How long does it take for a black hole to evaporate completely?

In one line

The rule

Black holes lose mass by emitting Hawking radiation, and the time for a black hole to evaporate depends on its mass.

The formula for the evaporation time is: T ≈ (5120 × π × G² × M³) / (ħ × c⁴) where:

• T = evaporation time (in seconds)
• G = gravitational constant
• M = mass of the black hole
• ħ (h-bar) = reduced Planck constant
• c = speed of light

Let's understand it simply

Imagine you have a pressure cooker on a low flame. The cooker slowly loses water as steam. A black hole is like that cooker, but instead of steam, it loses mass by giving off a special kind of radiation called Hawking radiation (tiny particles that escape from the black hole). But this process is very, very slow. For a black hole as heavy as our Sun, it would take much longer than all of human history—longer than the universe has existed!

Think of it like a giant ice block in a hot room. If the block is huge, it melts very slowly. If it is small, it melts faster. In the same way, big black holes evaporate slowly, and small ones evaporate quickly.

How it works

1. Hawking radiation is created near the black hole's edge (event horizon) due to quantum effects.
2. This radiation carries away a tiny bit of the black hole's mass as energy.
3. As the black hole loses mass, it gets smaller.
4. Smaller black holes emit more radiation and lose mass even faster.
5. The process speeds up as the black hole shrinks, until it finally disappears in a burst of energy.

The story behind it

The idea of black hole evaporation was proposed by Stephen Hawking in 1974. Before this, scientists thought nothing could escape a black hole. Hawking used quantum physics to show that black holes can emit radiation and slowly lose mass. This was a huge surprise to everyone, even to Hawking himself!

Hawking's discovery connected two big areas of science: quantum mechanics (the rules for tiny things) and general relativity (the rules for gravity and big things). This made black holes even more interesting to scientists.

Where you see it in real life

• Space: Real black holes in space are losing mass by Hawking radiation, but so slowly that we cannot detect it yet.
• Particle accelerators: Some scientists hope to create tiny black holes in labs to study their evaporation, but this has not happened yet.
• Cosmic rays: If tiny black holes were made in the early universe, they might be evaporating now, releasing bursts of energy we could detect.
• Science fiction: Many stories and movies use the idea of black holes evaporating or exploding.
• Physics research: Hawking radiation is a key idea in the search for a theory that unifies all of physics.
• Thermodynamics: The study of black hole evaporation helps us understand the laws of heat and energy in extreme conditions.

Why it matters

• Connects big and small physics: Shows how quantum effects can change our ideas about gravity.
• Predicts new things: Suggests black holes are not forever, but can disappear.
• Guides experiments: Helps scientists look for signals from evaporating black holes.
• Affects the future of the universe: Over trillions of years, all black holes may vanish, changing the fate of everything.

Worked example

Let's estimate how long it takes for a black hole with the mass of our Sun (about 2 × 10³⁰ kg) to evaporate.

Given:  M = 2 × 10³⁰ kg
Step 1: Write the rule        T ≈ (5120 × π × G² × M³) / (ħ × c⁴)
Step 2: Plug in the constants G = 6.67 × 10⁻¹¹, ħ = 1.05 × 10⁻³⁴, c = 3 × 10⁸
Step 3: Calculate M³         (2 × 10³⁰)³ = 8 × 10⁹⁰
Step 4: Calculate numerator   5120 × π × (6.67 × 10⁻¹¹)² × 8 × 10⁹⁰
Step 5: Calculate denominator (1.05 × 10⁻³⁴) × (3 × 10⁸)⁴
Step 6: Divide numerator by denominator
Step 7: Answer               T ≈ 2 × 10⁶⁷ years (about 100,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 years)

This is much longer than the current age of the universe (about 1.4 × 10¹⁰ years).

Common mistakes

• Thinking black holes last forever: They do evaporate, but it takes a very long time.
• Believing big black holes evaporate quickly: Actually, the bigger the black hole, the slower it evaporates.
• Confusing Hawking radiation with normal light: Hawking radiation is a special quantum effect, not ordinary light or heat.
• Forgetting the formula depends on mass cubed (M³): Small changes in mass make a huge difference in evaporation time.

Remember it

Big black holes take longer to evaporate—much, much longer than the universe's age.