Black Hole Evaporation Time Calculator

Black holes are not quite eternal. Stephen Hawking showed in 1974 that quantum effects near the event horizon let a black hole radiate energy away, slowly losing mass until — after an almost unimaginable stretch of time for anything astrophysical — it evaporates completely. How long that takes depends on exactly one quantity, raised to the third power.

The formula

This is the idealized lifetime of an isolated, non-rotating, uncharged (Schwarzschild) black hole sitting in a vacuum colder than its own Hawking temperature, so it only ever loses mass and never gains it. Every other factor in the formula — $G$ , $\hbar$ , $c$ — is a fixed constant of nature. Mass is the only variable, and it enters as $M^3$ .

Why the cube matters so much

Because evaporation time scales as $M^3$ , shrinking a black hole’s mass by a factor of 10 shortens its lifetime by a factor of 1,000. Shrink the mass by 1,000× and the lifetime drops by a billion times. This single exponent explains nearly everything about which black holes are stable and which aren’t:

• A stellar-mass black hole (a few to a few dozen solar masses) has an evaporation time enormously longer than the current age of the universe — around 10⁶⁷ years for one solar mass, a number so far beyond 13.8 billion years that “essentially permanent” undersells it.
• Sagittarius A*, the supermassive black hole at the center of the Milky Way (about 4.3 million solar masses), is even more stable still — the $M^3$ scaling pushes its lifetime tens of orders of magnitude further out.
• A hypothetical primordial black hole with a mass around 10¹¹–10¹² kilograms — roughly that of a small asteroid — would have an evaporation time comparable to the age of the universe itself. Ones even smaller than that would already be gone, having evaporated sometime in the universe’s past.

This is also why tiny black holes and large ones behave so differently in terms of temperature: Hawking temperature runs the other way, inversely with mass, so the smallest black holes are the hottest and radiate the most furiously — which is exactly why they burn through their mass so much faster. (Our companion Hawking temperature calculator covers that side of the relationship in detail — the two tools are two views of the same underlying physics.)

The one number worth remembering

Solve the formula for the mass at which $t_{evap}$ exactly equals the age of the universe (about 13.8 billion years), and you get a specific, finite answer: somewhere around 10¹¹ kilograms, a mass comparable to a small asteroid or mountain. Any black hole lighter than that, formed at the Big Bang, would already have evaporated by now. Any black hole anywhere near a stellar mass or heavier is so far above that threshold that “already evaporated” isn’t a remotely live possibility — which is the entire reason astrophysical black holes are treated as permanent fixtures on cosmological timescales, while sufficiently tiny ones are the only place Hawking evaporation could ever plausibly be observed.

Reading the log-log plot

Both axes of the chart are logarithmic, which turns the $M^3$ relationship into a straight line — three decades of mass become nine decades of lifetime, visibly. The current mass you’ve entered is marked directly on that line, alongside a few fixed reference points (a stellar-mass black hole, Sagittarius A*, and the crossing mass above), plus a dashed horizontal line at the age of the universe so you can see at a glance which side of “already evaporated” any given mass falls on.