About this calculator
Escape velocity is the speed an object needs to break free of a planet's or star's gravity and never fall back, without any further push. It is v = √(2GM ÷ r).
Choose a body, or enter your own mass and radius, and optionally a height above the surface. You also get the circular orbit speed at the same height and the local gravity.
Worked examples
Real numbers, worked out by the same calculator. Press “Use these numbers” to try one above.
Earth's surface
- Escape velocity
- 11,185.977892 m/s
- In kilometres per second
- 11.185978 km/s
- In miles per hour
- 25,022 mph
- Circular orbit speed at the same height
- 7,909.680822 m/s
- Gravity at that height
- 9.819973 m/s²
To escape the gravity of Earth from the surface you need to reach 11.185978 km/s (11,185.977892 m/s).
Show the working
- Escape velocity: v = √(2 G M ÷ r), where G = 6.6743 × 10⁻¹¹ N·m²/kg², M is the mass and r the distance from the centre.
- r = radius + height = 6.371 × 10^6 + 0 = 6.371 × 10^6 m, so v = √(2 × 6.6743 × 10^-11 × 5.972 × 10^24 ÷ 6.371 × 10^6) = 11,185.977892 m/s.
- It does not depend on the mass of the object leaving, and it ignores air resistance. An object doesn't have to reach this speed instantly: a rocket can climb slowly.
The Moon
- Escape velocity
- 2,375.063039 m/s
- In kilometres per second
- 2.375063 km/s
- In miles per hour
- 5,313 mph
- Circular orbit speed at the same height
- 1,679.423181 m/s
- Gravity at that height
- 1.623381 m/s²
To escape the gravity of the Moon from the surface you need to reach 2.375063 km/s (2,375.063039 m/s).
Show the working
- Escape velocity: v = √(2 G M ÷ r), where G = 6.6743 × 10⁻¹¹ N·m²/kg², M is the mass and r the distance from the centre.
- r = radius + height = 1.7374 × 10^6 + 0 = 1.7374 × 10^6 m, so v = √(2 × 6.6743 × 10^-11 × 7.342 × 10^22 ÷ 1.7374 × 10^6) = 2,375.063039 m/s.
- It does not depend on the mass of the object leaving, and it ignores air resistance. An object doesn't have to reach this speed instantly: a rocket can climb slowly.
Mars
- Escape velocity
- 5,027.083051 m/s
- In kilometres per second
- 5.027083 km/s
- In miles per hour
- 11,245 mph
- Circular orbit speed at the same height
- 3,554.684515 m/s
- Gravity at that height
- 3.727919 m/s²
To escape the gravity of Mars from the surface you need to reach 5.027083 km/s (5,027.083051 m/s).
Show the working
- Escape velocity: v = √(2 G M ÷ r), where G = 6.6743 × 10⁻¹¹ N·m²/kg², M is the mass and r the distance from the centre.
- r = radius + height = 3.3895 × 10^6 + 0 = 3.3895 × 10^6 m, so v = √(2 × 6.6743 × 10^-11 × 6.417 × 10^23 ÷ 3.3895 × 10^6) = 5,027.083051 m/s.
- It does not depend on the mass of the object leaving, and it ignores air resistance. An object doesn't have to reach this speed instantly: a rocket can climb slowly.
A custom body: the Sun's mass and radius
- Escape velocity
- 617,766.351625 m/s
- In kilometres per second
- 617.766352 km/s
- In miles per hour
- 1,381,904 mph
- Circular orbit speed at the same height
- 436,826.776423 m/s
- Gravity at that height
- 274.28149 m/s²
To escape the gravity of that body from the surface you need to reach 617.766352 km/s (617,766.351625 m/s).
Show the working
- Escape velocity: v = √(2 G M ÷ r), where G = 6.6743 × 10⁻¹¹ N·m²/kg², M is the mass and r the distance from the centre.
- r = radius + height = 6.957 × 10^8 + 0 = 6.957 × 10^8 m, so v = √(2 × 6.6743 × 10^-11 × 1.989 × 10^30 ÷ 6.957 × 10^8) = 617,766.351625 m/s.
- It does not depend on the mass of the object leaving, and it ignores air resistance. An object doesn't have to reach this speed instantly: a rocket can climb slowly.
The formula
v = √(2 G M ÷ r), with G = 6.6743 × 10⁻¹¹ N·m²/kg², M the mass of the body and r the distance from its centre (radius plus height). It comes from setting the kinetic energy ½mv² equal to the gravitational energy G M m ÷ r that must be overcome.
Typical values
- Earth: about 11.2 km/s (25,000 mph)
- The Moon: about 2.4 km/s
- Mars: about 5.0 km/s
- Jupiter: about 59.5 km/s
- The Sun's surface: about 618 km/s
What it does and doesn't mean
Escape velocity is independent of the mass of the object leaving. Rockets don't need to reach it at launch: they can climb slowly, and it is the speed needed at a given height for an unpowered escape. The calculation ignores air resistance. An object at escape velocity follows a parabola; slower and it orbits or falls back. The circular orbit speed at the same height is escape velocity divided by √2.
Frequently asked questions
What is escape velocity?
The minimum speed to leave a body's gravity for good, with no further thrust.
What is Earth's escape velocity?
About 11.186 km/s from the surface.
Does it depend on the object's mass?
No. A feather and a spacecraft need the same speed (ignoring air).
Why is escape speed larger than orbital speed?
Orbiting only needs enough speed to keep falling around the planet. Escape needs √2 times more.
Can I use my own planet?
Yes: choose 'Another body' and enter its mass and radius, writing large numbers like 5.972e24.
Formulas tested against hand-worked answers. Last reviewed 29 September 2026. These calculators do arithmetic only; they are not financial, tax or legal advice.