Escape Velocity Calculator - v = √(2GM/r)

Mass of Body

02,000,000

Radius of Body

11,000,000

Escape Velocity

11.186

Escape Velocity

11,185.726

Escape Velocity

40,268.615

This calculator computes your Escape Velocity, Escape Velocity, Escape Velocity from the values you enter.

Inputs

Mass of BodyRadius of Body

Outputs

Escape VelocityEscape VelocityEscape Velocity

What is a Escape Velocity?

The Escape Velocity Calculator computes the minimum speed an object needs to permanently escape a celestial body's gravity, using v = √(2GM ÷ r). Enter the body's mass (in units of 10²⁴ kg) and radius (in kilometers), and the calculator instantly returns the escape velocity in km/s, m/s, and km/h.

The default values are pre-filled with Earth's mass and radius, and the tooltip on each input lists reference values for the Moon, Mars, and the Sun so you can quickly compute escape velocity for any of these bodies by entering their known mass and radius.

Why Use an Escape Velocity Calculator?

Computing escape velocity by hand involves working with very large numbers (planetary masses in the 10²⁴ kg range and the tiny gravitational constant G), which is tedious and error-prone to do manually. This calculator handles the unit conversions and scientific notation automatically.

The result updates live as you adjust mass or radius, letting you quickly compare escape velocities across different bodies, from moons to stars, without re-deriving the formula each time.

The step-by-step breakdown shows the full substitution, which is useful for verifying homework, lab reports, or aerospace engineering back-of-envelope calculations.

Who Should Use This Calculator?

Physics and astronomy students studying orbital mechanics, gravitational potential energy, and planetary science.

Aerospace engineering students and enthusiasts estimating launch requirements for spacecraft leaving Earth or other bodies.

Science teachers demonstrating how escape velocity varies across planets, moons, and stars.

Astronomy hobbyists comparing gravitational properties of different celestial bodies.

Science writers and content creators who need quick, accurate escape velocity figures for different planets and moons.

What Insights Does This Calculator Give You?

Escape velocity, the primary result, showing the minimum launch speed needed to leave a body's gravity entirely, in three common units (km/s, m/s, km/h).

Mass-radius sensitivity, because escape velocity scales with √(M ÷ r), this calculator makes it easy to see how a body's compactness (mass relative to its size) drives its escape velocity, which is why white dwarfs and neutron stars, despite modest mass compared to stars, have extreme escape velocities due to their tiny radii.

Cross-body comparison, by entering different mass/radius pairs, you can directly compare how much harder it is to escape gravity giants like the Sun versus small bodies like the Moon.

How to use this Escape Velocity calculator

Enter the mass of the body, in units of 10²⁴ kg. Use the tooltip reference values for Earth, Moon, Mars, or the Sun, or enter a custom value.
Enter the radius of the body, in kilometers, measured from the center to the surface.
Read the escape velocity result, the highlighted result shows escape velocity in km/s, with m/s and km/h shown alongside.
Check the step-by-step breakdown, expand the calculation steps to see the full unit conversion and formula substitution.

Show formula & methodology ↓Show less ↑

Formula & Methodology

Escape velocity formula:
v = √(2GM ÷ r)

Variable definitions:
- G, gravitational constant, 6.674 × 10⁻¹¹ N·m²/kg²
- M, mass of the celestial body (kg)
- r, radius of the celestial body, or distance from its center (meters)
- v, escape velocity (meters per second)

Worked example (Earth):

M = 5.972 × 10²⁴ kg, r = 6,371 km = 6,371,000 m

v = √(2 × 6.674×10⁻¹¹ × 5.972×10²⁴ ÷ 6,371,000) ≈ 11.19 km/s

Note: This calculator assumes a spherical, non-rotating body with no atmosphere. Real-world launches also account for atmospheric drag and the body's rotational speed, which can reduce the effective velocity needed at the equator.

Frequently Asked Questions

What is the formula for escape velocity?

Escape velocity is calculated as v = √(2GM ÷ r), where G is the gravitational constant (6.674×10⁻¹¹ N·m²/kg²), M is the mass of the celestial body, and r is the distance from its center (typically its surface radius). This calculator applies that formula directly using the mass and radius you enter.

What is Earth's escape velocity?

Earth's escape velocity is approximately 11.2 km/s (about 40,270 km/h), using its mass of 5.972 × 10²⁴ kg and radius of 6,371 km, the default values pre-filled in this calculator. This is the minimum speed a rocket or object needs to permanently leave Earth's gravitational pull without further propulsion.

How does escape velocity differ for the Moon, Mars, and the Sun?

The Moon's escape velocity is about 2.4 km/s (much lower due to its smaller mass), Mars is about 5.0 km/s, and the Sun's is about 618 km/s, reflecting how escape velocity scales with the square root of mass divided by radius. Enter each body's mass and radius into this calculator to see the difference directly.

Does escape velocity depend on the mass of the escaping object?

No, escape velocity is independent of the escaping object's own mass. A pebble and a spacecraft launched from the same point at the same speed would both either escape or fall back, because the formula only involves the mass and radius of the body being escaped from, not the object leaving it.

Is escape velocity the same as orbital velocity?

No, orbital velocity (the speed needed to maintain a stable circular orbit) is escape velocity divided by √2, roughly 70.7% of escape velocity at the same radius. Escape velocity is always higher because it must overcome gravity entirely rather than balance against it.

What happens if an object travels faster than escape velocity?

An object launched faster than escape velocity will leave the gravitational influence of the body with excess kinetic energy remaining, meaning it will still be moving at a positive velocity once it's infinitely far away, rather than just barely reaching zero velocity at infinity.

Why does escape velocity decrease with altitude?

Escape velocity depends on distance from the center (r), as r increases with altitude, the required escape velocity decreases, since v = √(2GM ÷ r) shrinks as r grows. This is why spacecraft already in high orbit need less additional speed to escape than they would from the surface.

How is escape velocity relevant to black holes?

A black hole's event horizon is defined as the radius at which escape velocity equals the speed of light, beyond that point, not even light can escape, which is why black holes appear completely dark. This is a direct (relativistic) extension of the same escape velocity concept used for planets.

What's the relationship between escape velocity and gravitational potential energy?

Escape velocity is derived by setting an object's kinetic energy (½mv²) equal to the magnitude of its gravitational potential energy (GMm ÷ r) and solving for v, the escaping object needs just enough kinetic energy to counteract the gravitational potential well it's climbing out of. See the [Potential Energy Calculator](/potential-energy-calculator/) for related gravitational energy calculations.

Why do rockets need multiple stages to reach escape velocity?

Reaching orbital or escape velocity requires enormous kinetic energy, and multi-stage rockets shed the mass of spent fuel tanks and engines as they climb, so each subsequent stage accelerates a lighter vehicle more efficiently than a single-stage rocket carrying all that dead weight the whole way.

How accurate is this calculator for real spacecraft missions?

This calculator gives the theoretical escape velocity from a spherical, non-rotating body's surface, ignoring atmospheric drag, the body's rotation, and other gravitational influences (like the Sun's pull on an object escaping Earth). Real mission planning accounts for these factors, so treat this as a foundational estimate rather than a precise launch calculation.

How does escape velocity relate to free-fall acceleration?

Both depend on the same underlying gravitational parameters (mass and radius), but free-fall acceleration (g = GM ÷ r²) measures the acceleration an object experiences falling toward a body, while escape velocity measures the speed needed to leave it entirely. See the [Free Fall Calculator](/free-fall-calculator/) for the related falling-object calculation.

Also known as

v = sqrt(2GM/r) calculatorescape speed calculatorplanet escape velocity calculatororbital mechanics calculator