Quick answer
Escape velocity is v = √(2GM ÷ r). Earth's is 11.1862 km/s at the surface, where gravity is 9.82 m/s².
Choose a body. The calculator returns its escape velocity and surface gravity.
Related tools: Gravitational Force Calculator: Newtonian gravitational attraction between two masses. Angular Velocity Calculator: Angular velocity from rpm, frequency, or an angle and time. Water Velocity Calculator: Water velocity in a pipe from flow and inside diameter.
How to use the Escape Velocity Calculator
- Choose body: Earth, Moon, Mars, Sun and Custom.
- Optionally, enter mass (custom) (kg) (above 0).
- Optionally, enter radius (custom) (m) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Body | Choose one: Earth; Moon; Mars; Sun; Custom | Starts at Earth |
| Mass (custom) (optional) | A number, in kg | > 0 |
| Radius (custom) (optional) | A number, in m | > 0 |
Formula and method
Formula
v_esc = √(2GM ÷ r)
IEEE-754 double precision; shown to the decimals indicated.
Uses mean radius and IAU/NASA masses: Earth 5.9722×10²⁴ kg and 6,371 km; Moon 7.342×10²² kg and 1,737.4 km; Mars 6.4171×10²³ kg and 3,389.5 km; Sun 1.98847×10³⁰ kg and 695,700 km.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Body = Earth.
| Result | Value |
|---|---|
| Escape velocity | 11.1862 km/s |
| Surface gravity | 9.82 m/s² |
Example 2
Inputs: Body = Moon.
| Result | Value |
|---|---|
| Escape velocity | 2.3751 km/s |
| Surface gravity | 1.623 m/s² |
Example 3
Inputs: Body = Mars.
| Result | Value |
|---|---|
| Escape velocity | 5.0271 km/s |
| Surface gravity | 3.728 m/s² |
The first line is the headline result (escape velocity). Below it the escape Velocity Calculator lists surface gravity, which describe the same case from other angles. IEEE-754 double precision; shown to the decimals indicated.
What it means
It's the minimum speed to leave a body's gravity without further propulsion, ignoring drag. It is √2 times the circular orbital speed at the surface, which for Earth is 7.91 km/s.
Other bodies
The Moon's is about 2.38 km/s, Mars 5.03 km/s and Jupiter 59.5 km/s. Atmospheric drag and the planet's rotation are ignored. It doesn't depend on the mass of the escaping object.
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Mass (custom): left empty shows "Enter the mass." beside that field and no result.
- Radius (custom): left empty shows "Enter the radius." beside that field and no result.
Choosing between the Escape Velocity Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Gravitational Force Calculator](/science/gravitational-force-calculator/) | mass 1, mass 2 and distance between centers | Gravitational force |
| [Angular Velocity Calculator](/science/angular-velocity-calculator/) | starting from | Angular velocity |
| [Water Velocity Calculator](/science/water-velocity-calculator/) | flow and inside diameter | Velocity |
| [Terminal Velocity Calculator](/science/terminal-velocity-calculator/) | mass, frontal area and drag coefficient | Terminal velocity |
| [Dew Point Calculator](/science/dew-point/) | air temperature and relative humidity | Dew point |
Background: gravity, rotation and optics
Gravity and rotation calculations use a few core relations: a circular orbit has speed v = √(GM ÷ r), torque equals moment of inertia times angular acceleration (τ = Iα), and a thin lens obeys 1/f = 1/dₒ + 1/dᵢ. The moment of inertia depends on both the shape and the axis of rotation.
Use SI units (metres, kilograms, seconds) and check the sign conventions of the formula before interpreting a negative result.
Assumptions and limitations
- Ignores atmospheric drag and rotation
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for mass (custom) and radius (custom) to confirm this.
Frequently asked questions
Does a rocket need to reach escape velocity?
No, it can leave gradually under thrust.
What's the escape velocity of the Sun at Earth's orbit?
At Earth's distance from the Sun (1 AU) the escape velocity is about 42.1 km/s, which is √2 times Earth's orbital speed of about 29.8 km/s.
Why does the Moon have no atmosphere?
Low escape velocity.
What does the Escape Velocity Calculator calculate?
Speed needed to escape a body's gravity from its surface. It returns Escape velocity and Surface gravity.
What formula does the Escape Velocity Calculator use?
v_esc = √(2GM ÷ r). Uses mean radius and IAU/NASA masses: Earth 5.9722×10²⁴ kg and 6,371 km; Moon 7.342×10²² kg and 1,737.4 km; Mars 6.4171×10²³ kg and 3,389.5 km; Sun 1.98847×10³⁰ kg and 695,700 km.
What do I need to enter in the escape Velocity Calculator?
You enter Body. Optional: Mass (custom) (kg) and Radius (custom) (m).
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Ignores atmospheric drag and rotation.
What does the “Body” option change?
It sets how the escape Velocity is worked out. The choices are Earth, Moon, Mars, Sun and Custom.
What is an example of a escape Velocity result?
With body Earth, the escape velocity is 11.1862 km/s.
Where does the method come from?
The method follows: NASA Planetary Fact Sheets; CODATA 2018 / SI exact constants: g₀ = 9.80665 m/s², c = 299,792,458 m/s, h = 6.62607015×10⁻³⁴ J·s, e = 1.602176634×10⁻¹⁹ C, G = 6.67430×10⁻¹¹ m³/(kg·s²).
Related calculators
- Gravitational Force Calculator — Newtonian gravitational attraction between two masses.
- Angular Velocity Calculator — Angular velocity from rpm, frequency, or an angle and time.
- Water Velocity Calculator — Water velocity in a pipe from flow and inside diameter.
- Terminal Velocity Calculator — Terminal speed of a falling object from mass, area and drag coefficient.
- Dew Point Calculator — Dew point from temperature and relative humidity.
- Acceleration Calculator — Average acceleration from change in velocity over time.
Sources
- NASA Planetary Fact Sheets; CODATA 2018 / SI exact constants: g₀ = 9.80665 m/s², c = 299,792,458 m/s, h = 6.62607015×10⁻³⁴ J·s, e = 1.602176634×10⁻¹⁹ C, G = 6.67430×10⁻¹¹ m³/(kg·s²)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.