Escape Velocity Calculator
This escape velocity calculator works out the minimum speed an object needs to permanently break free of a celestial body's gravity, using the same physics that governs real rocket launches. Enter a mass and radius, or tap a preset for Earth, the Moon, the Sun, or Jupiter, and the result updates instantly in both km/s and mph — no submit button, nothing sent to a server.
What Is Escape Velocity?
Escape velocity is the minimum speed an object needs at a body's surface to escape its gravity forever, assuming no further thrust and no atmosphere to slow it down. It isn't a speed limit in the everyday sense — an object launched slower than escape velocity can still go up, it just eventually falls back, the way a thrown ball does on Earth. Cross escape velocity, and gravity can never quite pull the object all the way back.
Escape velocity depends entirely on the body being left — its mass and its radius — and not at all on the mass of whatever is escaping. A grain of dust and a fully fueled rocket leaving Earth's surface both need the same 11.19 km/s; the rocket just needs vastly more energy to reach that speed because it weighs so much more.
The Escape Velocity Formula
This calculator uses the standard escape velocity formula:
v = √(2GM / r)
Where G is the gravitational constant (6.6743×10⁻¹¹ N·m²/kg²), M is the mass of the celestial body in kilograms, and r is its radius in meters. The formula comes from setting an object's kinetic energy equal to the gravitational potential energy binding it to the body — the speed at which those two exactly balance is escape velocity. Because mass sits under a square root and radius sits under a square root in the denominator, doubling a body's mass multiplies escape velocity by only about 1.41×, while halving its radius has the same effect — size and density both matter, not just how big something is.
Escape Velocity of Earth, the Moon, Sun, and Jupiter
The table below shows what this calculator returns for each of its four built-in presets:
| Body | Mass | Radius | Escape velocity |
|---|---|---|---|
| Moon | 7.342×10²² kg | 1,737 km | 2.38 km/s (5,313 mph) |
| Earth | 5.972×10²⁴ kg | 6,371 km | 11.19 km/s (25,022 mph) |
| Jupiter | 1.898×10²⁷ kg | 71,492 km | 59.5 km/s (133,121 mph) |
| Sun | 1.989×10³⁰ kg | 696,000 km | 617.5 km/s (1,381,342 mph) |
The Moon's escape velocity is roughly a fifth of Earth's, which is the main reason the Apollo lunar module could leave the Moon's surface on a fraction of the fuel a rocket needs to leave Earth. Jupiter, despite being made mostly of gas, has over five times Earth's escape velocity because of its enormous mass. The Sun's escape velocity dwarfs every planet's — it holds more than 99.8% of the solar system's total mass.
How to Use This Calculator
- Tap a preset — Earth, Moon, Sun, or Jupiter — to instantly load its mass and radius, or type your own values
- Enter a Mass — scientific notation is supported (e.g.
5.972e24) - Enter a Radius
- Switch between SI units (kg / km) and Earth-relative units (Earth masses / Earth radii) at any time
The Escape Velocity card recalculates on every keystroke, showing the result in both km/s and mph together. Earth-relative units are handy for comparing a hypothetical planet to Earth directly — entering "2" for mass and "1" for radius, for instance, shows the escape velocity of a planet with twice Earth's mass packed into Earth's exact size.
Frequently Asked Questions
What is escape velocity?
Escape velocity is the minimum speed an object needs to break free of a celestial body's gravity permanently, without any further propulsion. It depends only on the body being escaped — its mass and radius — not on the mass of the object escaping: a pebble and a spacecraft leaving the same launch point both need exactly the same escape velocity.
What is the escape velocity of Earth?
Earth's escape velocity is about 11.19 km/s (roughly 25,020 mph), calculated from Earth's mass (5.972×10²⁴ kg) and mean radius (6,371 km). That's the speed a rocket would need at Earth's surface to leave and never fall back, ignoring air resistance.
How do you calculate escape velocity?
Escape velocity is calculated with v = √(2GM/r), where G is the gravitational constant (6.6743×10⁻¹¹ N·m²/kg²), M is the mass of the body in kilograms, and r is its radius in meters. Plugging in a planet, moon, or star's mass and radius gives the minimum speed needed to escape its gravity from the surface.
How does the Moon's escape velocity compare to Earth's?
The Moon's escape velocity is about 2.38 km/s, roughly a fifth of Earth's 11.19 km/s. The Moon is both far less massive and smaller than Earth, and since escape velocity depends on the square root of mass divided by radius, the Moon's much smaller mass dominates — which is why leaving the Moon needs so much less fuel than leaving Earth.
What are the escape velocities of Jupiter and the Sun?
Jupiter's escape velocity is about 59.5 km/s — over five times Earth's — because it's by far the most massive planet in the solar system. The Sun's is far higher still, about 617.5 km/s, since it holds more than 99.8% of the solar system's mass packed into one body.
Does escape velocity depend on the mass of the escaping object?
No. Escape velocity depends only on the mass and radius of the body being escaped, not on the mass of whatever is leaving it. A dust grain and a fully fueled rocket launched from Earth's surface both need the same 11.19 km/s — a heavier object just needs proportionally more energy (and fuel) to reach that same speed.
