Escape Velocity Calculator
Find the minimum speed an object needs to break free of a body’s gravity and never fall back. Choose a planet, moon or star, or enter a custom mass and radius, and this calculator returns the escape velocity, the orbital (first cosmic) velocity and the surface gravity. Switch units freely, or flip to reverse mode to find the mass a body would need to reach a target escape speed.
Formula
Worked example
For Earth, M = 5.972×10²⁴ kg and r = 6.371×10⁶ m. With G = 6.674×10⁻¹¹: v = √(2 × 6.674×10⁻¹¹ × 5.972×10²⁴ ÷ 6.371×10⁶) = √(1.251×10⁸) ≈ 11,186 m/s, or about 11.19 km/s. The orbital velocity is 11.19 ÷ √2 ≈ 7.91 km/s, and surface gravity is GM/r² ≈ 9.82 m/s².
What escape velocity actually means
Escape velocity is the minimum speed a projectile must have at a body’s surface to break free of its gravity and never fall back, assuming no further propulsion and no air resistance. It comes from setting the object’s kinetic energy equal to the gravitational potential energy needed to climb infinitely far from the body. Crucially, the projectile’s own mass cancels out, so a pebble and a spacecraft share the same escape velocity from the same point. The figure is a speed, not a direction: launched at that speed in any upward direction, an object on an airless world will coast away and slow asymptotically toward zero as it recedes.
How mass and radius drive the result
The formula v = √(2GM/r) shows escape velocity rising with the square root of mass and falling with the square root of radius. A more massive body pulls harder, so you need more speed; a larger radius means you start farther from the centre of mass, where gravity is weaker, so you need less. This is why Jupiter, despite being enormous, has an escape velocity around 60 km/s while the Sun’s reaches about 618 km/s, the Sun’s vastly greater mass dominates. Compact, dense objects are the most demanding: shrink a body without changing its mass and its escape velocity climbs, the principle that taken to the extreme defines a black hole, where the escape velocity reaches the speed of light.
Escape velocity, orbital velocity and surface gravity
This calculator reports three linked quantities. Escape velocity sends an object away forever, but most missions only need to reach orbit, which requires less speed. At a given radius the circular orbital velocity (the first cosmic velocity) is exactly 1/√2, about 70.7%, of the escape velocity, because a stable orbit balances gravity rather than overcoming it entirely. Surface gravity, g = GM/r², is the acceleration you feel standing on the body and the force a rocket fights at liftoff. Real rockets never launch straight up at full escape speed: they build velocity gradually while climbing through the atmosphere, so the energy budget differs from this idealised figure. Even so, escape velocity remains the benchmark that tells you how tightly a body grips anything trying to leave it.
Switching units and reverse solving
Velocities can be shown in km/s, m/s, mph or miles per second, and custom masses and radii accept kilograms, grams, tonnes, Earth masses or solar masses, plus metres, kilometres, miles or Earth radii. The reverse mode rearranges the same formula to M = v²r / (2G), so you can ask the opposite question: how massive must a body of a given radius be to produce a chosen escape velocity? That is useful for designing hypothetical worlds, sanity checking exoplanet figures, or understanding why a small dense body and a large diffuse one can share the same escape speed. The math is identical in both directions; only the unknown changes.
Escape velocity of bodies in the Solar System
| Body | Mass (kg) | Radius (km) | Escape velocity (km/s) | Gravity |
|---|---|---|---|---|
| Ceres | 9.39×10²⁰ | 473 | 0.51 | Low |
| Pluto | 1.30×10²² | 1,188 | 1.21 | Low |
| Moon | 7.34×10²² | 1,737 | 2.38 | Low |
| Mercury | 3.30×10²³ | 2,440 | 4.25 | Low |
| Mars | 6.42×10²³ | 3,390 | 5.03 | Low |
| Venus | 4.87×10²⁴ | 6,052 | 10.36 | Moderate |
| Earth | 5.97×10²⁴ | 6,371 | 11.19 | Moderate |
| Uranus | 8.68×10²⁵ | 25,362 | 21.3 | High |
| Neptune | 1.02×10²⁶ | 24,622 | 23.5 | High |
| Saturn | 5.68×10²⁶ | 58,232 | 35.5 | High |
| Jupiter | 1.90×10²⁷ | 69,911 | 60.2 | High |
| Sun | 1.99×10³⁰ | 696,340 | 617.5 | High |
Computed at each body’s mean surface radius using v = √(2GM/r).
Frequently asked questions
What is the escape velocity of Earth?
Earth’s escape velocity at the surface is about 11.19 km/s, or roughly 11,186 m/s (about 25,000 mph). That is the minimum speed needed to leave Earth’s gravity entirely, ignoring air resistance and any continued thrust from a rocket engine.
Does escape velocity depend on the mass of the object escaping?
No. The escaping object’s mass cancels out of the equation v = √(2GM/r), so a marble and a spaceship have the same escape velocity from the same point. Only the central body’s mass M and the distance r from its centre matter.
How is escape velocity different from orbital velocity?
Orbital velocity (the first cosmic velocity) keeps an object circling a body, while escape velocity lets it leave for good. At the same radius, orbital velocity is exactly 1/√2 (about 70.7%) of escape velocity, so reaching orbit takes noticeably less speed than escaping completely. This calculator shows both side by side.
Can I find the mass needed for a given escape velocity?
Yes. Switch to reverse mode and enter a target escape velocity and a radius. The calculator rearranges the formula to M = v²r / (2G) and returns the required mass in kilograms and in Earth masses, which is handy for designing hypothetical worlds or checking exoplanet numbers.
What units can I use?
Velocities display in km/s, m/s, mph or miles per second. Custom masses accept kilograms, grams, tonnes, Earth masses or solar masses, and radii accept metres, kilometres, miles or Earth radii. The calculator converts everything to SI internally so the physics stays exact.