Escape Velocity Calculator
Pick a body or enter its mass and radius — the escape velocity solves instantly, with a live 3D launch scene comparing your object’s speed to the escape threshold and two charts comparing planets and distance.
Reviewed by the ToolNestr Editorial Team — July 2026
Pick a body, or enter a custom mass and radius — escape velocity solves instantly.
Two ideas that trip students up
1. Three launch speeds, three fates
A short, grey launch falls back down. A medium, amber launch settles into orbit. Only the long, emerald launch — at or above escape velocity — leaves for good.
2. Escape velocity by body
Bar heights compare escape velocity for the Moon, Earth and Jupiter. Mass and radius both matter — Jupiter's huge mass gives it a far higher escape velocity despite being much less dense than Earth.
Escape velocity graphs
How it works
The core idea in one line: escape velocity is the minimum speed an unpowered object needs to coast away from a body’s gravity forever, without ever falling back.
vesc = √(2GM / r)
escape velocity from mass M and distance r
G = 6.674 × 10⁻¹¹ N·m²/kg²
universal gravitational constant
The formula comes from setting an object’s kinetic energy equal to the gravitational potential energy needed to reach infinity: ½mv² = GMm/r. The mass m of the escaping object cancels out entirely — escape velocity depends only on the mass and radius of the body being escaped, not on what is trying to leave it.
Worked example 1 — escaping Earth
Given: Earth’s mass M = 5.972 × 10²⁴ kg, surface radius r = 6.371 × 10⁶ m, G = 6.674 × 10⁻¹¹ N·m²/kg².
This matches the well-known reference value of Earth’s escape velocity, about 11.2 km/s (≈ 40,270 km/h).
Worked example 2 — escaping the Moon
Given: The Moon’s mass M = 7.342 × 10²² kg, surface radius r = 1.737 × 10⁶ m.
About one-fifth of Earth’s escape velocity — a major reason lunar-ascent rockets can be so much smaller than Earth-launch rockets.
Escape velocity across the solar system
Same formula, wildly different results — mass and radius both matter, not just size.
| Body | Masskg | Radiusm | v_esckm/s |
|---|---|---|---|
| Moon | 7.342 × 10²² | 1.737 × 10⁶ | 2.38 |
| Mars | 6.417 × 10²³ | 3.390 × 10⁶ | 5.03 |
| Earth ★ | 5.972 × 10²⁴ | 6.371 × 10⁶ | 11.19 |
| Jupiter | 1.898 × 10²⁷ | 6.991 × 10⁷ | 60.20 |
| Sun | 1.989 × 10³⁰ | 6.960 × 10⁸ | 617.62 |
★ Earth reference. v_esc ∝ √(M/r) — Jupiter’s far greater mass outweighs its larger radius, giving it a much higher escape velocity than Earth despite being 11× the size.
Where escape velocity actually matters
🚀 Rocket launches & interplanetary probes
Missions leaving Earth’s gravity for good — like Voyager or New Horizons — must reach hyperbolic excess speed at or above escape velocity. Mission planners use v_esc to size the rocket stages and fuel budget needed for a one-way trip out of Earth’s pull.
🛰️ Satellites vs. escaping spacecraft
Low-orbit satellites travel at only about 7.8 km/s — enough for a stable orbit but far below Earth’s 11.2 km/s escape velocity. The gap between orbital and escape speed is why staying in orbit takes far less energy than leaving Earth altogether.
🕳️ Black holes, conceptually
Treating light as if it obeyed the same escape-velocity formula gives the (non-relativistic) idea of a Schwarzschild radius — the boundary where the calculated escape velocity equals the speed of light, beyond which nothing can get out.
Common misconceptions
"Escape velocity means you need continuous thrust to leave forever."
The opposite — escape velocity is specifically the speed for an unpowered object (engines off) to never fall back. A rocket that keeps thrusting can leave a planet at almost any speed; escape velocity only matters once the fuel runs out.
"Escape velocity is the same everywhere around a planet."
It depends on distance from the centre: v_esc = √(2GM/r) shrinks as r grows. Escaping from a high orbit needs a lower speed than escaping from the surface, because you are already partway "up" the gravity well.
"A bigger planet always has a higher escape velocity."
Size alone is not enough — escape velocity depends on mass and radius together (√(M/r)). A large but low-density body can have a lower escape velocity than a smaller, denser one.
"Escaping means leaving gravity’s influence entirely."
Gravity technically never reaches zero, only approaches it. "Escaping" means having enough energy to reach an infinite distance with zero speed left over — the object slows forever but (in the idealised model) never actually turns back.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, University Physics Volume 1 — §13.4, Satellite Orbits and Energy (escape velocity) (free, peer-reviewed). openstax.org
- • Halliday, Resnick & Walker, Fundamentals of Physics — Chapter 13, Gravitation (Escape Speed).
- • Serway & Jewett, Physics for Scientists and Engineers — Chapter 13, Universal Gravitation (Energy Considerations).
Gravitational constant G = 6.674 × 10⁻¹¹ N·m²/kg² (CODATA). Preset masses and radii are standard textbook/NASA values. Results are rounded for display.
How to use this calculator
Pick a body
Select Earth, Moon, Mars or Sun to auto-fill mass and radius, or type your own.
Adjust r if needed
Use a larger r to find the escape velocity from orbit instead of the surface.
Compare on the chart
See how v_esc stacks up across bodies and how it falls off with distance.
Related tools
Frequently asked questions
What is escape velocity?
Escape velocity is the minimum speed an unpowered object needs at a given distance from a body to break free of its gravity forever, without any further thrust. Below this speed the object eventually falls back or settles into orbit; at or above it, the object never returns.
What is the formula for escape velocity?
v_esc = √(2GM/r), where G is the gravitational constant (6.674 × 10⁻¹¹ N·m²/kg²), M is the mass of the body being escaped, and r is the distance from the body’s centre — usually its surface radius.
What is Earth’s escape velocity?
About 11.2 km/s (roughly 40,270 km/h) from the surface, using M = 5.972 × 10²⁴ kg and r = 6.371 × 10⁶ m. This is why rockets need enormous speed and fuel to leave Earth permanently, versus the ~7.8 km/s needed just to reach low orbit.
Do rockets need to travel at escape velocity the whole way up?
No. Escape velocity is the speed needed for an object coasting with no further thrust. A rocket burns fuel continuously and can leave gravity at almost any speed, as long as it keeps thrusting — escape velocity only applies once the engines stop.
How is escape velocity related to black holes?
A black hole’s event horizon is, loosely, the radius at which escape velocity equals the speed of light. Because nothing can exceed light speed, nothing — not even light — can escape from within that radius, which is why the region appears black.