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Science

Escape Velocity Calculator

Escape velocity is the minimum speed an unpowered object must have at a body's surface to leave its gravitational field entirely — arriving at infinity with zero kinetic energy left. Pick a preset (Earth, Moon, Mars, the Sun, …) for textbook values, or enter any custom mass and radius to compute the escape speed from a planet, moon, asteroid or even the surface of a compact object.

Escape velocity v

Other units

Kilometres / second (km/s)
Kilometres / hour (km/h)
Miles / hour (mph)

Formula

v = √(2 · G · M / r), G ≈ 6.6743 × 10⁻¹¹ m³·kg⁻¹·s⁻²

Uses the CODATA 2018 value G = 6.6743 × 10⁻¹¹ m³·kg⁻¹·s⁻². Assumes a non-rotating, spherically symmetric body with no atmosphere. Real rockets need an extra 1.5–2 km/s of Δv on top to overcome drag and gravity losses.

Formula

v_esc = √(2 · G · M / r), G ≈ 6.6743 × 10⁻¹¹ m³·kg⁻¹·s⁻²

Frequently asked

How is escape velocity different from orbital velocity?

Orbital velocity (v_orb = √(GM/r)) is just enough tangential speed to stay in a circular orbit at radius r — about 7.8 km/s at Earth's low orbit (~200 km altitude). Escape velocity v_esc = √(2GM/r) is always √2 ≈ 1.414× larger, ~11.19 km/s at Earth's surface. Reach v_esc and the object follows a hyperbolic trajectory away from the body forever. Speeds in between produce elliptical orbits (every satellite, the Moon, the ISS).

Why doesn't escape velocity depend on the escaping object's own mass?

From energy conservation, an object starting at radius r and reaching infinity (where gravitational PE = 0) with zero kinetic energy left needs ½mv² ≥ GMm/r. The m on both sides cancels, leaving v ≥ √(2GM/r). A pebble and a spaceship therefore need the same escape speed from the same surface — although accelerating more mass to that speed obviously costs more fuel.

Is a black hole's escape velocity really the speed of light?

Yes — setting v = c in the escape-velocity formula gives r_s = 2GM/c², the Schwarzschild radius. Below this radius light itself isn't fast enough to escape, which is exactly the definition of the event horizon. A one-solar-mass black hole has r_s ≈ 2.95 km; Sagittarius A* at the centre of the Milky Way (≈ 4.3 million solar masses) has r_s ≈ 12.7 million km, smaller than Mercury's orbit. Note that near v ≈ c the Newtonian formula is no longer the right physics — general relativity is — but it does correctly identify where the horizon sits.

Why does a real rocket need more Δv than the escape velocity?

Escape velocity assumes the object is already at the surface and instantly has the right speed, in vacuum. A real rocket leaving Earth must overcome (1) atmospheric drag — especially during the dense lower atmosphere, (2) gravity losses — gravity decelerates the rocket throughout the burn, and (3) the rocket equation itself, since fuel mass must be accelerated too. Net result: launching to escape Earth typically needs ~12.5–13.5 km/s of total Δv versus the 11.19 km/s ideal. The Saturn V used ~18 km/s total Δv to lift Apollo from the pad onto a trans-lunar trajectory.

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