# What is the escape velocity?

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.

- Page: https://www.acalculator.org/physics/escape-velocity-calculator
- JSON spec: https://www.acalculator.org/physics/escape-velocity-calculator.json
- Version: 65fc9ec3f6ab

## Default answer

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).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| body | Body | The planet, moon or star to escape from, or your own mass and radius. |
| M | Mass (M) | The mass of the body. |
| R | Radius (R) | The radius of the body, from its centre to its surface. |
| h | Height above the surface (h) | Where you start: 0 at the surface. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| result | Answer | The escape velocity to 6 significant figures, in km/s and mph. |
| escape | Escape velocity (m/s) | v = √(2GM ÷ r), in metres per second. |
| kms | Escape velocity (km/s) | v in kilometres per second. |
| kmh | Escape velocity (km/h) | v in kilometres per hour. |
| mph | Escape velocity (mph) | v in miles per hour. |
| orbit | Circular orbit speed (m/s) | √(GM ÷ r): the speed of a circular orbit at that distance, v ÷ √2. |
| gravity | Gravity there (m/s²) | g = GM ÷ r², the pull of the body at that distance. |
| distance | Distance from the centre (km) | r = R + h, in kilometres. |

## 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.

## Assumptions

- 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.

## Worked examples

1. body = earth, h = 0 gives escape = 11,186.128229, mph = 25,022.656203, gravity = 9.820224, result = 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 = custom, M = 5,960,000,000,000,000,000,000,000, R = 6,370,000, h = 0 gives escape = 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 = custom, M = 1,990,000,000,000,000,000,000,000,000,000, R = 150,000,000,000, h = 0 gives escape = 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, h = 0 gives kms = 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, h = 400,000 gives kms = 10.850686, orbit = 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, h = 0 gives kms = 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).

## FAQ

### 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.

## Sources

- OpenStax, University Physics Volume 1, §13.3 Gravitational Potential Energy and Total Energy: Equation 13.6, v_esc = √(2GM ÷ R); Example 13.7 (from the Earth with M = 5.96 × 10²⁴ kg and R = 6.37 × 10⁶ m: 1.12 × 10⁴ m/s; from the Sun at 1.50 × 10¹¹ m with M = 1.99 × 10³⁰ kg: 4.21 × 10⁴ m/s), retrieved 2026-10-19. https://openstax.org/books/university-physics-volume-1/pages/13-3-gravitational-potential-energy-and-total-energy
- OpenStax, University Physics Volume 1, §13.4 Satellite Orbits and Energy: Equation 13.7, v_orbit = √(GM ÷ r); Example 13.9 (the ISS at 400 km: 7.67 × 10³ m/s), retrieved 2026-10-19. https://openstax.org/books/university-physics-volume-1/pages/13-4-satellite-orbits-and-energy
- NASA JPL Solar System Dynamics, Astrodynamic Parameters: GM of the Sun 1.32712440041279419 × 10²⁰ m³/s², of the Earth 398,600.435507 km³/s², of the Moon 4,902.800118 km³/s², of Mercury 22,031.868551 km³/s² and of Venus 324,858.592 km³/s² (DE440), retrieved 2026-10-19. https://ssd.jpl.nasa.gov/astro_par.html
- NASA JPL Solar System Dynamics, Planetary Satellite Physical Parameters: planet GM values (Mars 42,828.37362; Jupiter 126,686,531.9; Saturn 37,931,206.23; Uranus 5,793,951.3; Neptune 6,835,099.97; Pluto 869.3 km³/s²) and the Moon’s mean radius 1,737.4 km, retrieved 2026-10-19. https://ssd.jpl.nasa.gov/sats/phys_par/
- NASA JPL Solar System Dynamics, Planetary Physical Parameters: mean radii (Mercury 2,439.4; Venus 6,051.8; Earth 6,371.0084; Mars 3,389.50; Jupiter 69,911; Saturn 58,232; Uranus 25,362; Neptune 24,622; Pluto 1,188.3 km) and escape velocities (Earth 11.19, Jupiter 60.20 km/s), retrieved 2026-10-19. https://ssd.jpl.nasa.gov/planets/phys_par.html
- NASA NSSDCA, Sun Fact Sheet: volumetric mean radius 695,700 km, retrieved 2026-10-19. https://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html
- NIST, CODATA 2022: Newtonian constant of gravitation G = 6.67430(15) × 10⁻¹¹ m³ kg⁻¹ s⁻², retrieved 2026-10-19. https://physics.nist.gov/cgi-bin/cuu/Value?bg