The black hole that is lighter than air
The black hole in the first-ever black-hole photograph holds 6.5 billion Suns. Divide that mass by the volume inside its event horizon and the average comes out at 0.44 kilograms per cubic metre: thinner than the air you are breathing.
This month a reader asked Astronomy magazine a tidy question: if a black hole weighs a billion Suns, how big is it, compared with the Sun itself?
The answer, from the astrophysicist Misty Bentz, is the textbook one. A black hole’s size is taken to be its event horizon, the boundary past which nothing comes back. For a black hole that isn’t spinning, the radius of that horizon depends on just one thing, the mass, and it grows in direct proportion to it: about 3 kilometres for every Sun’s worth of mass. A billion Suns gives about 3 billion kilometres, roughly the distance from the Sun to Uranus.
“We use the event horizon as a convenient reference for the black hole’s size.”
That is Bentz’s own caveat, and it is a fair one: nobody knows what the mass inside has collapsed into. But her answer stops at size. One more line of arithmetic turns it into something far stranger.
The step the answer doesn’t take
If the radius grows in step with the mass, the volume inside the horizon grows with the cube of the mass. Ten times the mass, ten times the radius, a thousand times the volume. So mass divided by volume, the average density, falls with the square of the mass. Ten times heavier means a hundred times less dense.
Run that across real black holes and the familiar picture of black holes as the densest things in the universe falls apart. Cygnus X-1, a black hole of about 21 Suns, has a horizon 63 kilometres in radius and an average density around a fifth of an atomic nucleus. Sagittarius A*, at the centre of our own galaxy, holds 4.3 million Suns and averages about a thousand times the density of water. A billion-Sun black hole averages 18 kilograms per cubic metre, a fifty-fourth of water. And M87*, the 6.5-billion-Sun black hole the Event Horizon Telescope photographed in 2019, averages 0.44 kilograms per cubic metre. Air at sea level is 1.225. The air in the room you are sitting in is 2.8 times denser.
Calculator
Weigh a black hole
Enter a mass in Suns, or tap a real black hole. The page works out how big its horizon is, how dense it is on average, and how hard it would stretch you at the edge.
Try doubling any mass: the horizon doubles, and the density drops to a quarter. Somewhere around 3.9 billion Suns, a black hole crosses below the density of air.
The gentle giants
The same arithmetic changes what it would feel like to fall in. What tears a falling body apart is the difference in pull between its head and its feet. At the horizon, that difference also falls with the square of the mass. At Cygnus X-1’s horizon a person would be stretched by about 4.7 million times Earth’s gravity, and would have been pulled apart long before arriving. At Sagittarius A*’s horizon the stretch is about a ten-thousandth of Earth’s gravity. Anything heavier than about 46,000 Suns, you could cross the horizon without feeling a thing.
You still could not come back. That is what makes a horizon a horizon. But the most dangerous black holes to approach are the small ones, not the giants.
Which mass do you trust?
Here the tidy story meets a real, unresolved argument. M87*’s mass has been measured in more than one way. The Event Horizon Telescope’s image gives 6.5 billion Suns, and a 2011 study of the motions of stars near the galaxy’s centre gave 6.6 billion. But a 2013 study of a disk of gas orbiting the same black hole gave 3.5 billion, and that figure has never been fully reconciled with the others.
At 3.5 billion Suns, the average density comes out at 1.50 kilograms per cubic metre, denser than air. So the headline verdict flips depending on which measurement you believe. And because density goes with the square of the mass, the disagreement grows: the masses differ by a factor of 1.86, the densities by 3.45. Squaring a measurement squares its uncertainty too.
What the number does, and doesn’t, mean
A black hole is not a gas you could bottle, and its mass is not spread evenly through the space inside the horizon. “Average density” here means exactly what it says: the mass divided by the volume of an ordinary sphere the size of the horizon. It is a model, not a measurement, and the space inside a horizon is anything but ordinary. Spin matters too: Bentz notes that a rapidly spinning black hole’s horizon shrinks by about 30 per cent, and at the theoretical maximum spin it would be half the size.
What the model does capture is real, and it is the kind of reasoning that matters more than any single number: before trusting a formula, ask what happens when the input is ten times bigger. Size goes up by ten. Volume goes up by a thousand. And the densest-sounding objects in the universe turn out, on average, to be among the emptiest.
For the classroom
How Big Is a Black Hole?
A 90-minute case study for grades 10–12 and introductory college courses, built from the same article and the same published masses.
- Students vote first, then derive the 0.44 number themselves and plot five real black holes on a log–log grid.
- Design-backwards problems: the black hole with the density of water, and the smallest one you could fall into unharmed.
- A written claim on the M87* mass dispute, scored with a four-level rubric.
- Teacher guide, minute-by-minute pacing, a two-period split and a fully worked answer key. Every figure was checked in code.
Left: the classroom packet on Teachers Pay Teachers. Right: The Little Book of Black Holes by Steven Gubser and Frans Pretorius, a short tour of black-hole physics from Einstein’s equations to the X-ray binary stars that first revealed black holes, the class Cygnus X-1 belongs to — an Amazon affiliate link. As an Amazon Associate this site earns from qualifying purchases, at no additional cost to you.
Sources
The question and Misty Bentz’s answer: Astronomy magazine, Ask Astro, November 2026 issue. Source of every measured figure: M87* mass 6.5 ± 0.7 billion Suns, Event Horizon Telescope Collaboration (2019), Astrophysical Journal Letters 875, L1; 6.6 billion from stellar motions, Gebhardt and colleagues (2011), Astrophysical Journal 729, 119; 3.5 billion (+0.9/−0.7) from gas motions, Walsh and colleagues (2013), Astrophysical Journal 770, 86. Sagittarius A* 4.30 million Suns, GRAVITY Collaboration (2023), Astronomy & Astrophysics 677, L10. Cygnus X-1 21.2 Suns, Miller-Jones and colleagues (2021), Science 371, 1046. Planetary distances from the NASA Planetary Fact Sheet; sea-level air density from the US Standard Atmosphere. Modelled, not measured: the average densities (mass divided by an ordinary sphere’s volume), the head-to-toe stretch (Newton’s law applied at the horizon) and the assumption that the black holes do not spin.