What is escape velocity?

Escape velocity is the minimum speed an object needs to overcome a celestial body's gravitational pull and travel to infinity without any further propulsion. It is derived from conservation of energy: setting kinetic energy equal to gravitational potential energy gives v = √(2GM/r), where G is the gravitational constant, M is the body's mass, and r is the distance from its center (usually its surface radius).

What is the escape velocity of Earth?

Earth's escape velocity from its surface is approximately 11.19 km/s (about 40,270 km/h or 25,020 mph). This is the speed a rocket must reach to leave Earth without any further thrust.

Does escape velocity depend on the object being launched?

No. Escape velocity depends only on the mass and radius of the celestial body, not on the mass or direction of the escaping object. A tennis ball and a rocket need the same speed to escape Earth's gravity.

What is a black hole in terms of escape velocity?

A black hole forms when the escape velocity at the surface equals or exceeds the speed of light (≈ 299,792 km/s). The radius at which this occurs is called the Schwarzschild radius: r = 2GM/c². No light or matter can escape from inside this boundary.

Is escape velocity the same as orbital velocity?

No. Orbital velocity (for a circular orbit just above the surface) is v_orb = √(GM/r), which is escape velocity divided by √2 (roughly 70.7% of escape velocity). To orbit, you need less speed than to escape entirely.

What units does this calculator use?

Mass is entered in kilograms (kg), radius in meters (m), and the result is given in km/s. The gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg² is used internally.

Escape Velocity Calculator

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

Calculate the minimum speed needed to escape a celestial body's gravity using v = √(2GM/r).

Inputs

Select what to solve for, then fill in the required values.

Solve for

Preset celestial body (optional)

Body Mass (M)

Body Radius (r)

G = 6.674 × 10⁻¹¹ N·m²/kg² (universal gravitational constant)

Result

Enter values and click Calculate.

Formula Reference

Find Velocity

v = √(2GM / r)

Find Mass

M = v² · r / (2G)

Find Radius

r = 2GM / v²

Summary

Calculate the minimum speed needed to escape a celestial body's gravity using v = √(2GM/r).

How it works

Select what you want to solve for: Escape Velocity, Body Mass, or Body Radius.
Choose a preset celestial body to auto-fill common values, or enter custom mass and radius.
Click Calculate to apply the formula v = √(2GM/r).
The result is displayed in km/s alongside a step-by-step breakdown.
Use the Reset button to clear all fields and start fresh.

Use cases

Astrophysics and orbital mechanics coursework and exam problems.
Comparing escape velocities of planets, moons, and stars in our solar system.
Spacecraft and rocket mission planning for trajectory design.
Exploring how black holes form when escape velocity exceeds the speed of light.
Teaching Newton's law of gravitation and its real-world applications.
Verifying textbook values for escape speeds of known celestial bodies.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu