Hawking Radiation Timer: Black Hole Evaporation
Calculate how long black holes survive before evaporating through Hawking radiation. Discover why nothing in the universe is truly eternal—not even black holes.
In 1974, Stephen Hawking made a revolutionary discovery: black holes aren’t truly black. Through quantum effects near the event horizon, they emit Hawking radiation—a faint glow of particles that causes black holes to slowly lose mass and eventually evaporate completely. This insight connected quantum mechanics, general relativity, and thermodynamics in ways that transformed physics. Our calculator lets you explore black hole evaporation times—from stellar-mass black holes lasting 10⁶⁷ years to hypothetical primordial black holes that might be evaporating right now.
The physics is deeply counterintuitive. Near the event horizon, quantum fluctuations constantly create virtual particle-antiparticle pairs. Normally these annihilate instantly, but the extreme curvature can separate them—one falls in, one escapes. The escaping particle carries positive energy (becoming real), so the black hole must lose energy (mass) to compensate. Smaller black holes radiate faster: temperature T = ℏc³/(8πGMk), so halving the mass doubles the temperature and increases luminosity 16-fold. This runaway acceleration causes smaller black holes to explode catastrophically in their final moments.
The timescales are staggering. A stellar black hole (10 solar masses) would take ~10⁶⁷ years to evaporate—far longer than the current age of the universe (13.8 billion years) and longer than stars will exist (10¹⁴ years). The supermassive black hole at our galaxy’s center (4 million solar masses) would last ~10⁸⁷ years. Yet hypothetical primordial black holes formed in the early universe with mass ~10¹² kg would evaporate in roughly the universe’s current age—meaning we might detect their final gamma-ray bursts today.
Calculate Black Hole Evaporation
Explore Hawking temperature, luminosity, and evaporation timescales
⚫ Hawking Radiation Timer
Discover how long it takes for black holes to evaporate through quantum radiation!
🧪 The Science Behind Hawking Radiation
🕳️ Choose a Black Hole
🔢 Or Enter Custom Mass
How to Use the Hawking Radiation Timer
1. Enter Black Hole Mass
Input mass in solar masses, kilograms, or Earth masses. Choose from presets: primordial (10¹² kg), stellar (~10 M☉), intermediate (~1000 M☉), or supermassive (~10⁶ M☉). Each mass range exhibits dramatically different radiation properties.
2. View Hawking Temperature
See the black hole’s temperature in Kelvin. Stellar black holes are incredibly cold (~10⁻⁸ K)—colder than the CMB. Primordial black holes can be billions of degrees, glowing in gamma rays. Temperature determines what particles are radiated.
3. Calculate Lifetime
Discover evaporation time: t ∝ M³. Stellar black holes outlast everything else in the universe. The calculator shows lifetime in years, comparing to universe age, stellar era, and other cosmic timescales—revealing the ultimate fate of matter.
Why Hawking Radiation Matters
🔬 Quantum Gravity
Hawking radiation merges quantum mechanics with general relativity—the holy grail of physics. It’s our best window into quantum gravity without a complete theory. Understanding it may lead to unified physics. Explore more with our Black Hole Survival Timer.
♾️ Information Paradox
If black holes evaporate completely, what happens to the information they swallowed? This paradox has occupied theoretical physics for 50 years. Hawking radiation appears thermal (random), seemingly destroying information—violating quantum mechanics. The resolution remains debated.
🌌 Ultimate Fate
Hawking radiation determines the universe’s ultimate fate. In the far future, after stars die and galaxies dissolve, only black holes remain—then they too evaporate. Nothing is eternal. Explore this with our Heat Death Countdown.
🔭 Observational Search
Astronomers search for evaporating primordial black holes—their final explosions would produce distinctive gamma-ray bursts. Detection would confirm Hawking radiation experimentally and reveal early universe conditions. Track cosmic rays with our Cosmic Ray Detector.
The Physics of Hawking Radiation
Hawking Temperature
T = ℏc³/(8πGMk) ≈ 6.17×10⁻⁸ K × (M☉/M). Inversely proportional to mass: smaller = hotter. A 10 M☉ black hole is 6×10⁻⁹ K—far colder than the CMB (2.7 K). A 10¹² kg primordial black hole reaches 10¹¹ K—hotter than any star.
Evaporation Time
t = 5120πG²M³/(ℏc⁴) ≈ 8.4×10⁻¹⁷ s × (M/kg)³. Scales as M³—doubling mass increases lifetime 8×. A 10 M☉ black hole: ~10⁶⁷ years. The Sun’s mass: ~10⁶⁴ years. Mount Everest’s mass: ~10⁵ years. A 10¹² kg primordial: ~13.8 billion years (now!).
Final Explosion
As black holes shrink, they radiate faster (T ∝ 1/M, luminosity ∝ T⁴ ∝ 1/M⁴). In the final second, a black hole releases ~10³⁰ J—equivalent to millions of hydrogen bombs—in a gamma-ray burst. The explosion leaves nothing behind; mass converts entirely to radiation.
Frequently Asked Questions
Has Hawking radiation been detected?
Not directly from astrophysical black holes—the radiation is far too faint (stellar black holes are colder than the cosmic microwave background, so they absorb more than they emit). However, analogue experiments using sonic black holes in fluids and optical systems have observed phenomena consistent with Hawking’s predictions. Direct detection would require finding evaporating primordial black holes.
How does radiation escape a black hole?
Hawking radiation doesn’t escape from inside the event horizon—nothing can. Instead, quantum fluctuations create particle pairs near (but outside) the horizon. One particle falls in; the other escapes. The escaping particle wasn’t inside the black hole—it forms from vacuum energy in curved spacetime. The black hole loses mass because it “pays” for the escaped particle’s energy.
Why are smaller black holes hotter?
Temperature relates to surface gravity (tidal forces at the horizon), which is stronger for smaller black holes. Equivalently: smaller horizon = more curved spacetime = more energetic particle creation. Temperature T ∝ 1/M means a black hole half the mass is twice as hot, radiates 16× more power (Stefan-Boltzmann), and evaporates in 1/8 the time (M³ scaling).
What happens to information?
The “information paradox” asks: if a book falls into a black hole that later evaporates into thermal radiation, is the book’s information destroyed? Quantum mechanics forbids information destruction; Hawking radiation appears thermal (information-free). Proposed solutions include information escaping in subtle correlations, holographic encoding, or remnants. This remains physics’ biggest unsolved problem.
Related Black Hole & Physics Tools
- Black Hole Survival Timer – Survive near event horizons
- Time Dilation Calculator – Gravitational time effects
- Gravity Simulator – Extreme gravity effects
- Heat Death Countdown – Universe’s ultimate fate
- Cosmic Ray Detector – High-energy particle physics
- Deep Time Visualizer – Cosmic timescales
Scientific References & Further Reading
- Hawking Radiation – Wikipedia comprehensive overview
- Stephen Hawking – Biography and contributions
- Black Hole Thermodynamics – Temperature and entropy
- Information Paradox – The deepest mystery
- Primordial Black Holes – Early universe relics
- Hawking’s Original Paper – “Particle Creation by Black Holes”
- Analogue Hawking Radiation – Laboratory experiments
- Quanta Magazine – Accessible explanation