Escape Velocity Calculator
Escape velocity is the minimum speed an object must reach to escape a gravitational field without further propulsion. This calculator computes escape velocity from the mass and radius of any celestial body.
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Formula
v_e = √(2GM/r)
Escape velocity v_e = √(2GM/r), where G = 6.674×10⁻¹¹ N·m²/kg² is the gravitational constant, M is the mass of the celestial body, and r is the distance from the center (usually the radius for surface escape). This is derived by setting kinetic energy equal to gravitational potential energy: ½mv² = GMm/r.
How to use the Escape Velocity Calculator
- 1
Enter your mass of celestial body
Value should be in kg.
- 2
Enter your radius of celestial body
Value should be in m.
- 3
Read your results instantly
Results update in real time as you type.
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What escape velocity really means
Escape velocity is the speed needed to escape a gravitational field with no further thrust — like a ball thrown upward. If thrown at or above escape velocity, it keeps moving away forever (slowing, but never stopping and falling back). Below escape velocity, it eventually turns around.
Crucially, escape velocity doesn't mean constant speed — it means the initial speed in a ballistic trajectory. Rockets continuously thrust and don't need to reach escape velocity at launch. The Space Shuttle reached orbit at about 7.8 km/s (well below Earth's 11.2 km/s escape velocity) because it was going into orbit, not escaping. Escape velocity sets the minimum for an unthrusted trajectory.
Escape velocities across the solar system
Escape velocities vary enormously by body mass and radius: - Moon: 2.38 km/s — why Apollo's ascent stage used a small engine - Mars: 5.03 km/s — much easier than Earth for launching return missions - Earth: 11.19 km/s - Jupiter: 59.5 km/s — enormous gravity well makes missions very challenging - Sun: 617.5 km/s — to escape the solar system from Earth's orbit requires ~42 km/s - Neutron star: ~200,000 km/s (0.67c) — over half the speed of light - Black hole (at event horizon): equals speed of light (c) — nothing escapes
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Schwarzschild radius and black holes
The Schwarzschild radius is where escape velocity equals the speed of light: r_s = 2GM/c². For Earth's mass, r_s ≈ 8.9 mm — if you compressed all of Earth into a sphere smaller than a marble, it would become a black hole. For the Sun, r_s ≈ 3 km. For a stellar-mass black hole (10 solar masses), r_s ≈ 30 km.
At the event horizon (Schwarzschild radius), the escape velocity equals c. Beyond the horizon, even light can't escape — which is why black holes are black. This demonstrates that escape velocity is fundamental to understanding extreme gravity.
Tips & Insights
Earth defaults are pre-loaded
The default values are Earth's mass (5.972×10²⁴ kg) and radius (6.371×10⁶ m), giving 11.19 km/s.
Moon escape velocity is low
Moon mass = 7.342×10²² kg, radius = 1.737×10⁶ m. Escape velocity ≈ 2.38 km/s — about 21% of Earth's. This is why Apollo could use small, lightweight rocket stages to lift off the Moon.
Escape from orbit is less than from surface
From the ISS at 400 km altitude, you're already 400 km higher, so r is larger and escape velocity is lower: ≈ 10.9 km/s vs. 11.2 km/s from the surface.
Worked Examples
Earth's escape velocity
v_e = √(2 × 6.674×10⁻¹¹ × 5.972×10²⁴ / 6,371,000) ≈ 11,186 m/s = 11.19 km/s = 40,275 km/h.
Moon's escape velocity
v_e ≈ 2,376 m/s = 2.38 km/s. Only 21% of Earth's — making lunar liftoff relatively easy.
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Frequently Asked Questions
What is escape velocity?
The minimum speed needed to escape a gravitational field without further propulsion. For Earth: 11.19 km/s (40,270 km/h).
Do rockets need to reach escape velocity?
Not necessarily. Rockets continuously thrust and can escape at much lower speeds. Escape velocity applies to unthrusted ballistic projectiles.
Why is the Moon's escape velocity lower?
Lower mass and smaller size than Earth. Escape velocity scales with √(M/r) — the Moon's ratio gives only 2.38 km/s vs. Earth's 11.19 km/s.
What is the escape velocity of a black hole?
At the event horizon (Schwarzschild radius), escape velocity equals the speed of light (c ≈ 300,000 km/s). Inside the horizon, nothing escapes.
Is escape velocity the same as orbital velocity?
No. Orbital velocity (for circular orbit) = √(GM/r). Escape velocity = √(2GM/r) = orbital velocity × √2 ≈ 1.414 × orbital velocity.
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