Black Hole Size Calculator
Black hole event horizon radius from mass.
What it does
Every mass hides an event horizon far inside itself. Squeeze Earth to 8.87 mm across its radius and escape velocity hits light speed; the Sun needs 2.95 km while Sagittarius A* spans 12.18 million km. Radius scales linearly with mass.
The tool above runs the Schwarzschild radius for three presets plus custom kilograms. Enter or pick mass and it prints radius with auto mm/m/km units, diameter, and light-crossing time. Defaults show Earth; the Sun gives 5.91 km across with 19.7 microseconds of light.
Space agencies and textbooks agree. NASA Goddard derives R from escape velocity with a 3 km Sun, OpenStax works Earth at 1 cm order with Sgr A* near Mercury-orbit fractions, and Caltech lecture notes cover the Schwarzschild metric formally. Constants G with c carry every digit.
Spin and charge complicate reality beyond this page. Real black holes rotate, dragging horizons inward toward half the Schwarzschild value, while shadows span about twice the event horizon in telescope images. Tidal forces shred infallers long before small horizons.
How to use
- Pick Earth, Sun, Sgr A*, or custom.
- Enter custom kg when picked.
- Read radius first, then diameter.
- Read light-crossing time.
- Compare masses by radius.
- Remember spin shrinks reality.
Formula
- M
- Mass in kg: presets or custom.
NASA Goddard derives R from escape velocity; OpenStax works Sun/Earth/Sgr A* identically; Caltech covers the Schwarzschild metric.
Worked example
Example: Earth mass
Defaults: Earth preset.
- Input: Earth preset, 5.972e24 kg.
- Numerator: 2 x 6.674e-11 x 5.972e24 = 7.97e14.
- Denominator: c squared = 8.99e16.
- Radius: 7.97e14 / 8.99e16 = 0.00887 m.
- Shown as 8.87 mm radius. Tool shows 8.87 mm, 0.02 m across.
Reference table
| Mass | Radius | Diameter |
|---|---|---|
| Earth 5.972e24 kg | 8.87 mm | 0.02 m |
| Sun 1.989e30 kg | 2.95 km | 5.91 km |
| Sgr A* 8.2e36 kg | 12.18M km | 24.36M km |
Limits
- Non-rotating only. Spin shrinks horizons.
- Newtonian-flavored derivation; GR differs inside.
- Custom inputs need exact kg.
- Tidal lethality unmanaged.
Common mistakes
- Expecting volume to scale with radius cubed intuition.
- Mixing radius with diameter.
- Forgetting spin corrections.
- Reading shadows as horizons.
- Typing kg with commas.
Try it yourself
Quick checks. Answers sit tucked under each question.
Sun mass?
Numerator 2 x 6.674e-11 x 1.989e30 = 2.65e20. Radius 2.65e20 / 8.99e16 = 2.95 km. Diameter 5.91 km.
Sagittarius A* mass?
Numerator 1.0945e27. Radius 1.2177e10 m = 12.18M km. Diameter 24.36M km. Light 81.2 s.
Questions
How is the radius figured?
2GM/c squared. Earth gives 8.87 mm; Sun 2.95 km; Sgr A* 12.18M km.
Does spin matter?
Non-rotating case; spin shrinks real horizons toward half.
What is the shadow size?
About twice the event horizon per NASA animations.
Can I enter custom mass?
Yes. Custom kilograms accept any mass from dust to clusters.
How fast is light across it?
Yes. Light-crossing time prints beside each radius: 59.2 ps for Earth.
Could I survive crossing?
No. Tidal forces shred infallers long before small horizons.
Sources
- NASA Goddard: Black Holes (R = 2GM/c^2)
- OpenStax Astronomy 24.5: Black Holes (worked Sun/Earth)
- Caltech Carroll Notes: Schwarzschild Solution