v_esc = √(2·G·M / r) G = 6.674 × 10⁻¹¹ N·m²/kg²

Escape Velocity: Minimum speed to break free of a body’s gravity. This free calculator solves for Escape speed, mass, radius and shows every step.

The physics

Escape velocity is the minimum speed at which an object can leave a body's gravity and never fall back, with no further propulsion. It depends only on the body's mass and radius — not on the escaping object's mass. Earth's is about 11.2 km/s.

Worked example

Earth: M = 5.97 × 10²⁴ kg, r = 6.37 × 10⁶ m. v = √(2·6.674e−11·5.97e24 / 6.37e6) ≈ 11,180 m/s (11.2 km/s).

Common uses

Rocket and mission design, planetary science, understanding why small bodies cannot retain atmospheres, black-hole intuition.

Frequently asked questions

What is the formula for Escape Velocity?

Escape Velocity uses the formula v_esc = √(2·G·M / r). Minimum speed to break free of a body’s gravity.

How do you calculate Escape Velocity?

Choose which variable to solve for, enter the values you know (in any supported unit), and the calculator substitutes them into v_esc = √(2·G·M / r) and shows every step of the working. It can solve for Escape speed, mass, radius.

Is the Escape Velocity calculator free to use?

Yes — every Physics Fundamentals calculator is completely free, with no login, no ads and no usage limits.