The escape velocity calculator above turns two properties of a body — its mass and its radius — into the speed something must reach to leave it permanently without further propulsion. It also returns the three numbers that give that speed context: the surface gravity you would feel standing there, the speed needed to circle the body instead of leaving it, and the specific energy the escape represents. Presets cover the eight planets, the Moon and the Sun using published mass and radius figures, and the custom option handles asteroids, moons and hypothetical bodies.
Arb Digital builds free calculators that keep their constants honest. The gravitational constant here is the CODATA value rather than a rounded textbook figure, and the planetary data comes from a NASA source rather than from memory. This page also explains what escape velocity really means, why it is independent of the escaping object's mass, and where the concept quietly stops applying — which is more often than most explanations admit.
What This Escape Velocity Calculator Does
It solves the escape-velocity equation for any body you describe. The hero shows escape velocity in your chosen speed unit, and the grid gives four supporting figures. Surface gravity is the acceleration due to gravity at the radius you entered, computed from the same mass and radius rather than looked up. Circular orbital speed is the speed needed to stay in a circular orbit at that radius, which is always escape velocity divided by the square root of two. Energy per kilogram is the specific kinetic energy of an object travelling at escape velocity, in megajoules. The last item compares the result with Earth's, which is the most useful single sanity check available.
The altitude field matters more than it first appears. Escape velocity depends on distance from the centre of mass, so starting from orbit rather than from the ground reduces the requirement. At 400 km altitude, roughly the height of the International Space Station, Earth's escape velocity drops from about 11.19 km/s to around 10.85 km/s. That is a real saving, and it is part of why staged missions depart from parking orbits rather than directly from the pad.
Selecting a preset writes its mass and radius into the input fields. Editing either field switches the preset selector to custom, so the tool never shows a planet name next to numbers that no longer describe that planet.
How to Use It
- Pick a body or enter your own. Presets fill the mass and radius fields. Type over either one and the tool treats it as a custom body from then on.
- Enter mass in units of 1024 kilograms. This keeps planetary figures readable — Earth is 5.97217 rather than a string of zeros. For a small asteroid, a value like 0.0000001 is perfectly acceptable.
- Enter the mean radius in kilometres. Use mean radius rather than equatorial radius for a rotating body, since the equator bulges and gives a slightly lower figure.
- Add an altitude if you are not starting from the surface. The tool adds it to the radius before computing, which is what lowers the requirement.
- Compare against Earth. The final grid item expresses your result as a multiple of Earth's escape velocity, which makes an unfamiliar number immediately meaningful.
The Formula: How Escape Velocity Is Calculated
Escape velocity is vesc = √(2GM ÷ R), where G is the gravitational constant, M the body's mass and R the distance from its centre. OpenStax University Physics Volume 1, section 13.3 on gravitational potential energy and total energy, derives it by setting total energy to zero: an object just barely escapes when its kinetic energy exactly cancels its gravitational potential energy, arriving at infinity with no speed left.
The constant comes from measurement. NIST's CODATA value for the Newtonian constant of gravitation is 6.674 30 × 10−11 m3 kg−1 s−2, and that is the figure used here. It is worth noting that G is the least precisely known of the major physical constants, with a relative uncertainty around two parts in one hundred thousand — orders of magnitude worse than the speed of light or the elementary charge.
Work the default. Using Earth's mass of 5.97217 × 1024 kg and mean radius of 6,371.0084 km from NASA JPL's planetary physical parameters table, the calculation gives √(2 × 6.6743 × 10−11 × 5.97217 × 1024 ÷ 6.3710084 × 106) = 11,186 m/s, or 11.186 km/s. Surface gravity from the same figures is 9.820 m/s2, and circular orbital speed at that radius is 7.910 km/s.
Why the Escaping Object's Mass Does Not Appear
The mass of whatever is escaping cancels out of the derivation, and this genuinely surprises people. Set kinetic energy equal to the magnitude of gravitational potential energy: one half mv2 equals GMm divided by R. The small m appears on both sides and divides away, leaving a speed that depends only on the body being escaped from.
A grain of dust and a fully fuelled rocket therefore need the same 11.186 km/s to leave Earth ballistically. What differs is the energy required to get them there, which is proportional to mass — and that is why the grid reports energy per kilogram rather than total energy. Multiply that specific energy by your payload mass and you have the minimum energy for the journey, ignoring every real-world loss.
The word "velocity" is also slightly misleading, because direction does not matter. Any direction that avoids hitting the surface works equally well, since gravitational potential energy depends only on distance. The quantity is really an escape speed, and some textbooks now call it that.
Where the Concept Stops Applying
Escape velocity assumes a single instantaneous impulse followed by unpowered coasting through a vacuum. Real launches satisfy neither condition, which is why no rocket ever actually travels at 11.186 km/s at ground level. A vehicle under continuous thrust can leave a planet at any speed at all, given enough propellant — a lift climbing a sufficiently tall tower would escape at walking pace. Escape velocity is the ballistic answer, not the propulsion answer.
Atmosphere breaks the assumption in the other direction. An object launched from Earth's surface at 11.186 km/s would be destroyed by aerodynamic heating long before it cleared the atmosphere, so the figure is a lower bound on the ballistic case rather than a practical launch specification. It is also why rockets fly relatively slowly through the dense lower atmosphere and accelerate hard only once they are above most of it. Our drag force calculator shows how steeply that penalty scales with speed.
Finally, escape velocity assumes the body is alone. Leaving Earth's gravity does not free you from the Sun's, and escaping the solar system from Earth's orbit needs roughly 42 km/s relative to the Sun, of which Earth's orbital motion already supplies about 30. Multi-body problems need the tools of orbital mechanics rather than a single square root, and the Kepler's third law calculator is the next step for orbital periods.
Escape Velocity and Whether a Body Keeps an Atmosphere
There is a neat connection between this number and planetary science. Gas molecules in an atmosphere have a distribution of speeds set by temperature, and molecules in the fast tail of that distribution can exceed escape velocity and be lost to space. Lighter molecules move faster at the same temperature, so hydrogen and helium escape most readily.
The rough rule used by planetary scientists is that a body retains a gas over geological time if its escape velocity is around six times the typical molecular speed of that gas. This is why the Moon, at 2.376 km/s, holds essentially nothing; why Mars at 5.027 km/s has lost most of a thicker early atmosphere; and why Jupiter at 60.2 km/s retains even hydrogen. Run the presets in this tool and the pattern of which worlds have atmospheres lines up almost perfectly with the escape-velocity column.
Why Surface Gravity and Escape Velocity Disagree
The two numbers in the results describe the same gravity field but weight mass and radius differently, and comparing them across bodies is instructive. Surface gravity scales as mass divided by radius squared; escape velocity scales as the square root of mass divided by radius. A large, low-density body can therefore have gentle surface gravity and a high escape velocity, while a small dense body does the reverse.
Saturn is the clearest example in the preset list. Its surface gravity at the mean radius works out close to Earth's, yet its escape velocity is more than three times higher, because it is vastly more massive and correspondingly larger. Standing on a hypothetical surface there you would feel roughly familiar weight while being far more deeply trapped. Uranus makes the same point more mildly, with surface gravity slightly below Earth's and escape velocity nearly double.
Note also that the surface gravity this tool reports for Earth is 9.820 m/s2, slightly above the standard 9.80665 m/s2 defined for weights and measures. That is not an error. The standard value accounts for the centrifugal effect of Earth's rotation and its equatorial bulge, neither of which a spherical point-mass model includes.
How This Differs From the Site's Converters
The boundary in one sentence: a converter rescales a quantity between units, while this calculator derives a speed from a formula. The speed converter will turn 11.186 km/s into miles per hour or Mach numbers, but it cannot tell you why that particular speed matters for Earth. This page produces the number; the converter reformats it, and the unit dropdown here covers the common cases so you usually will not need to.
The same applies across the physics set. The energy converter rescales the specific-energy figure into calories or kilowatt-hours. Calculators such as the gravitational force calculator, the kinetic energy calculator and the free fall calculator derive new quantities from formulas, exactly as this one does, and they cover the same gravitational ground from different angles.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Including the escaping object's mass — it cancels out of the derivation entirely, so a pebble and a spacecraft need identical speeds.
- Using diameter instead of radius — the equation wants distance from the centre, and using diameter understates escape velocity by a factor of the square root of two.
- Treating it as a launch requirement — a vehicle under sustained thrust can leave at any speed. Escape velocity applies to unpowered ballistic trajectories only.
- Forgetting the Sun — leaving Earth's gravitational well does not leave the solar system, which needs a much larger figure measured relative to the Sun.
- Mixing kilometres and metres — the radius field expects kilometres and the constant is in metres, so a raw metre value entered there inflates the result enormously.
Related Free Tools From Arb Digital
Reformat results with the speed converter or the energy converter, and manage very large figures with the scientific notation converter. For related gravitational problems, the gravitational force calculator gives the force between two masses, the Kepler's third law calculator gives orbital periods, and the free fall calculator handles motion near a surface. The kinetic energy calculator converts the escape speed into an energy for a real payload mass. The full free online tools hub lists everything.
Frequently Asked Questions
No. The escaping mass appears on both sides of the energy equation and cancels, leaving a speed determined only by the mass and radius of the body being escaped. A dust grain and a spacecraft need exactly the same speed, though not the same energy.
About 11.186 kilometres per second at the surface, calculated from a mass of 5.97217 times ten to the twenty-fourth kilograms and a mean radius of 6,371.0084 kilometres. At 400 kilometres altitude it falls to roughly 10.85 kilometres per second.
Because staying in orbit requires only enough speed to keep falling around the body, while escaping requires enough energy to reach infinite distance. Circular orbital speed at a given radius is always escape velocity divided by the square root of two, about 71 per cent of it.
No. Escape velocity describes an unpowered ballistic trajectory. A rocket under sustained thrust can leave at any speed given enough propellant, and flying at 11 kilometres per second through the lower atmosphere would destroy the vehicle through aerodynamic heating.
No, which is why some textbooks call it escape speed instead. Gravitational potential energy depends only on distance from the centre, so any direction that does not intersect the surface requires the same speed.
The CODATA value of 6.67430 times ten to the minus eleven cubic metres per kilogram per second squared, published by NIST. G is the least precisely measured of the major physical constants, which limits how accurately any escape velocity can be stated.
Because gas molecules have a spread of thermal speeds, and those in the fast tail can exceed escape velocity and be lost. Lighter gases move faster, so low-escape-velocity bodies such as the Moon lose everything while high-escape-velocity bodies such as Jupiter retain even hydrogen.
This tool is provided for educational and study use. It models a single spherical body in a vacuum and ignores rotation, oblateness, atmospheric drag and the gravity of every other body, so treat its output as an idealised physics result rather than a mission parameter.
