Escape Velocity Calculator

Escape velocity is the minimum speed needed to reach infinite distance with zero remaining speed, assuming a non-rotating spherical body and no atmosphere.

Escape velocity: v = √(2GM / r)

Orbital speed at the surface: vorb = √(GM / r)

Surface gravity: g = GM / r²

1. Choose a body preset, or switch to custom values.
2. If using custom mode, enter mass and radius with units.
3. Pick a primary output unit and precision.
4. Press Calculate to see results above.
5. Use Download CSV or Download PDF after calculating.

Values are approximate and depend on the chosen parameters.

1) Escape velocity in one idea

Escape velocity is the smallest launch speed that lets an object climb away forever, ending with zero speed far from the body. It depends on mass and radius, not on the object’s mass. At Earth’s surface it is about 11.2 km/s, while the Moon needs about 2.4 km/s.

2) Why mass and radius matter

The calculator uses v = √(2GM/r), so doubling mass raises escape speed by √2 at the same radius. Doubling radius lowers escape speed by √2 at the same mass. Dense, compact bodies can therefore be harder to leave than larger, lighter ones.

3) Comparing common worlds

Typical values show the range of gravity wells. Mars is about 5.0 km/s, so departures need less speed than Earth. Jupiter is roughly 59.5 km/s near the cloud tops. The Sun is extreme at about 617 km/s close to its visible surface.

4) Orbit speed versus escape speed

Circular orbital speed is vorb = √(GM/r). Escape speed is √2 times larger, so Earth’s near-surface orbital speed is about 7.9 km/s. The results panel shows both, helping you compare “staying in orbit” versus “leaving entirely.”

5) Energy view: J/kg you must supply

Compare bodies using specific kinetic energy: E = ½v². Earth’s 11.2 km/s corresponds to roughly 62 million J/kg. The Moon’s 2.4 km/s is near 2.8 million J/kg. Small speed differences can therefore hide big energy gaps.

6) Gravity at the surface

Surface gravity is computed from g = GM/r². Earth is about 9.81 m/s², while Mars is about 3.7 m/s². Higher gravity increases ascent losses, so real rockets often need more than the ideal escape figure.

7) Atmosphere, rotation, and altitude

This model ignores drag, heating, and steering losses. Rotation can reduce required speed if you launch eastward near the equator. Altitude helps too: escape speed drops as r increases. Use the calculator as a clean baseline, then add margins for real missions.

8) Using the tool for quick checks

Start with a preset to sanity-check your output, then switch to custom mode for asteroids, exoplanets, or engineered spheres. Choose units carefully to avoid scale mistakes. Export CSV for comparisons, or PDF for sharing a clear summary. It also helps validate homework problems and quick mission trade studies reliably today.

1) What is the difference between escape velocity and orbital velocity?

Orbital velocity keeps you circling at a chosen altitude. Escape velocity is the threshold to leave forever with zero speed at infinity, assuming no atmosphere and no thrust after launch.

2) Why does escape velocity equal √2 times the circular orbital speed?

Both come from the same gravity model. Circular orbit needs GM/r worth of energy per unit mass, while escape needs 2GM/r. Taking square roots gives v_esc = √2 · v_orb.

3) Does atmosphere change the required speed?

Yes. Drag and climbing through dense air add losses, and heating may limit trajectories. The calculator provides the ideal gravitational baseline; real missions typically need additional margin.

4) If I start higher than the surface, will escape velocity be lower?

Yes. Escape velocity decreases with distance from the center because r increases. Enter a larger radius if you want to approximate a launch from altitude above the mean surface.

5) Can I escape without ever reaching the listed speed instantly?

Yes. Continuous thrust over time can add the necessary energy even if your instantaneous speed is lower early on. The escape value describes total energy needed, not a single mandatory moment.

6) Why can I edit the gravitational constant?

It helps for sensitivity checks, classroom demonstrations, or alternative unit systems. For normal physics use, keep the default value. Small changes in G proportionally affect all computed results.

7) How accurate are the presets?

Presets use typical mean masses and radii, so results are approximate. Real bodies vary with latitude, altitude, and rotation. For higher fidelity, enter custom values matching your reference source.