Black Hole Evaporation Time Calculator
Compute how long any black hole survives via Hawking radiation evaporation, from femtoseconds to zettayears.
⏳ What is the Black Hole Evaporation Time Calculator?
Black hole evaporation time is the duration a black hole survives before it completely vanishes by emitting Hawking radiation, a quantum thermal process predicted by Stephen Hawking in 1974. This calculator uses the exact formula t = 5120pi G^2 M^3 / (hbar c^4) to compute how long any black hole, from a microscopic speck to a stellar remnant, takes to radiate away all of its mass.
The tool is useful in three main research and educational contexts. Astrophysicists studying primordial black holes (PBHs) use it to determine which PBH masses correspond to evaporation at a given cosmic epoch. Particle physicists modeling microscopic black holes produced in high-energy collisions use it to check that these objects evaporate instantaneously (less than a nanosecond). Physics students use it to build intuition for why Hawking radiation is negligible for astrophysical black holes but potentially observable for primordial ones.
A common misconception is that black holes evaporate quickly. In reality, stellar-mass black holes (several solar masses) have evaporation timescales of 10^74 years, many orders of magnitude longer than the current age of the universe (13.8 billion years). Only sub-mountain-mass primordial black holes formed in the early universe could be evaporating today. The evaporation time scales as M cubed, so even a small increase in mass produces a dramatic increase in lifetime.
This calculator also shows the Hawking temperature and luminosity at the moment the black hole first forms, providing additional context for understanding the radiation environment surrounding newly-formed micro or primordial black holes. The Time to Mass reverse mode lets you ask a different question: given a desired evaporation timescale, what initial mass was required?
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Mountain-mass primordial black hole (M = 109 kg)
A primordial black hole with the mass of a small mountain
Example 2 — Asteroid-mass black hole (M = 1012 kg)
A black hole with the mass of a large asteroid
Example 3 — Mass that evaporates in the age of the universe (Time to Mass mode)
What mass evaporates in exactly 13.8 Gyr?
❓ Frequently Asked Questions
🔗 Related Calculators
How long does it take a black hole to evaporate via Hawking radiation?
The evaporation time is t = 5120pi G^2 M^3 / (hbar c^4), approximately 8.41e-17 * M^3 seconds when M is in kilograms. A 1 kg black hole evaporates in about 84 femtoseconds. A billion-kilogram black hole lasts about 2665 years. Stellar-mass black holes have lifetimes of 10^74 years or more, far exceeding the current age of the universe.
What is the formula for black hole evaporation time?
t_evap = 5120pi G^2 M^3 / (hbar c^4), where G is the gravitational constant, hbar is the reduced Planck constant, c is the speed of light, and M is the initial black hole mass. The key scaling is t proportional to M^3.
What is a primordial black hole and when would it evaporate?
Primordial black holes (PBHs) are hypothetical black holes that formed in the early universe from density fluctuations, not stellar collapse. A PBH that formed with a mass of about 1.73e11 kg would be finishing its evaporation today, after 13.8 billion years. PBHs lighter than this threshold would have already evaporated.
Does black hole evaporation time depend on temperature?
Yes. The Hawking temperature T = hbar c^3 / (8pi G M k_B) is inversely proportional to mass. As the black hole shrinks it gets hotter, radiates more power, and loses mass faster, so the final stages are runaway. Most of the time is spent at the initial low-temperature phase.
What happens as a black hole evaporates completely?
As a black hole approaches zero mass its temperature and luminosity diverge theoretically. In practice quantum gravity effects are expected to become important at the Planck scale. The final burst is thought to release energy comparable to a nuclear explosion for small primordial black holes.
How does mass affect black hole evaporation time?
Evaporation time scales as M^3. Doubling the mass increases the lifetime by 8 times. A black hole 10 times as massive lasts 1000 times longer. This cubic dependence means there is a sharp threshold: primordial black holes slightly heavier than 1.73e11 kg are still evaporating today, while heavier ones will survive for trillions of years.
Can we observe black hole evaporation?
No direct observation has been confirmed. The Hawking radiation from astrophysical black holes is far too faint to detect. However, if primordial black holes exist near the evaporation threshold, their final gamma-ray bursts might be detectable by space observatories such as Fermi-LAT.
What is the Hawking luminosity during evaporation?
The Hawking luminosity is L = hbar c^6 / (15360 pi G^2 M^2), approximately 3.56e32 / M^2 watts when M is in kg. A 1 kg black hole radiates at 3.56e32 W initially. A billion-kg black hole radiates at 356.258 TW. Luminosity increases as mass decreases.
How is the black hole evaporation time related to the Hawking temperature?
Both are derived from the same semiclassical Hawking radiation formula. Temperature T = hbar c^3/(8pi G M k_B) is inversely proportional to mass, while evaporation time is proportional to M^3. A higher initial temperature corresponds to a shorter lifetime.
What mass of black hole evaporates in exactly the age of the universe?
A black hole with an initial mass of approximately 1.730e11 kg, roughly the mass of a small mountain or large asteroid, would evaporate over exactly 13.8 billion years. Use the Time to Mass mode to find the initial mass for any target evaporation timescale.