Event Horizon Size of a Black Hole 🕳️

Somewhere out in the galaxy, a star has collapsed into a region so dense that nothing — not even light — can climb back out. The boundary of that region is called the event horizon, and it has a surprisingly simple size.

Feed the calculator above a mass, and it hands you the answer: how wide is the point of no return? 🔭

The Point of No Return 🚪

Think of a rocket trying to leave a planet. To escape, it has to reach escape velocity — about $11.2\ \text{km/s}$ for Earth. Push the mass of the object up, or squeeze the same mass into a smaller ball, and that escape velocity climbs.

Keep squeezing, and eventually something remarkable happens: the escape velocity reaches the speed of light, $c = 299{,}792{,}458\ \text{m/s}$. Since nothing can travel faster than light, nothing can leave. That is a black hole, and the radius where this happens is the event horizon.

The horizon is not a solid surface. It is not a wall you could touch or burn up against. It is simply the last place from which the outside universe is still reachable. Cross it, and every path that leads forward in time leads inward. ⏳

The Schwarzschild Radius 📐

In 1916, only months after Einstein published general relativity, Karl Schwarzschild solved the equations for a perfectly simple case: a non-rotating, uncharged sphere of mass $M$. The result gives the horizon radius directly:

$r_s = \frac{2GM}{c^2}$

Where:

• $r_s$ is the Schwarzschild radius — the event horizon radius, in metres.
• $G = 6.674 \times 10^{-11}\ \text{m}^3\text{kg}^{-1}\text{s}^{-2}$ is Newton’s gravitational constant.
• $M$ is the total mass of the black hole.
• $c$ is the speed of light.

The most striking thing about this formula is how little is in it. There is no density, no pressure, no chemistry — just mass. A black hole of a given mass has exactly one horizon size, no matter what it was made of or how violently it formed. 💫

One Number to Remember 🔢

Because the formula is a straight multiplication, the horizon grows in lock-step with the mass. Plug in the Sun’s mass ($M = 1\ M_\odot$) and you get:

$r_s = 2.95\ \text{km}$

So every solar mass of black hole buys you about 3 kilometres of horizon. That single number lets you estimate almost anything:

• A 10-solar-mass stellar black hole: a horizon radius of about 30 km — roughly the size of a small city.
• Earth, crushed into a black hole: the whole planet would become a horizon only 8.9 mm wide, smaller than your little fingernail. 🌍
• Sagittarius A*, our galaxy’s monster: $4.3$ million solar masses give a horizon of about 12.7 million km — more than 18 times the radius of the Sun itself, and roughly one-twelfth of the way from the Sun to Earth.
• M87*, the first black hole ever photographed: $6.5$ billion solar masses stretch the horizon radius to about 128 AU, wider than our entire solar system out to the heliopause. 📸

Why Doubling the Mass Doubles the Size 📈

Drag the mass slider in the calculator and watch the graph. On a log-log plot the horizon size is a perfectly straight line — the signature of a direct proportion.

This is wonderfully counter-intuitive. A bigger black hole is less dense, not more! The Schwarzschild radius grows as $M$, so a sphere of that radius has volume growing as $M^3$. Density, mass over volume, therefore falls as $1/M^2$:

$\rho \propto \frac{M}{r_s^3} \propto \frac{M}{M^3} = \frac{1}{M^2}$

A supermassive black hole is actually a gentle place compared with a stellar one — its horizon is so enormous that the tidal forces at the edge are mild enough to survive. The tiny ones are the shredders. 🪐

🔬 Try This with the Calculator Above!

1. The Sun, Shrunk: Leave the mass at 1 M☉. The horizon comes out at roughly 2.95 km — the Sun compressed into a sphere the size of a small town. Its light-crossing time is only about 10 microseconds, and a photon racing around that 18.6 km circumference could circle it roughly 1,600 times in the blink of an eye.
2. The Stellar Shredder: Click Stellar BH (~10). The horizon jumps to ~30 km. Real stellar-mass black holes tear apart anything that wanders too close.
3. Meet Sagittarius A*: Click Sagittarius A*. At 4.3 million solar masses the horizon radius tops 12.7 million km — over 18 times the Sun’s own radius, so the entire Sun would vanish inside it with room to spare. This is the object at the centre of the Milky Way, and its shadow was imaged by the Event Horizon Telescope in 2022.
4. Go Supermassive: Click M87*. The horizon balloons past 128 AU. Now read the “How Big Is That?” panel — this single black hole’s horizon is wider than the whole planetary neighbourhood, and its enormous mass is the reason we could photograph it at all.
5. Push the Extremes: Drag the slider down to 0.1 M☉ and then all the way to 10¹⁰ M☉. That is fourteen orders of magnitude in mass, and the graph still traces the same unbroken straight line.

🌌 What the Horizon Actually Looks Like

If you could somehow hover just outside a black hole, the horizon itself would be invisible — it emits nothing. What astronomers actually see is the shadow: a dark disc a bit larger than the horizon, traced by a blazing ring of light from gas swirling in around it.

For a non-rotating black hole the shadow is about 2.6 times the Schwarzschild radius:

$r_{\text{shadow}} = \frac{\sqrt{27}}{2} \, r_s \approx 2.6 \, r_s$

This is a beautiful link back to our Resolving Power of a Lens lab. That glowing ring is only about 50 microarcseconds across as seen from Earth — which is precisely why it took a planet-sized radio telescope, the Event Horizon Telescope, to capture the first image of M87* in 2019. 🔭

Other landmarks hide near the horizon too:

• Photon sphere at $1.5\ r_s$ — the last orbit where light itself can circle the black hole.
• Innermost stable circular orbit (ISCO) at $3\ r_s$ — inside this distance, no stable orbit exists and matter simply plunges in.
• Time dilation — to a distant observer, anything falling in appears to slow down and fade, never quite crossing. The horizon is a one-way door for time as well as space.

⚠️ Good to Know

• This calculator assumes a Schwarzschild black hole: non-rotating and uncharged. Real black holes spin, and rapid spin shrinks the horizon (in the extreme Kerr case down to half the Schwarzschild radius) while dragging space around with it.
• Mass is entered in solar masses. The conversion is $1\ M_\odot = 1.989 \times 10^{30}\ \text{kg}$.
• The formula describes the horizon only. It says nothing about what lies inside — general relativity loses its predictive power at the singularity at the centre.

The next time you look up at the night sky, remember: any of those pinpricks of light would need to be squeezed into a ball just a few kilometres wide to become a black hole. A few kilometres, and it becomes a place with no way back. ✨