Escape Velocity Calculator
The speed needed to break free of gravity.
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Escape velocity is the speed an object needs to break free of a world's gravity and never fall back. Pick a planet or enter a custom mass and radius, and this calculator works out that speed — the reason rockets have to be so powerful.
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Escape Velocity — The Quick Answer
Escape velocity depends on a body's mass and radius: v = √(2GM/r). Earth's is about 11.2 km/s — roughly 40,000 km/h — which is why reaching orbit takes so much energy.
Shortcut
v = √(2 × G × M ÷ r)
Escape velocities in the Solar System
| Body | Escape velocity |
|---|---|
| The Moon | 2.38 km/s |
| Mars | 5.03 km/s |
| Earth | 11.19 km/s |
| Jupiter | 59.5 km/s |
| The Sun | 617.5 km/s |
Escape velocity doesn't depend on the mass of the escaping object — a pebble and a spacecraft need the same speed. It also assumes no air resistance and no further thrust after launch.
How It Works
The Formula
Mass and radius set the speed
Formula
v = √(2GM / r)
Variables
Gravitational constant
6.674 × 10⁻¹¹ N·m²/kg², the fundamental constant linking mass and gravity.
Mass of the body
The mass you're escaping from, in kilograms. More mass means higher escape velocity.
Radius
The distance from the centre of mass — usually the body's radius if launching from the surface. A larger radius lowers escape velocity.
Note: Escape velocity is the speed for a single 'ballistic' launch with no further propulsion. Real rockets instead apply continuous thrust, so they never need to actually reach 11.2 km/s all at once at the surface.
Worked Example: Earth's Escape Velocity
Where 11.2 km/s comes from
Gather the inputs
Earth's mass M = 5.97×10²⁴ kg, radius r = 6.371×10⁶ m, G = 6.674×10⁻¹¹.
Apply v = √(2GM/r)
2GM = 2 × 6.674×10⁻¹¹ × 5.97×10²⁴ ≈ 7.97×10¹⁴; divide by r ≈ 1.25×10⁸.
Take the square root
√(1.25×10⁸) ≈ 11,180 m/s ≈ 11.2 km/s — about 40,000 km/h.
Reference Guide
| Body | Escape velocity | × Earth |
|---|---|---|
| The Moon | 2.38 km/s | 0.21 |
| Mars | 5.03 km/s | 0.45 |
| Earth | 11.19 km/s | 1.00 |
| Jupiter | 59.5 km/s | 5.3 |
| The Sun | 617.5 km/s | 55 |
What the Speed Does and Doesn't Mean
An idealised figure with specific assumptions
More mass raises escape velocity; a larger radius lowers it. The escaping object's own mass is irrelevant.
Best for: Comparing worlds fairly
Escape velocity is for a single ballistic shot with no further thrust. Rockets thrust continuously and gain speed with altitude, so they climb more gradually.
Best for: Understanding why launch isn't 11.2 km/s instantly
The figure assumes no atmosphere and no engine after launch — real launches must also overcome drag.
Best for: Knowing the idealised assumptions
Common Mistakes
Thinking a heavier craft needs more speed
Escape velocity is identical for a pebble and a spaceship. Heavier craft need more energy and fuel to reach that speed, not a higher speed.
Assuming rockets reach it at liftoff
Launch vehicles apply thrust continuously and gain speed with altitude; they never need the full 11.2 km/s right at the pad.
Ignoring the radius term
Escape velocity depends on distance from the centre. Launch from higher up (larger r) and the required speed drops — it isn't a property of mass alone.
Confusing it with orbital velocity
Orbital speed to circle a body is lower than escape speed — about 7.9 km/s for low Earth orbit versus 11.2 km/s to leave entirely.
Research & Citations
Sources and standards referenced for the factual claims on this page
- [nasa]
NASA / NSSDCA (D. R. Williams) (2024). Planetary Fact Sheet — masses, radii, and escape velocities. NASA Goddard Space Flight Center.
Reference masses and radii for the Solar System bodies used here.
- [codata]
CODATA / NIST (2018). Recommended value of the Newtonian constant of gravitation, G = 6.674×10⁻¹¹ N·m²/kg². NIST.
The gravitational constant used in v = √(2GM/r).
This calculator is a reference tool, not a substitute for professional advice. Verify important health, financial, legal, or safety decisions with a suitably qualified professional.
Last updated: October 8, 2026
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Frequently Asked Questions
What is Earth's escape velocity?
About 11.2 km/s, or roughly 40,000 km/h. That's the speed an object would need from the surface (ignoring air resistance) to escape Earth's gravity without any further push.
How is escape velocity calculated?
With the formula v = √(2GM/r), where G is the gravitational constant, M is the body's mass, and r is the distance from its centre. This calculator does it for you using known masses and radii.
Does a heavier rocket need a higher escape velocity?
No — escape velocity is the same regardless of the escaping object's mass. A feather and a spaceship need the same speed. Heavier rockets just need more total energy and fuel to reach that speed.
Why is the Sun's escape velocity so high?
Because the Sun is enormously massive — about 333,000 times Earth's mass. Its escape velocity is around 617 km/s at the surface, over 55 times Earth's, reflecting that immense gravitational pull.