This escape velocity calculator finds the speed an object needs to leave a body’s gravity forever — from the body’s mass and radius — with presets for the solar system’s famous (and infamous) gravity wells.

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v = √(2GM/R) — Where Kinetic Energy Outruns Gravity

Set kinetic energy ½mv² equal to the gravitational potential well’s depth GMm/R and the m cancels: escape speed depends only on the body you’re leaving. It’s also independent of direction (straight up, sideways — any unpowered trajectory that doesn’t intersect the planet). Staying instead of leaving: our Orbital Velocity Calculator. Part of our Physics Calculators collection.

Worked Examples (Verified, via Presets)

  • Earth: √(2 × 6.674×10⁻¹¹ × 5.972×10²⁴ ÷ 6.371×10⁶) = 11.19 km/s — about Mach 33, and the reason chemical rockets are mostly fuel
  • Moon: 2.38 km/s — the Apollo lunar modules’ modest ascent stage sufficed; no atmosphere, small well
  • Jupiter: 59.5 km/s — leaving the king is five Earths’ worth of hard; probes exploit gravity assists precisely because direct escape is ruinous
  • Sun (from its surface): 617.5 km/s; from Earth’s orbit (1 AU) it’s 42.1 km/s — Parker Solar Probe’s “fastest object” records play in this arithmetic

Clarifications That Matter

  • Escape velocity is a speed (scalar): direction only matters insofar as the trajectory must not hit the body or plow through too much atmosphere.
  • Powered flight can leave at ANY speed given enough thrust duration (a space elevator ascends at m/s) — escape velocity is the *ballistic* requirement: one push, no engine, coast forever.
  • It decreases with altitude as 1/√r — leaving from a high orbit is cheaper, which is why departure stages wait for orbit before burning for deep space.
  • Nothing escapes a black hole because the formula (Newtonian coincidence) meets c at the Schwarzschild radius — general relativity’s home turf.

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Frequently Asked Questions

What is Earth’s escape velocity?

11.19 km/s (about 40,300 km/h) from the surface, ignoring atmosphere and rotation. This calculator reproduces it from Earth’s mass (5.972×10²⁴ kg) and radius (6,371 km) via v = √(2GM/R) — and gives any other body’s figure from the same formula.

Does escape velocity depend on the object’s mass?

No — the object’s mass appears on both sides of the energy equation and cancels. A gram and a gigaton need the same 11.19 km/s from Earth. What scales with mass is the energy (½mv²) someone must supply, which is why launch costs are quoted per kilogram.

Why don’t rockets launch at 11.2 km/s?

They accelerate gradually (an instant 11.2 km/s at sea level would mean lethal g-forces and atmospheric incineration), lose speed to drag and gravity along the way, and typically target orbit (7.8 km/s) rather than escape. Total velocity budget (delta-v) to low orbit is ~9.4 km/s including losses — the rocket equation’s tyranny is about budgets, not a single speed.

What is the escape velocity from the Sun?

From the solar surface: 617.5 km/s. From Earth’s location in the Sun’s gravity well: 42.1 km/s (which is √2 × Earth’s 29.8 km/s orbital speed — the same √2 relation as surface orbits). Probes leaving the solar system stack Earth’s orbital motion, planetary assists and their own burns to reach it.

Escape velocity vs orbital velocity — what’s the relation?

At any given distance, escape = √2 × circular-orbit velocity. Orbit is “falling around” the body at v = √(GM/r); multiply by 1.414 and the trajectory opens into a parabola that never returns. Both calculators show their side of that relation.

Is this escape velocity calculator free?

Yes — free, instant, no sign-up.