Escape Velocity Calculator
Calculate escape velocity for any celestial body using the formula v_e = sqrt(2GM/R). Free online physics calculator for students, educators, and space enthusiasts.
About This Calculator
Escape velocity is the minimum speed a non-propelled object must attain to break free from a celestial body's gravitational pull without any further acceleration. Governed by Newton's law of universal gravitation and the conservation of energy, the formula v_e = sqrt(2GM/R) shows that escape velocity depends only on the mass M and radius R of the celestial body — the escaping object's own mass is irrelevant. Our calculator supports six celestial bodies (Earth, Sun, Moon, Mars, Jupiter, Saturn) with accurate mass and radius data from NASA and JPL.
For each calculation, you get three key results: escape velocity (km/s), first cosmic velocity also known as orbital velocity (km/s), and surface gravity (m/s²). The Velocity vs Radius chart shows how escape velocity decreases as the distance from the body's center increases, illustrating the inverse square root relationship. The Body Comparison chart lets you compare surface escape velocities across all six bodies at a glance — from the Moon's gentle 2.4 km/s to Jupiter's immense 59.6 km/s.
Understanding Escape Velocity
The formula v_e = sqrt(2GM/R) is derived from setting kinetic energy (1/2 mv^2) equal to gravitational potential energy (GMm/R). The constant G = 6.674 x 10^-11 N-m^2/kg^2 is the universal gravitational constant. For Earth (mass 5.972 x 10^24 kg, radius 6371 km), escape velocity is approximately 11.2 km/s. This is sqrt2 times the orbital velocity (7.9 km/s), which is the speed needed to maintain a circular low Earth orbit. Rockets launching from Earth must reach this speed to send payloads beyond Earth's influence — the foundation of all interplanetary exploration.
ISRO's Chandrayaan and Mangalyaan missions, NASA's Artemis lunar program, and ESA's planetary missions all depend on precise escape velocity calculations. The first cosmic velocity result tells you the minimum speed for stable orbit, while the escape velocity tells you what is needed for interplanetary travel. Students and researchers worldwide can use this calculator for academic study, mission planning, and understanding the fundamental physics that governs space exploration.
Frequently Asked Questions
What is escape velocity and how is it calculated?
Escape velocity is the minimum speed a non-propelled object needs to break free from a celestial body's gravitational pull without further acceleration. It is calculated using the formula v_e = sqrt(2GM/R), where G is the gravitational constant (6.674 x 10^-11 N-m^2/kg^2), M is the mass of the body in kilograms, and R is the radius from the center in meters. For Earth at sea level, escape velocity is approximately 11.2 km/s.
What is the difference between escape velocity and orbital velocity?
Orbital velocity (v = sqrt(GM/R)) is the speed needed to maintain a stable circular orbit around a body, while escape velocity (v_e = sqrt(2GM/R)) is the speed needed to leave its gravitational influence entirely. Escape velocity is exactly sqrt2 times the orbital velocity at the same radius. For Earth, orbital velocity at sea level is about 7.9 km/s, while escape velocity is about 11.2 km/s.
What is the escape velocity of Earth in km/s and mph?
Earth's escape velocity is 11.2 km/s at the surface, which is approximately 6.96 miles per second or about 25,000 mph (40,270 km/h). This is the speed a rocket must reach to leave Earth's gravity without continuous thrust, disregarding atmospheric drag.
How does escape velocity vary between different celestial bodies?
Escape velocity depends on the mass and radius of the celestial body. Larger mass and smaller radius both increase escape velocity. Mercury has 4.3 km/s, Venus 10.3 km/s, Earth 11.2 km/s, Moon 2.4 km/s, Mars 5.0 km/s, Jupiter 59.6 km/s, Saturn 35.6 km/s, Uranus 21.3 km/s, and Neptune 23.8 km/s. Our calculator's Body Comparison chart visualizes these differences.
What is the first cosmic velocity?
The first cosmic velocity, also known as orbital velocity, is the minimum speed an object needs to achieve a stable circular orbit around a celestial body. It is equal to the escape velocity divided by sqrt2. For Earth, the first cosmic velocity is about 7.9 km/s. Satellites in low Earth orbit travel at approximately this speed to maintain their orbit.
Can this calculator help with Indian, US, and UK space missions?
Yes. ISRO, NASA, ESA, and UK Space Agency all use the same Newtonian mechanics. ISRO's Chandrayaan missions needed to exceed Earth's escape velocity (11.2 km/s) to reach the Moon. NASA's Artemis program requires precise escape velocity calculations for lunar trajectories. UK-built satellites deployed from ISS also rely on accurate orbital and escape velocity data from the same formulas.
Does the mass of the escaping object affect escape velocity?
No, escape velocity is independent of the mass of the escaping object. This comes from the cancellation of mass m in the energy conservation equation: the kinetic energy (1/2 mv^2) and gravitational potential energy (-GMm/R) both contain m, which cancels out. A 1 kg satellite and a 1,000 kg spacecraft both need the same speed to escape from the same celestial body.
What happens if an object travels exactly at escape velocity?
If an object reaches exactly escape velocity, its kinetic energy equals the gravitational potential energy binding it to the body. As it moves away, gravity continuously slows it down, and its speed approaches zero at infinite distance. To leave the body with residual speed for interplanetary travel, the object must exceed escape velocity. Rockets typically reach about 11.2 km/s to escape Earth.