Escape Velocity Black Hole Calculator

Summary

Escape velocity is the minimum speed needed to escape a gravitational field from a given distance, without further thrust. The formula is v = sqrt(2GM/r), where G is the gravitational constant, M is the mass, and r is the distance from the center. For a black hole, the Schwarzschild radius r_s = 2GM/c² is the point where escape velocity equals the speed of light — the event horizon. This calculator lets you enter any mass and distance to find the escape velocity at that point, and computes the Schwarzschild radius so you can see how close you are to the event horizon.

How it works

1. Enter the mass of the body in kilograms or solar masses.
2. The Schwarzschild radius r_s = 2GM/c² is computed immediately.
3. Enter the distance from the center (must be greater than zero).
4. The calculator applies v = sqrt(2GM/r) to find escape velocity at that radius.
5. The result is shown in m/s, km/s, and as a fraction of the speed of light.
6. A warning appears when your distance is at or inside the event horizon (r ≤ r_s).

Use cases

• Understand why nothing escapes a black hole from within the event horizon.
• Calculate the escape velocity at various distances from a stellar-mass black hole.
• Verify textbook black hole physics for astrophysics coursework.
• Explore supermassive black hole escape speeds at the galactic center.
• Illustrate how escape velocity approaches c as you approach the Schwarzschild radius.
• Support science outreach and astronomy education materials.

Frequently Asked Questions