Escape Velocity Calculator

Select a celestial body or enter custom mass and radius below.

Escape Velocity Formula

Escape velocity is the minimum speed an object must reach to break free from a celestial body's gravitational pull without further propulsion. It is derived by equating kinetic energy to gravitational potential energy:

Where:

• v_e — Escape velocity (m/s)
• G — Gravitational constant (6.674 × 10⁻¹¹ m³ kg⁻¹ s⁻²)
• M — Mass of the celestial body (kg)
• r — Radius from the center of the body (m)

Key Concepts

• Escape velocity is independent of the escaping object's mass.
• It assumes launch from the surface with no atmospheric drag.
• At escape velocity, the object follows a parabolic trajectory and reaches zero speed at infinity.
• Any speed above escape velocity results in a hyperbolic trajectory.

Derivation

Setting kinetic energy equal to gravitational potential energy:

Solving for v and cancelling the object mass m gives the escape velocity formula above.

Examples

• Earth — ~11.2 km/s from the surface.
• Moon — ~2.4 km/s, low enough that no atmosphere is retained.
• Jupiter — ~59.5 km/s, the highest of any planet in our Solar System.
• Sun — ~617.5 km/s from the photosphere.