Escape Velocity Calculator - Speed to Leave a Body

An escape velocity calculator finds the minimum speed an unpowered object must reach to coast away from a celestial body without ever falling back, assuming a spherically symmetric gravitational field and no atmospheric drag. This one turns the central body's mass and the launch radius into that critical speed in metres per second, kilometres per second, and miles per hour, so you can compare Earth against the Moon, Mars, Jupiter, the Sun, or a custom asteroid in a single pass.

• • Compare planetary launch speeds: see how Earth's 11.186 km/s stacks up against the Moon's 2.38 km/s, Mars's 5.03 km/s, and Jupiter's 60.20 km/s before you plan a mission profile.
• • Estimate rocket delta-v budget: use the result as the theoretical delta-v floor for a launch from rest to infinity, before gravity and drag losses are added.
• • Evaluate asteroids and small bodies: plug a custom mass and radius for a near-Earth asteroid and find out that its escape speed can fall below walking pace.
• • Reason about altitude trade-offs: raise the launch altitude and watch the speed fall with the inverse square root of distance, just like in textbook derivations.

This number is sometimes called the second cosmic velocity because it is the second of the standard 'cosmic velocities' taught in physics courses, after the circular orbit speed and before the solar system escape speed from Earth's neighbourhood. Real mission planners use the escape velocity as a starting estimate before adding gravity and drag losses, then refine the number with a full trajectory simulation.

The result here and the orbital period calculator share the same gravitational constant and central-body mass, so you can flip between 'how fast to leave' and 'how long one orbit takes' without retyping the inputs.

The calculator reads a body preset (or your custom mass and radius), adds the launch altitude to that radius, and applies v = sqrt(2 G M / r). It then reports the result in m/s, km/s, and mph, the equivalent circular orbit speed, and the specific kinetic energy per kilogram.

• G: Newtonian gravitational constant, 6.67430e-11 m^3 kg^-1 s^-2 in CODATA 2018.
• M: Mass of the central body in kilograms, taken from the body preset or your custom value.
• r: Effective launch distance from the body center in meters, equal to body radius plus altitude.
• altitude: Optional launch height above the surface in meters, defaults to 0 for a surface launch.

Because the formula depends on mass over radius, a heavier body at the same radius needs a higher speed, and a larger body with the same mass needs a lower one. Doubling the radius drops the result by a factor of sqrt(2), which is why a launch from a 400 km low-Earth orbit only needs about 10.85 km/s instead of 11.19 km/s from the surface.

The equivalent circular orbit speed v_circ = sqrt(GM/r) is reported as a sanity check: the escape speed is always exactly sqrt(2) larger than the circular orbit speed at the same radius, no matter which body or altitude you pick.

According to NASA Planetary Fact Sheet, Earth escape speed is 11.186 km/s, Moon 2.38 km/s, Mars 5.027 km/s, Jupiter 60.20 km/s, and Sun 617.5 km/s from the surface

Once you know the result, the ideal rocket equation calculator converts it into a delta-v budget by adding exhaust velocity, propellant mass fraction, and gravity losses for a real launch.

Four ideas combine to set the escape speed. None of them dominates on its own; it is the ratio of mass to radius that drives the number.

These four ideas also explain why a small asteroid can have a speed lower than walking pace: a small radius and a tiny mass both push the number toward zero, so an astronaut could in principle jump off a 200 m asteroid.

The escape speed comes from the same inverse-square law the Newton's laws force calculator applies to surface gravity, so the two calculators share the G M / r^2 starting point.

Run the calculator in five steps, then read the m/s, km/s, and mph outputs together with the equivalent circular orbit speed.

1. 1 Pick a central body: Choose Earth, Moon, Mars, Jupiter, Sun, or Custom from the dropdown. The mass and radius fields will auto-fill with NASA values.
2. 2 Override mass or radius if needed: Edit the mass in kilograms or the radius in meters to model an asteroid, an exoplanet, or a hypothetical body.
3. 3 Set the launch altitude: Type 0 for a surface launch or a positive number for a higher altitude above the surface, for example 400,000 m for low Earth orbit.
4. 4 Read the speed row: Use the m/s value for textbook checks, the km/s value for planetary comparison, and the mph value for cross-checking US sources.
5. 5 Check the secondary rows: Use the equivalent circular orbit speed to size a low orbit and the specific kinetic energy to estimate the rocket's kinetic load at burnout.

Pick Earth at zero altitude: the calculator returns 11,186.17 m/s, which matches NASA's published 11.186 km/s to four significant figures. Change the body to the Moon and the same screen shows 2,375.06 m/s, again matching NASA's 2.38 km/s.

If the body you are escaping is compact enough that Newton's formula becomes inaccurate, the gravitational time dilation calculator shows when the relativistic correction matters and how to apply it.

A single numeric answer is more useful than a memorized table. These are the practical decisions the calculator supports.

• • Compare planetary numbers instantly: Switch between Earth, Moon, Mars, Jupiter, and Sun to see how launch difficulty scales with mass and radius.
• • Set a delta-v floor: Use the result as the lower bound on rocket delta-v from rest to infinity, before gravity and drag losses.
• • Reason about small bodies: Plug in an asteroid mass and radius and find out that the required speed can fall below 1 m/s for the smallest objects.
• • Sanity-check orbital speeds: Use the equivalent circular orbit speed as a cross-check against your mission's low-orbit target velocity.
• • Teach energy conservation: Show students why the projectile's own mass cancels out of the formula while the central body's mass does not.
• • Plan altitude trade-offs: Raise the launch altitude and watch the result fall with the inverse square root of distance in real time.

The escape speed is a textbook idealization. Atmospheric drag, the gravitational pull of other bodies, and the rotation of the launch site can each change the actual energy budget by hundreds of m/s, so treat the calculator's number as a theoretical floor, not a flight-ready prediction.

Once you have the speed, the work, energy, and power calculator turns the kinetic energy per kilogram into the actual work your propulsion system has to deliver during the burn.

The calculator prints the Newtonian ideal value. Real-world factors below can change the actual number a launch vehicle has to overcome.

• • The Newtonian formula assumes a spherically symmetric gravitational field and no air. Inside Earth's atmosphere, the actual delta-v budget is 1.5 to 2.0 km/s larger than the escape velocity predicted here.
• • For very compact bodies such as neutron stars and black holes, the Newtonian escape velocity exceeds c, which signals the breakdown of Newtonian gravity rather than a real physical speed.

According to Britannica - Escape velocity, escape velocity is the second cosmic velocity and assumes a spherically symmetric gravitational field with no atmospheric drag

When the escape speed reaches the speed of light, Newtonian gravity stops working, and the black hole calculator describes the Schwarzschild radius where that happens for a chosen mass.