Calculate black hole event horizon radius or mass from the other value, with support for km, m, mi, ly, solar masses, kg, and lb units.

Estimate the Schwarzschild radius from mass.

Scientific notation is accepted. One solar mass is approximately 1.988 × 10³⁰ kg.

Black Hole Size Formula

This calculator uses R = 2GM/c² for a non-rotating, uncharged black hole, with G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻², c = 299,792,458 m/s and 1 solar mass ≈ 1.988 × 10³⁰ kg. This gives approximately 2.952641 km per solar mass.

R ≈ 2.952641M
M ≈ R / 2.952641
  • R = radius of the event horizon, in kilometers
  • M = black hole mass, in solar masses
  • 2.952641 = approximate radius factor in km per solar mass; calculations use the constants above

If you enter the black hole mass, the calculator uses R ≈ 2.952641M to estimate the event horizon radius. If you enter the event horizon radius, it uses M ≈ R/2.952641 to estimate the black hole mass. Choose the value to solve for, enter the known quantity and select Calculate. Units convert the current quantity. The formulas above express kilometers and solar masses; the calculation uses SI units without rounding the intermediate factor.

Typical Event Horizon Radius by Black Hole Mass

Black hole mass Approximate event horizon radius Type of scale
1 solar mass 2.953 km One-solar-mass reference (not a minimum)
10 solar masses 29.526 km Stellar-mass black hole
1,000 solar masses 2,952.641 km Intermediate-mass range
1,000,000 solar masses 2,952,641 km Supermassive range

Radius Unit Reference

Unit Equivalent in kilometers When it is useful
1 meter 0.001 km Small event horizon values
1 mile 1.609344 km Converting radius to imperial distance
1 light year 9,460,730,472,580.8 km Very large astronomical distances

Examples

Example 1: Find the event horizon radius from mass

If a black hole has a mass of 10 solar masses, use:

R ≈ 2.952641M

Substitute 10 for M:

R ≈ 2.952641 × 10 ≈ 29.5264 km

The estimated event horizon radius is 29.5264 kilometers.

Example 2: Find the mass from event horizon radius

If a black hole has an event horizon radius of 150 kilometers, use:

M ≈ R / 2.952641

Substitute 150 for R:

M ≈ 150 / 2.952641 ≈ 50.802

The estimated mass is 50.802 solar masses.

FAQ

What does black hole size mean?

In this calculator, black hole size means the radius of the event horizon. The event horizon is the boundary around a black hole where the escape velocity reaches the speed of light. The calculator gives the radius, not the diameter. To estimate the diameter, double the radius.

Why is the radius about 3 kilometers per solar mass?

The Schwarzschild radius for 1 solar mass is about 2.95 kilometers. This calculator uses the stated physical constants instead of rounding the factor to 3. The solar-mass conversion is approximate, so displayed digits are not a claim of measurement accuracy.

Does this work for every black hole?

This is a simplified estimate for a non-rotating, uncharged black hole. Real black holes can rotate, and rotation changes the exact shape and boundary behavior near the event horizon. The 3 km per solar mass rule remains a rough mental estimate; it is not the factor used here.