Escape Velocity Calculator
Compute the minimum speed needed to escape any planetary body at any altitude, plus the circular orbital velocity and orbital period.
🚀 What is Escape Velocity?
Escape velocity is the minimum speed a free-flying object must reach to permanently escape a gravitational field without further propulsion. Once an object is launched at or above escape velocity in any direction, gravity will continuously decelerate it but will never bring it to a complete stop, allowing it to travel infinitely far from the source body. The concept was formalized by Isaac Newton in his 1687 Principia Mathematica and is now a foundational quantity in orbital mechanics, planetary science, and spacecraft mission design.
The formula is derived by equating kinetic energy with gravitational potential energy: setting (1/2)mv squared equal to G x M x m / r gives v_esc = sqrt(2 x G x M / r) = sqrt(2 x mu / r). Three real-world facts follow immediately: escape velocity depends only on the mass of the body and the distance from its center, not on the mass of the escaping object; escape velocity decreases with altitude (doubling the distance from center reduces v_esc by a factor of sqrt(2)); and escape velocity is always exactly sqrt(2) = 1.4142 times the circular orbital velocity at the same altitude.
This calculator covers both major uses. The Escape Velocity mode computes the speed needed to escape from any altitude above eight solar system bodies (including a custom body option for exoplanets, asteroids, or comets) and shows how much additional delta-V a spacecraft would need if it is already moving at a given speed. The Orbital Velocity mode computes the circular orbital speed, the altitude for a desired orbital speed, and the resulting orbital period, all derived from the same gravitational parameter.
Practical applications range from launch vehicle design (what speed must the final stage reach to leave Earth?) to planetary protection (can an asteroid escaping its parent body reach Earth?) to habitability studies (does a planet retain its atmosphere against solar radiation stripping?). For atmosphere retention, the thermal escape criterion states that a planet can hold onto a gas species if the mean thermal speed of that gas is less than about one sixth of the planet's escape velocity.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Earth Escape Velocity at 200 km LEO
Find escape velocity from a 200 km circular parking orbit around Earth
Example 2 - Moon Surface Escape Velocity
Apollo ascent stage: what speed is needed to escape the Moon from the surface?
Example 3 - Jupiter Escape at 50,000 km Altitude
Escape velocity at 50,000 km above Jupiter cloud tops (Galileo probe entry altitude reference)
❓ Frequently Asked Questions
🔗 Related Calculators
What is escape velocity and how is it calculated?
Escape velocity is the minimum speed needed to escape a gravitational field without further propulsion. It is derived by setting kinetic energy equal to gravitational potential energy: (1/2)mv^2 = G*M*m/r, giving v_esc = sqrt(2*G*M/r) = sqrt(2*mu/r), where mu = G*M is the gravitational parameter and r is the distance from the body's center. For Earth at the surface: v_esc = sqrt(2 x 3.986e14 / 6378100) = 11.19 km/s. No thrust is needed after the initial burn since the object continues to slow down but never quite stops.
What is the escape velocity of Earth from the surface?
Earth's escape velocity at the surface (sea level) is 11.186 km/s (40,270 km/h or 25,020 mph). This assumes no atmospheric drag. In practice, rockets do not fly straight up at escape velocity; instead, they follow a gravity turn trajectory to reach orbit, then burn to escape. The actual delta-V needed from Earth's surface to escape the solar system is about 8.8 km/s when launched from LEO, plus 3.2 km/s to reach LEO, totaling around 12 km/s from the ground including gravity and drag losses.
What is the difference between escape velocity and orbital velocity?
Orbital velocity (first cosmic velocity) is the speed needed to maintain a circular orbit just above a planet's surface. Escape velocity (second cosmic velocity) is the speed needed to escape the gravitational field entirely. The ratio is always sqrt(2): v_esc = sqrt(2) x v_orb = 1.4142 x v_orb. For Earth at the surface: v_orb = 7.91 km/s and v_esc = 11.19 km/s. A spacecraft already in low circular orbit needs to increase its speed by only 41.4% to reach escape velocity.
Does escape velocity depend on the direction of launch?
No. Escape velocity is a scalar magnitude, not a vector. A spacecraft launched radially outward, tangentially, or at any angle needs the same total speed to escape. The direction only affects the trajectory shape. However, launching tangentially in the direction of the planet's rotation gives a free boost from the planet's rotational speed, which is why equatorial launch sites like Kourou and Cape Canaveral are preferred. Earth's equatorial rotation adds about 0.465 km/s to an eastward launch.
What is the escape velocity of the Moon?
The Moon's escape velocity at the surface is 2.376 km/s (8,553 km/h). This is about one fifth of Earth's escape velocity, which is why returning from the Moon requires far less propellant than launching from Earth. The Apollo lunar module ascent stage used a single Ascent Propulsion System engine to reach lunar orbit, achieving a velocity of about 1.68 km/s, well below lunar escape velocity, to rendezvous with the command module in low lunar orbit.
What is the escape velocity of Mars?
Mars escape velocity at the surface is 5.027 km/s, about 45% of Earth's. Orbital velocity at Mars surface is 3.555 km/s, giving an orbital period of about 1.76 hours for a surface-skimming orbit. The escape velocity at 300 km altitude (a practical low Mars orbit) is 4.81 km/s. Mars Return Vehicle designs for human exploration must achieve this to leave Mars, which is a significant propellant mass constraint and a key design driver for in-situ propellant production on the Martian surface.
How does altitude affect escape velocity?
Escape velocity decreases with altitude as v_esc = sqrt(2*mu/r), where r = body radius + altitude. Since r appears in the denominator under a square root, v_esc is proportional to 1/sqrt(r). Doubling the distance from the center (roughly doubling altitude for low altitudes) reduces escape velocity by 1/sqrt(2) = 29.3%. For Earth: surface v_esc = 11.19 km/s, at 200 km = 11.01 km/s, at 400 km = 10.84 km/s, at GEO (35,786 km) = 4.35 km/s, at lunar distance (384,400 km) = 1.44 km/s.
What is the escape velocity of Jupiter?
Jupiter's surface escape velocity is 59.54 km/s, the highest of any planet in the solar system. At 50,000 km altitude above the cloud tops: v_esc = 45.65 km/s. This enormous escape velocity is what makes the Oberth effect so powerful for Jupiter flybys: firing even a small burn at Jupiter periapsis is amplified enormously by the high local speed. The Galileo probe that descended into Jupiter's atmosphere was moving at about 48 km/s when it entered the atmosphere.
Can escape velocity be exceeded gradually?
Yes. The escape velocity formula assumes a single instantaneous burn with no further thrust (ballistic trajectory). Ion engines and other low-thrust propulsion systems can escape a gravitational field by thrusting continuously at speeds below escape velocity, gradually spiraling outward. The total delta-V needed for a spiral escape from a circular orbit is slightly more than the single-burn value (about 3-5% more for typical cases), but the advantage is that ion engines have far higher Isp than chemical rockets, making the overall propellant efficiency much better.
What is third cosmic velocity?
The three cosmic velocities are defined for Earth. First cosmic velocity (7.91 km/s) is the circular orbital speed just above Earth's surface. Second cosmic velocity (11.19 km/s) is Earth's surface escape velocity. Third cosmic velocity (16.6 km/s from Earth's surface, or about 12.3 km/s added to Earth's orbital speed from a starting point at Earth's distance from the Sun) is the speed needed to escape the entire solar system. This was achieved by Voyager 1 and 2 using gravity assists from Jupiter and Saturn.
What is the escape velocity of a neutron star or black hole?
For a neutron star of mass 1.4 solar masses and radius 10 km: v_esc = sqrt(2 x 1.327e20 x 1.4 / 10000) = sqrt(3.72e16) = 193,000 km/s, which is 64% of the speed of light. At this level, relativistic effects are significant and the Newtonian formula underestimates the true escape speed. For a black hole, the escape velocity at the event horizon (Schwarzschild radius) equals c (the speed of light), which is why nothing, not even light, can escape. The Schwarzschild radius for an Earth-mass black hole would be about 8.9 mm.
How do I use this calculator for a rocket mission?
Select the destination body, enter the planned periapsis or departure altitude in km, and read the escape velocity. For the Escape Velocity mode, optionally enter your current speed to see the additional delta-V needed. For the Orbital Velocity mode, enter your planned orbital speed to find what altitude that corresponds to and the orbital period. These values are the starting points for Tsiolkovsky rocket equation calculations to determine the required propellant mass fraction for the escape maneuver.
What is the escape velocity of the Sun at Earth's distance?
The Sun's escape velocity at Earth's mean orbital distance of 1 AU (149.6 million km) is 42.1 km/s. Earth's orbital speed is 29.78 km/s, so a spacecraft at Earth's orbit moving purely radially would need 42.1 km/s to escape the Sun. However, since Earth is already orbiting at 29.78 km/s, a tangential burn needs to add only sqrt(42.1 squared minus 29.78 squared) minus 29.78 = 12.3 km/s beyond Earth's orbital speed to escape the solar system. This is why New Horizons needed a large Jupiter gravity assist to reach Pluto within a decade.