acalculator

What is the escape velocity?

Pick the Earth, the Moon, the Sun or a planet, or type a mass and radius, and the height you start from. The escape velocity calculator gives the speed needed to leave for good, with the circular orbit speed and the gravity at that distance.

Your numbers

Units
Answer
v = 11.1861 km/s (25,022.7 mph)

The escape velocity is 11.1861 km/s (25,022.7 mph).

Escape velocity (m/s)
11,186.1
Escape velocity (km/s)
11.1861
Escape velocity (km/h)
40,270.1
Escape velocity (mph)
25,022.7
Circular orbit speed (m/s)
7,909.79
Gravity there (m/s²)
9.82022
Distance from the centre (km)
6,371.01

Answer: v = 11.1861 km/s (25,022.7 mph). The escape velocity is 11.1861 km/s (25,022.7 mph).

How to calculate

Escape velocity calculator: v = √(2GM ÷ r) from the Earth, Moon, Sun, a planet or any mass and radius, at the surface or a height above it, with the orbital speed and gravity there.

Example with the default inputs (Body Earth, Height above the surface (h) 0 mi): The escape velocity is 11.1861 km/s (25,022.7 mph).

Method: v_esc = √(2GM ÷ r), r = R + h; circular orbit speed √(GM ÷ r); gravity GM ÷ r²; G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻² for a typed mass.

  • The body is a sphere with no air: no drag, and no help from its spin or its motion around the Sun.
  • Newton’s gravity: an escape velocity at or above the speed of light (a black hole) has no answer.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Body Earth, Height above the surface (h) 0 mi gives Escape velocity (m/s) 11,186.128229, Escape velocity (mph) 25,022.656203, Gravity there (m/s²) 9.820224, Answer v = 11.1861 km/s (25,022.7 mph).Source: NASA JPL Solar System Dynamics: Astrodynamic Parameters (GM of the Sun, Earth and Moon, DE440), https://ssd.jpl.nasa.gov/astro_par.html; Planetary Physical Parameters (mean radii; escape velocity of the Earth 11.19 km/s, Jupiter 60.20 km/s), https://ssd.jpl.nasa.gov/planets/phys_par.html (retrieved 2026-10-19) (11.19 km/s); OpenStax, University Physics Volume 1, §13.3 Gravitational Potential Energy and Total Energy (Equation 13.6, v_esc = √(2GM ÷ R); Example 13.7: 1.12 × 10⁴ m/s from Earth with M = 5.96 × 10²⁴ kg and R = 6.37 × 10⁶ m, 4.21 × 10⁴ m/s from the Sun at 1.50 × 10¹¹ m with M = 1.99 × 10³⁰ kg), https://openstax.org/books/university-physics-volume-1/pages/13-3-gravitational-potential-energy-and-total-energy (retrieved 2026-10-19)
  2. Body Other: type the mass and radius, Mass (M) 5,960,000,000,000,000,000,000,000 kg, Radius (R) 6,370 km, Height above the surface (h) 0 mi gives Escape velocity (m/s) 11,175.61092.Source: OpenStax, University Physics Volume 1, §13.3 Gravitational Potential Energy and Total Energy (Equation 13.6, v_esc = √(2GM ÷ R); Example 13.7: 1.12 × 10⁴ m/s from Earth with M = 5.96 × 10²⁴ kg and R = 6.37 × 10⁶ m, 4.21 × 10⁴ m/s from the Sun at 1.50 × 10¹¹ m with M = 1.99 × 10³⁰ kg), https://openstax.org/books/university-physics-volume-1/pages/13-3-gravitational-potential-energy-and-total-energy (retrieved 2026-10-19)
  3. Body Other: type the mass and radius, Mass (M) 1,990,000,000,000,000,000,000,000,000,000 kg, Radius (R) 150,000,000 km, Height above the surface (h) 0 mi gives Escape velocity (m/s) 42,082.232197.Source: OpenStax, University Physics Volume 1, §13.3 Gravitational Potential Energy and Total Energy (Equation 13.6, v_esc = √(2GM ÷ R); Example 13.7: 1.12 × 10⁴ m/s from Earth with M = 5.96 × 10²⁴ kg and R = 6.37 × 10⁶ m, 4.21 × 10⁴ m/s from the Sun at 1.50 × 10¹¹ m with M = 1.99 × 10³⁰ kg), https://openstax.org/books/university-physics-volume-1/pages/13-3-gravitational-potential-energy-and-total-energy (retrieved 2026-10-19)
  4. Body Moon, Height above the surface (h) 0 mi gives Escape velocity (km/s) 2.375676.Source: NASA JPL Solar System Dynamics: Astrodynamic Parameters (GM of the Sun, Earth and Moon, DE440), https://ssd.jpl.nasa.gov/astro_par.html; Planetary Physical Parameters (mean radii; escape velocity of the Earth 11.19 km/s, Jupiter 60.20 km/s), https://ssd.jpl.nasa.gov/planets/phys_par.html (retrieved 2026-10-19)
  5. Body Earth, Height above the surface (h) 248.5 mi gives Escape velocity (km/s) 10.850686, Circular orbit speed (m/s) 7,672.593829.Source: OpenStax, University Physics Volume 1, §13.3 Gravitational Potential Energy and Total Energy (Equation 13.6, v_esc = √(2GM ÷ R); Example 13.7: 1.12 × 10⁴ m/s from Earth with M = 5.96 × 10²⁴ kg and R = 6.37 × 10⁶ m, 4.21 × 10⁴ m/s from the Sun at 1.50 × 10¹¹ m with M = 1.99 × 10³⁰ kg), https://openstax.org/books/university-physics-volume-1/pages/13-3-gravitational-potential-energy-and-total-energy (retrieved 2026-10-19)
  6. Body Jupiter, Height above the surface (h) 0 mi gives Escape velocity (km/s) 60.201521.Source: NASA JPL Solar System Dynamics: Astrodynamic Parameters (GM of the Sun, Earth and Moon, DE440), https://ssd.jpl.nasa.gov/astro_par.html; Planetary Physical Parameters (mean radii; escape velocity of the Earth 11.19 km/s, Jupiter 60.20 km/s), https://ssd.jpl.nasa.gov/planets/phys_par.html (retrieved 2026-10-19) (60.20 km/s)

How it works

To escape for good, an object's kinetic energy ½mv² must at least match the gravitational potential energy GMm ÷ r that holds it. Its own mass cancels:

  • Escape velocity: v = √(2GM ÷ r), with r = R + h, the body's mean radius R plus the starting height h.
  • Circular orbit speed at the same distance: √(GM ÷ r), which is v ÷ √2.
  • Gravity at that distance: GM ÷ r².

The escape velocity shows in m/s, km/s, km/h and mph, and the distance r in km.

Bodies (GM in km³/s², mean radius in km): Earth 398,600.435507 and 6,371.0084; Moon 4,902.800118 and 1,737.4; Sun 132,712,440,041.279419 and 695,700; Mercury 22,031.868551 and 2,439.4; Venus 324,858.592 and 6,051.8; Mars 42,828.37362 and 3,389.5; Jupiter 126,686,531.9 and 69,911; Saturn 37,931,206.23 and 58,232; Uranus 5,793,951.3 and 25,362; Neptune 6,835,099.97 and 24,622; Pluto 869.3 and 1,188.3. These GM values are taken as exact; 1 km³/s² = 10⁹ m³/s². For your own body, GM = G × M with G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻².

Units (exact): 1 t = 1,000 kg; 1 lb = 0.45359237 kg; 1 km = 1,000 m; 1 mi = 1,609.344 m; 1 ft = 0.3048 m; 1 km/h = 1 ÷ 3.6 m/s; 1 mph = 0.44704 m/s; the speed of light c = 299,792,458 m/s.

Rules

  • Your own mass from 10⁻⁶ kg to 10⁴⁰ kg and radius from 0.001 m to 10¹⁵ m; height from 0 to 10¹⁵ m. Limits are in SI units and include their ends; a value typed in another unit is converted first.
  • If 2GM ÷ r is c² or more, the escape velocity would reach the speed of light (a black hole, where Newton's formula fails): there is no answer.
  • A result too large or too small to show as a number gives no answer. Within these limits it does not happen.

Output format

The answer line reads v = a km/s (b mph). It and every number show to 6 significant figures, rounded half up, with trailing zeros dropped and thousands commas, and below 10⁻⁶ or from 10¹⁵ up as a × 10ⁿ. Typed values are read back as the exact decimals you typed, and every unit size is exact, so 2GM ÷ r is an exact fraction; each speed is its square root (in that unit), rounded once, and the gravity and distance are exact fractions rounded once.

Worked examples by hand

The Earth. GM = 3.98600435507 × 10¹⁴ m³/s², R = 6,371,008.4 m: v = √(2 × 3.98600435507 × 10¹⁴ ÷ 6,371,008.4) = √125,128,465 = 11,186.1 m/s, shown as v = 11.1861 km/s (25,022.7 mph). The gravity there is GM ÷ R² = 9.82022 m/s².

OpenStax's Earth. Example 13.7 with M = 5.96 × 10²⁴ kg and R = 6.37 × 10⁶ m: v = √(2 × 6.6743 × 10⁻¹¹ × 5.96 × 10²⁴ ÷ 6.37 × 10⁶) = 11,175.6 m/s (OpenStax: 1.12 × 10⁴ m/s with G = 6.67 × 10⁻¹¹).

Leaving the Sun from the Earth's orbit. M = 1.99 × 10³⁰ kg, r = 1.50 × 10¹¹ m: v = √(2 × 6.6743 × 10⁻¹¹ × 1.99 × 10³⁰ ÷ 1.5 × 10¹¹) = 42,082.2 m/s (OpenStax: 4.21 × 10⁴ m/s).

The Moon. √(2 × 4,902.800118 ÷ 1,737.4) = 2.37568 km/s.

From the height of the ISS. r = 6,371.0084 + 400 = 6,771.0084 km: v = √(2 × 398,600.435507 ÷ 6,771.0084) = 10.8507 km/s, and the circular orbit speed is √(398,600.435507 ÷ 6,771.0084) = 7.67259 km/s (OpenStax Example 13.9: 7.67 × 10³ m/s).

Jupiter. √(2 × 126,686,531.9 ÷ 69,911) = 60.2015 km/s (JPL: 60.20 km/s).

Other questions people ask

How do you calculate escape velocity?

v_esc = √(2GM ÷ r), with G the gravitational constant, M the mass of the body and r the distance from its centre. From the Earth’s surface, √(2 × 3.986 × 10¹⁴ ÷ 6.371 × 10⁶) = 11,186 m/s, about 11.2 km/s or 25,000 mph.

What is the escape velocity of the Earth?

About 11.19 km/s (40,270 km/h, 25,023 mph) from the surface. It is lower higher up: from 400 km, the height of the International Space Station, it is 10.85 km/s.

Does escape velocity depend on the mass of the rocket?

No. The mass of the escaping object cancels: kinetic energy ½mv² must equal the potential energy GMm ÷ r, so v = √(2GM ÷ r) for a pebble or a spacecraft.

How is escape velocity related to orbital speed?

A circular orbit at distance r needs √(GM ÷ r), so escape velocity is √2 = 1.414 times the orbit speed. At 400 km above the Earth the orbit speed is 7.67 km/s and escape needs 10.85 km/s.

What is the escape velocity of the Moon, the Sun and Jupiter?

From the surface: the Moon 2.38 km/s, Mars 5.03 km/s, Jupiter 60.2 km/s and the Sun 617.7 km/s. From the Earth’s distance (1.50 × 10¹¹ m), leaving the Sun takes about 42.1 km/s.

Is escape velocity the speed a rocket must reach?

Only for an object coasting from the start, with no air and no further thrust. A rocket keeps burning, so it can leave more slowly; launching east also borrows nearly 460 m/s from the Earth’s spin at the equator.