Escape Velocity Calculator
Find the minimum speed an object must reach to escape a celestial body's gravity without further propulsion. Essential for mission planning, planetary science, and understanding why some atmospheres are retained.
About this calculator
Escape velocity is the minimum speed needed for an object to break free from a gravitational field without any additional thrust. It is derived by setting kinetic energy equal to gravitational potential energy: ½mv² = GMm/r, which simplifies to v_e = √(2GM/r). Here G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²), M is the mass of the celestial body in kilograms, and r is its radius in metres. The result is converted from m/s to km/s for practical use. Crucially, escape velocity does not depend on the mass of the escaping object — only on the body being escaped from. It also has no dependence on direction, assuming no atmosphere. Earth's escape velocity is approximately 11.2 km/s, while the Moon's is only 2.4 km/s.
How to use
Let's calculate the escape velocity from Earth. Earth's mass is 5.972 × 10²⁴ kg and its radius is 6,371 km. Plug into the formula: v_e = √(2 × 6.674 × 10⁻¹¹ × 5.972 × 10²⁴ / (6,371 × 1,000)). First compute the numerator: 2 × 6.674 × 10⁻¹¹ × 5.972 × 10²⁴ ≈ 7.972 × 10¹⁴. Divide by 6,371,000 m ≈ 1.251 × 10⁸. Take the square root: √(1.251 × 10⁸) ≈ 11,185 m/s ≈ 11.19 km/s. Enter any body's mass in kg and radius in km to get its escape velocity instantly.
Frequently asked questions
What is escape velocity and why does it matter for space missions?
Escape velocity is the minimum launch speed required for an object to leave a planet or moon's gravitational influence without further engine burn. Below this speed, gravity will eventually pull the object back. For space missions, reaching escape velocity means a spacecraft can travel to other planets or leave the solar system entirely. Engineers use it to calculate minimum fuel requirements for interplanetary probes and rockets. Earth's escape velocity of about 11.2 km/s is a key design constraint for every launch vehicle.
How does a planet's size and mass affect its escape velocity?
Escape velocity scales with the square root of a body's mass-to-radius ratio: v_e = √(2GM/r). A more massive body has higher escape velocity, but a larger radius reduces it. For example, Mars is less massive than Earth but also much smaller, giving it an escape velocity of about 5 km/s — roughly half Earth's. Gas giants like Jupiter, being vastly more massive, have escape velocities exceeding 60 km/s. This relationship also explains why small asteroids cannot retain atmospheres — their escape velocities are too low to prevent gas molecules from drifting away.
Does escape velocity change with altitude above a planet's surface?
Yes — escape velocity decreases as you move farther from the planet's centre, because gravitational potential energy diminishes with distance. The formula v_e = √(2GM/r) uses r as the distance from the planet's centre, so increasing altitude increases r and lowers v_e. This is why rockets don't need to reach 11.2 km/s at ground level — they accelerate continuously, gaining altitude while the required escape velocity drops. In practice, air resistance near the surface makes high speeds costly, so rockets ascend slowly through the atmosphere before accelerating to orbital or escape speeds.