Escape Velocity Calculator

What is Escape Velocity?

Escape velocity is the minimum speed an object needs to break free from a celestial body's gravitational pull without any additional propulsion. At this speed, the object's kinetic energy exactly equals the gravitational potential energy binding it to the body.

Key insight: Escape velocity depends only on the mass and radius of the celestial body—not on the mass of the escaping object. A feather and a rocket have the same escape velocity from Earth.

The Key Formulas

The √2 Relationship

A remarkable fact: escape velocity is always exactly √2 (≈1.414) times the circular orbit velocity at any given altitude:

This means to escape, you need about 41.4% more speed than to orbit. Or equivalently, you need exactly twice the kinetic energy (since KE ∝ v²).

Effect of Altitude

Escape velocity decreases with altitude. The farther you are from a body's center, the easier it is to escape:

• • At Earth's surface: v_esc ≈ 11.2 km/s
• • At 400 km (ISS orbit): v_esc ≈ 10.9 km/s
• • At Moon's distance: v_esc ≈ 1.4 km/s

This is why rockets continue accelerating as they climb—the required velocity keeps dropping.

Solar System Escape Velocities

Real-World Considerations

The theoretical escape velocity is just the starting point. Real rockets need more delta-v because of:

• Gravity losses: Fighting gravity during ascent
• Atmospheric drag: Air resistance on Earth, Venus, etc.
• Rotation bonus: Launching east from equator saves ~0.5 km/s on Earth
• Trajectory constraints: Real missions rarely launch straight up