Escape Velocity Calculator
Escape velocity is the minimum speed needed to break free of a body's gravity entirely, without further propulsion — the number that made getting to the Moon meaningfully harder than getting to low Earth orbit.
Inputs
Result
11,185.7 m/s
11.186 km/s
How the escape velocity calculator works
v_escape = √(2Gm ÷ r), where G is the gravitational constant (6.674×10⁻¹¹), m is the body's mass, and r is its radius.
Worked example: Earth (mass 5.972×10²⁴ kg, radius 6,371,000 m)
- v = √(2 × 6.674×10⁻¹¹ × 5.972×10²⁴ ÷ 6,371,000).
- ≈ √(1.253×10⁸) ≈ 11,190 m/s.
- In km/s: ≈ 11.19 km/s — the well-known figure for Earth's escape velocity.
Common mistakes to avoid
Assuming escape velocity depends on the escaping object's own mass
The escaping object's mass cancels out of the derivation entirely — a feather and a spacecraft need the identical escape velocity from a given body, though obviously very different amounts of energy to reach it.
Confusing escape velocity with orbital velocity
Escape velocity is the speed needed to leave a gravitational field entirely; orbital velocity (needed to maintain a stable circular orbit) is lower — for a given body, orbital velocity is escape velocity divided by √2.
Frequently asked questions
Why doesn't the escaping object's own mass matter?
In the energy-conservation derivation, the object's mass appears on both sides of the equation (in its kinetic energy and in its gravitational potential energy) and cancels out — only the mass of the body being escaped from matters.
How does escape velocity relate to a black hole?
A black hole's escape velocity at its event horizon equals the speed of light — since nothing can exceed that speed, nothing, including light, can escape from within that boundary.
Why is the Moon's escape velocity so much lower than Earth's?
The Moon has both much less mass and a smaller radius than Earth, and since escape velocity depends on √(mass/radius), the combined effect makes lunar escape velocity roughly one-fifth of Earth's — about 2.4 km/s.
Does escape velocity depend on the direction of launch?
The formula gives the minimum speed regardless of direction (assuming no atmosphere to fight through) — real launches account for atmospheric drag and often use Earth's rotation to reduce the effective speed needed.
Learn more
Escape Velocity: Why Mass Doesn't Matter (But Direction Sort Of Does)
A feather and a rocket need exactly the same escape velocity from Earth — here's the counterintuitive reason why.
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