Astronomy

Escape Velocity Calculator

v = √(2GM / r)
Calculator
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Writing tips
  • Use * for multiplication: write G*M*m, not GMm.
  • Use ^ for powers: r^2 means r squared.
  • After a /, wrap the whole denominator in brackets: 1/(4*pi*eps0) puts everything in brackets below the line.
  • Scientific notation: write 6*10^-7 or 6e-7 — both mean 6×10⁻⁷.
  • Functions need brackets: sqrt(2*G*M/r), sin(x), ln(x).
  • Define the result with =: e.g. F = G*M*m/r^2 so the answer is labelled F.
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This calculator finds the escape velocity — the minimum speed an object needs to break free of a body's gravity without further propulsion. Enter the body's mass and radius.

What the symbols mean

Worked example

For Earth (M = 5.97×10²⁴ kg, r = 6.37×10⁶ m) the escape velocity is about 11,200 m/s — roughly 40,300 km/h.

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