Escape Velocity Calculator

How Escape Velocity Is Calculated

An object escapes when its kinetic energy, ½mv², at least equals the energy needed to climb out of the gravity well, GMm/r. The object’s own mass cancels, so the formula is v = √(2GM/r), the same for a pebble or a spacecraft. OpenStax University Physics Volume 1 works it for Earth: with M = 5.96 × 10²⁴ kg, R = 6.37 × 10⁶ m and G = 6.67 × 10⁻¹¹ N·m²/kg², v = 1.12 × 10⁴ m/s, about 11 km/s.

1. Take GM for the body. NASA lists it directly (Earth: 0.39860 × 10⁶ km³/s²), which is more precise than multiplying G by the mass.
2. Add the altitude to the radius to get r, the distance from the center.
3. Compute √(2 × 398,600 ÷ 6,378.137) = 11.18 km/s.

Escape Velocity Across the Solar System

The giant planets’ radii are at the 1-bar pressure level, and the Sun uses its mean radius. Small differences from NASA’s listed values come from rounding and the radius used.

Leaving the Solar System

Escape velocity depends on where you start. OpenStax’s Example 13.7 computes escape from the Sun at Earth’s distance (M = 1.99 × 10³⁰ kg, r = 1.50 × 10¹¹ m): about 42 km/s. Because Earth already orbits at about 30 km/s, a probe launched in the direction of Earth’s motion needs only about 12 km/s more relative to Earth (plus what it takes to climb out of Earth’s own gravity). Enter “Custom” with the Sun’s mass and 150,000,000 km to reproduce it.

Orbit vs Escape

A circular orbit at the same distance needs √2 times less speed: about 7.9 km/s at Earth’s surface radius. Any speed between the two gives an elliptical orbit; below orbital speed the object falls back.

Common Mistakes

• Using the altitude instead of the distance from the center. From 400 km up, r is 6,778 km, not 400.
• Mixing units. With G in SI units, mass must be in kilograms and radius in meters; the answer is in m/s.
• Thinking a rocket must reach escape velocity at launch. The formula is for an unpowered object; a rocket that keeps thrusting can leave at any speed.
• Forgetting the factor of 2. √(GM/r) is circular orbit speed, not escape speed.

What This Calculator Does Not Cover

It treats the body as a non-rotating sphere with no atmosphere, ignores the gravity of other bodies, and gives the speed relative to the body’s center. Real launch planning also accounts for drag, the planet’s rotation and the Sun’s gravity.

Frequently Asked Questions

How to Use This Calculator

1. Choose a body — Earth, the Moon, a planet, Pluto, the Sun, or Custom.
2. Add an altitude if needed — to start from orbit or a mountaintop instead of the surface.
3. For a custom body — enter its mass in kg and radius in km.
4. Read the results — escape velocity in km/s, m/s, km/h and mph, plus circular orbit speed.