Escape Energy Calculator
Find the minimum kinetic energy an object needs to escape a planet’s gravity — and the matching escape velocity.
How it works
E_escape = G·M·m ÷ r · equals ½·m·v_esc² with v_esc = √(2·G·M ÷ r)
To escape a gravitational well, an object must be given enough kinetic energy to climb out of it entirely — reaching zero speed only at infinite distance. That minimum energy equals the depth of the gravitational potential well, GMm/r. It is exactly ½mv² for the escape velocity √(2GM/r), so the two views are equivalent.
Worked example
Launching a 1,000 kg craft from Earth’s surface (M = 5.972×10²⁴ kg, r = 6.371×10⁶ m): E = 6.674×10⁻¹¹ × 5.972×10²⁴ × 1000 ÷ 6.371×10⁶ ≈ 6.26×10¹⁰ J ≈ 62,600 MJ, matching an escape velocity of about 11.19 km/s.
Sources: Escape velocity — Wikipedia
Frequently asked questions
Is escape energy the real fuel needed for a rocket?
No — it is the ideal minimum ignoring air drag, the energy spent lifting and accelerating fuel, and the fact that rockets don’t reach escape speed instantly. Real launches need far more energy, but this sets the theoretical floor.
Why does escape not depend on launch direction?
Energy is a scalar, so only the amount of kinetic energy matters, not its direction (ignoring air and terrain). Escape velocity is the same whether you fire straight up or at an angle.
How does escape energy relate to escape velocity?
They describe the same threshold: escape energy is ½mv_esc². The energy scales with the object’s mass, while escape velocity is independent of it.
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This calculator is for educational purposes. Double-check important results before acting on them.