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.
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Black Hole Size Formula
This calculator uses the rounded Schwarzschild radius relationship for a non-rotating, uncharged black hole. In this approximation, each solar mass gives an event horizon radius of about 3 kilometers.
- R = radius of the event horizon, in kilometers
- M = black hole mass, in solar masses
- 3 = rounded Schwarzschild radius factor, about 3 km per solar mass
If you enter the black hole mass, the calculator uses R = 3M to estimate the event horizon radius. If you enter the event horizon radius, it uses M = R/3 to estimate the black hole mass. Unit selections are converted before and after the formula is applied, so the formula itself is still based on kilometers and solar masses.
Typical Event Horizon Radius by Black Hole Mass
| Black hole mass | Approximate event horizon radius | Type of scale |
|---|---|---|
| 1 solar mass | 3 km | Minimum stellar-scale reference |
| 10 solar masses | 30 km | Stellar-mass black hole |
| 1,000 solar masses | 3,000 km | Intermediate-mass range |
| 1,000,000 solar masses | 3,000,000 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 | 1.60934 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:
Substitute 10 for M:
The estimated event horizon radius is 30 kilometers.
Example 2: Find the mass from event horizon radius
If a black hole has an event horizon radius of 150 kilometers, use:
Substitute 150 for R:
The estimated mass is 50 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 does the formula use 3 kilometers per solar mass?
The Schwarzschild radius for 1 solar mass is about 2.95 kilometers. This calculator rounds that value to 3 kilometers, which makes the relationship easier to use while staying close to the standard estimate.
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. For most basic size estimates, the 3 km per solar mass rule is a useful approximation.
