Escape Velocity Calculator
The escape velocity calculator is a tool that lets you find the minimum speed an object needs to break free from the gravitational pull of any celestial body — a planet, moon, star, or asteroid — without any additional propulsion after launch.
Escape Velocity Equation
The escape velocity formula depends only on the mass and radius of the celestial body, not on the mass of the escaping object:
Ve = √(2GM / R)
Where:
- M — mass of the planet or star (kg)
- R — radius of the planet or star (m)
- G = 6.674 × 10−11 N⋅m²/kg² — gravitational constant
How to Calculate Escape Velocity
The escape velocity formula is derived from the law of conservation of energy. At launch, the object has kinetic energy KE and potential energy PE:
PE + KE = −GMm/R + ½mv²
where m is the mass of the escaping object and v is the launch speed
At escape, the object is infinitely far away: PE = 0 and KE = 0, so the total final energy = 0. By conservation of energy, the initial total energy must also be zero:
−GMm/R + ½mve² = 0
Ve = √(2GM / R)
Notice that the mass of the escaping object m cancels out — escape velocity is the same for a tennis ball and a spacecraft.
First Cosmic Velocity
The first cosmic velocity (V1) is the minimum speed needed to enter a circular orbit just above the planet's surface:
V1 = √(GM / R) = Ve / √2
The escape velocity (second cosmic velocity) is always exactly √2 ≈ 1.414 times greater than the first cosmic velocity.
Typical Escape Velocity Values
| Celestial Body | Escape Velocity (km/s) | Escape Velocity (mi/s) | 1st Cosmic (km/s) |
|---|---|---|---|
| 🌙 Moon | 2.38 | 1.48 | 1.68 |
| 🔴 Mars | 5.03 | 3.13 | 3.56 |
| 🌍 Earth | 11.19 | 6.95 | 7.91 |
| 🪐 Jupiter | 59.54 | 37.00 | 42.10 |
| ☀️ Sun | 617.70 | 383.74 | 436.80 |
FAQs
What is escape velocity?
Escape velocity is the minimum speed an object must reach to escape a planet's (or any celestial body's) gravitational field without further propulsion. Below this speed, gravity will eventually pull the object back; at or above it, the object can travel infinitely far away.
Does escape velocity depend on the direction of launch?
The formula gives the escape speed — the magnitude of velocity required. The direction matters only for efficiency: launching radially outward (straight up) gives the cleanest calculation, but any direction works as long as the speed is sufficient and the trajectory doesn't intersect the planet.
Why don't rockets need to reach escape velocity?
Escape velocity applies to an object launched with a single impulse (like a cannonball). Rockets apply continuous thrust, so they can escape Earth's gravity while traveling much slower — as long as they keep burning fuel. Spacecraft like the Voyager probes, however, did exceed Earth's escape velocity of 11.19 km/s.
What is the second cosmic velocity?
The escape velocity is also called the second cosmic velocity. The first (orbital) velocity is V1 = Ve/√2. The third cosmic velocity (~16.7 km/s from Earth's surface) is the speed needed to escape the Solar System entirely.
Can anything have an escape velocity greater than the speed of light?
Yes — that is the definition of a black hole. Its escape velocity equals or exceeds the speed of light, so not even photons can escape from within the event horizon (Schwarzschild radius). The Schwarzschild radius is given by Rs = 2GM/c².
How does surface gravity relate to escape velocity?
Surface gravity g = GM/R². Substituting into the escape velocity formula: Ve = √(2gR). So a planet with stronger surface gravity or larger radius will have a higher escape velocity.