magnitude interpretation: the results are best read as theoretical scaling estimates, not as precision predictions for an observed black hole embedded in a realistic astrophysical environment.
If your goal is intuition, these limitations are usually acceptable and even helpful because they keep the main dependencies visible. If your goal is a high-precision model of a specific black hole, then the calculator should be treated as a starting point rather than a final answer. That distinction is exactly what makes a focused educational calculator valuable: it clarifies the core Hawking-radiation picture before more complicated astrophysical effects are layered on top.
Optional mini-game: Hawking Tuner
This optional arcade mini-game is tied directly to the same black-hole mass relationships used in the calculator. Hold to radiate mass away, release to let accretion win, and try to line the black hole up with each target band before the scan ring arrives. It does not change the calculator math; it simply turns the mass-temperature-lifetime tradeoff into a fast visual challenge.