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Escape Velocity Calculator

Calculate the speed needed to escape a body’s gravity without further propulsion.

About Escape Velocity Calculator

Escape velocity is exactly √2 times the circular orbital velocity at the same radius, because escaping requires twice the specific energy of orbiting. It is independent of the escaping object’s mass. Reaching orbit is far cheaper than escaping, which is why almost all missions stage through a parking orbit first.

Formula

Escape Velocity

v_esc = √(2 G M ÷ r)

G
Gravitational constant
M
Mass of the body
r
Distance from its centre

Worked example

With the default values below, Escape Velocity Calculator returns Escape Velocity of 11,185.73. Change any input above and every figure here is recalculated in your browser.

Inputs used

Mass of the bodyminimum 1 kg
5,972,000,000,000,000,000,000,000 kg
Radius of the bodyminimum 1 m
6,371,000 m
Altitude above the surfaceminimum 0 m
0 m

Results

Escape Velocity
11,185.73 m/s
Escape Velocity
11.1857 km/s
Circular Orbital Velocity at That Radius
7,909.50 m/s
Gravitational Acceleration There
9.8195 m/s2
Energy Needed per Kilogram
62,560,239 J/kg

Step by step

  1. 1Values used
  2. 2Escape Velocity
  3. 3Escape Velocity= 11,185.73 m/s
  4. 4Escape Velocity= 11.1857 km/s
  5. 5Circular Orbital Velocity at That Radius= 7,909.50 m/s
  6. 6Gravitational Acceleration There= 9.8195 m/s2
  7. 7Energy Needed per Kilogram= 62,560,239 J/kg

Assumptions and limits

  • The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Escape Velocity calculated?

v_esc = √(2 G M ÷ r) Escape velocity is exactly √2 times the circular orbital velocity at the same radius, because escaping requires twice the specific energy of orbiting. It is independent of the escaping object’s mass.

Why does Escape Velocity matter?

Reaching orbit is far cheaper than escaping, which is why almost all missions stage through a parking orbit first.

What values do I need to enter?

This calculator takes 3 inputs: Mass of the body, Radius of the body, Altitude above the surface. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.

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