Escape Velocity Calculator
Enter a body's mass and radius to get the escape velocity in metres per second — plus kilometres per second — and see how gravity sets the speed needed to break free.
Two units at once
Enter the mass and radius and the calculator returns the escape velocity √(2GM / r) in metres per second and the same value in kilometres per second together.
Use SI units
Mass in kilograms and radius in metres give the speed in metres per second — use scientific notation (5.972e24) for very large values.
What is escape velocity?
The speed needed to break free
Escape velocity is the minimum speed an object needs to break free of a celestial body's gravity and never fall back, with no further propulsion. It depends only on the body's mass and the distance from its centre — not on the escaping object's own mass. The escape velocity calculator turns two measurements, the mass in kilograms and the radius in metres, into the speed in metres per second, alongside the same figure in kilometres per second. It is the number behind rocket launches, the reason spacecraft need staged boosters, and why a small moon is far easier to leave than a giant planet.
Enter a mass in kilograms and a radius in metres to get the escape velocity in metres per second and kilometres per second instantly.
Escape velocity is the square root of twice the gravitational constant times the mass, divided by the radius, and the km/s figure is simply that speed divided by 1000.
v = √(2 × G × M / r)Here G is the gravitational constant, 6.674 30 × 10⁻¹¹ N·m²/kg² (NIST CODATA). The mass M sits inside the square root, so quadrupling the mass only doubles the escape velocity; the radius r is in the denominator, so launching from farther out actually lowers the speed needed. Use kilograms and metres and the speed comes back in metres per second, which we also report in kilometres per second.
Suppose we want Earth's surface escape velocity, using a mass of 5.972e24 kg and a radius of 6.371e6 m.
Multiply 2 × G × M
2 × 6.6743e-11 × 5.972e24 ≈ 7.973e14 — twice the gravitational pull factor.
Divide by the radius
7.973e14 / 6.371e6 ≈ 1.2515e8 — the squared escape speed.
Take the square root
√(1.2515e8) ≈ 11,186 m/s — the escape velocity. Dividing by 1000 gives about 11.19 km/s.
The escape velocity tells you how fast an object must be moving, in any direction away from the body's surface, to escape its gravity forever without a continuous push. Earth's 11,186 m/s (about 40,270 km/h) is why orbital rockets are so large — they must reach orbital speed and then more to leave entirely. The Moon, with far less mass, needs only about 2,375 m/s, which is why the Apollo ascent module could lift off on a small engine. Jupiter, by contrast, demands roughly 60,200 m/s. The crucial insight is that mass and radius pull in opposite directions: more mass raises the escape velocity, but a larger radius lowers it, because gravity weakens with distance from the centre. That is why escape velocity from a planet's surface differs from escape velocity at the top of its atmosphere, and why a dense, compact body can demand a far higher speed than a diffuse one of the same mass.
The formula is exact for an idealised body, but a couple of practical points are worth keeping in mind.
Idealised body and consistent units
This calculator assumes a spherically symmetric, non-rotating body and ignores atmospheric drag, the pull of nearby bodies, and relativistic effects, which only matter near the speed of light. It also gives the speed for an unpowered projectile, not a rocket under continuous thrust. Keep your units consistent — kilograms for mass and metres for radius — or the metres per second will be wrong.