Escape Velocity Calculator
Calculate escape velocity, orbital velocity, and gravitational parameters for celestial bodies.
About this calculator
This calculator applies the classical two-body escape velocity formula v = sqrt(2GM/r), where G is Newton's gravitational constant, M is the body's mass, and r is the distance from its center. Mass and Radius are both entered in Earth units (Earth = 1) and converted to kilograms and meters internally using Earth's real mass (5.972 x 10^24 kg) and radius (6.371 x 10^6 m) before the formula runs. Because v scales with the square root of mass and inversely with the square root of radius, both inputs move Escape Velocity by roughly the same proportional amount for the same percentage change -- doubling Mass raises escape velocity by about 41%, and halving Radius does the same.
Orbital Velocity uses the companion circular-orbit formula v = sqrt(GM/r), which is always exactly Escape Velocity divided by the square root of 2 (about 70.7% of it) at the same radius -- this is why a spacecraft needs roughly 41% more speed to escape a body entirely than to stay in a low circular orbit around it. Orbital Distance only feeds the separate "Escape from Orbit" output, which recomputes escape velocity at that specific altitude rather than at the surface; it has no effect on the surface-based Escape Velocity or Orbital Velocity outputs. Surface Gravity (g = GM/r^2) and the Schwarzschild Radius (r_s = 2GM/c^2, the size a body's mass would need to be compressed to for light itself to be unable to escape) are computed directly from the same Mass and Radius/speed-of-light values, with no dependence on Orbital Distance either.
Inputs
Results
Escape Velocity
11.19 km/s
Orbital Velocity
7.91 km/s
How to Use This Calculator
- Enter the Mass (Earth masses) of the body — Earth is 1, Mars is 0.107, Jupiter is 317.8.
- Enter the Radius (Earth radii) of the surface or object — Earth is 1, the Moon is 0.27.
- Set the Orbital Distance (Earth radii) from the center for computing circular orbital velocity at that altitude.
- Read Escape Velocity (km/s): Earth's surface value is 11.2 km/s; this is the speed needed to leave the body entirely.
- Note the Schwarzschild Radius (m) output — if the object's physical radius were compressed to this size it would become a black hole.
How the result changes with Mass
| Mass | Escape Velocity | Orbital Velocity |
|---|---|---|
| 0.5 | 7.91 km/s | 5.59 km/s |
| 0.75 | 9.69 km/s | 6.85 km/s |
| 1.5 | 13.7 km/s | 9.69 km/s |
| 2.5 | 17.69 km/s | 12.51 km/s |
What each input means
- Mass
- Mass of celestial body
- Radius
- Radius of celestial body
- Orbital Distance
- Distance from center for orbital escape
How this is calculated
Formula
v_escape = √(2GM/r)Worked example, using the default values
- Identify Input ParametersMass = 1, Radius = 1, Orbital Distance = 1 = 3 input(s) provided
- Calculate Escape VelocityEscape Velocity11.19 = 11.19
- Calculate Orbital VelocityOrbital Velocity7.91 = 7.91
- Calculate Escape from OrbitEscape from Orbit11.19 = 11.19
- Calculate Surface GravitySurface Gravity9.82 = 9.82
Engine last updated . Checked against 4 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why do Mass and Radius both change escape velocity by similar amounts?
Escape velocity is v = sqrt(2GM/r), so it grows with the square root of Mass and shrinks with the square root of Radius -- both have the same 0.5 exponent, just with opposite sign. A given percentage increase in Mass and the same percentage decrease in Radius therefore move Escape Velocity by nearly identical amounts, which is why denser, more compact bodies of the same mass have dramatically higher escape velocities.
Does the Orbital Distance input change the main Escape Velocity result?
No. Orbital Distance only affects the separate "Escape from Orbit" output, which answers a different question: what speed is needed to escape starting from a given altitude rather than from the surface. The primary Escape Velocity and Orbital Velocity outputs are always computed at the body's own Radius and never reference Orbital Distance.
Why is orbital velocity always about 71% of escape velocity?
Orbital Velocity uses v = sqrt(GM/r) while Escape Velocity uses v = sqrt(2GM/r) -- the only difference is that factor of 2 under the square root. Dividing the two shows orbital velocity is always exactly escape velocity divided by sqrt(2), or about 70.7% of it, regardless of the body's actual mass or radius.
What does the Schwarzschild Radius output mean for an ordinary planet?
It is a purely hypothetical size: the radius the body's actual Mass would need to be compressed into before its own escape velocity reached the speed of light, at which point it would be a black hole. For Earth's real mass this works out to under 9 millimeters -- Earth's actual radius is billions of times larger, so Earth is nowhere close to being a black hole.
How is Mass converted from Earth masses into the actual formula?
The Mass input (in Earth masses) is multiplied by Earth's real mass, 5.972 x 10^24 kg, and the Radius input (in Earth radii) is multiplied by Earth's real radius, 6.371 x 10^6 meters, before either value enters v = sqrt(2GM/r). Entering Mass = 1 and Radius = 1 therefore reproduces Earth's actual surface escape velocity of about 11.2 km/s.
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