Escape Velocity Calculator
Escape velocity calculator: the speed needed to escape a planet’s or star’s gravity from its mass and radius, plus circular orbit speed.
v = √2 G Mr
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
v = √(2GM/r). It does not depend on the mass of the escaping object or the launch direction (ignoring air).
Formula
v = √2 G Mr
| Symbol | Quantity | Units |
|---|---|---|
| M | Mass of the body | kg, g, mg, µg, t, lb, oz, st, US ton, ct, Da |
| r | Distance from the center | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
| v | Escape velocity | m/s, km/h, mph, kn, ft/s, c |
Constants used: G = 6.6743 × 10⁻¹¹ N m² kg⁻²
Worked example
Given: M = 5.972 × 1024 kg · r = 6 371 km
v = √2GMr
Result: v = 11 186 m/s
Escape velocity for different values of Mass of the body
| M · Mass of the body | v · Escape velocity |
|---|---|
| 2.986 × 1024 kg | 7 909.7 m/s |
| 4.479 × 1024 kg | 9 687.3 m/s |
| 5.375 × 1024 kg | 10 612 m/s |
| 5.972 × 1024 kg | 11 186 m/s |
| 6.569 × 1024 kg | 11 732 m/s |
| 7.465 × 1024 kg | 12 506 m/s |
| 8.958 × 1024 kg | 13 700 m/s |
| 1.194 × 1025 kg | 15 819 m/s |
Other values as in the worked example.
Frequently asked questions
Escape velocity from Earth’s surface?
About 11.19 km/s (40,270 km/h).
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