What is the escape velocity formula?

v = sqrt(2GM/r), where G = 6.674 × 10⁻¹¹ N·m²/kg² is the gravitational constant, M is the mass in kg, and r is the distance from the center in meters. The result is in m/s.

What is the Schwarzschild radius?

The Schwarzschild radius r_s = 2GM/c² is the radius at which escape velocity equals the speed of light. Any mass compressed below this radius becomes a black hole from which no signal can escape.

What happens at exactly the Schwarzschild radius?

At r = r_s, the escape velocity equals the speed of light (c ≈ 299,792 km/s). Since nothing with mass can reach c, nothing can escape — this is the event horizon of a black hole.

Can this formula be used for ordinary stars and planets?

Yes. v = sqrt(2GM/r) applies to any spherically symmetric mass. For Earth at its surface the result is about 11.2 km/s; for the Sun it is about 617 km/s.

Why does the escaping object's mass not matter?

Mass cancels in the energy-balance derivation: (1/2)mv² = GMm/r simplifies to v = sqrt(2GM/r). The escape speed depends only on the source mass and the distance.

What is the escape velocity of a typical stellar-mass black hole (10 solar masses) at 100 km from its center?

The Schwarzschild radius of 10 solar masses is about 29.5 km, so 100 km is outside the event horizon. The escape velocity there is approximately 213,000 km/s — about 71% of the speed of light.

Escape Velocity Black Hole Calculator

Name: Escape Velocity Black Hole Calculator
Availability: InStock
Author: Nham Vu

Enter a mass and a distance from it to find the escape velocity at that point — and see how it compares to the speed of light at the event horizon.

Inputs

Mass Unit

Mass (kg)

Presets

Distance from Center

Schwarzschild Radius (r_s = 2GM/c²)

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Escape Velocity at Given Distance

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Summary

Enter a mass and a distance from it to find the escape velocity at that point — and see how it compares to the speed of light at the event horizon.

How it works

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

Last updated: 2026-07-23 · Reviewed by Nham Vu