Home › Calculators › Escape Velocity Calculator
Escape Velocity Calculator
Find how fast something must go to escape the gravity of Earth, the Moon, Mars, the Sun or any body you define. You also get the circular orbital velocity, the orbital period at that height and the surface gravity.
Last updated:
km
0 = from the surface
Enter your values to see the result.
Advertisement
Advertisement
How to use the Escape Velocity Calculator
- Choose a body or pick Custom and enter its mass and radius.
- Add an altitude if you start above the surface.
- Read the escape velocity in km/s, m/s and km/h.
- Compare with orbital velocity and other bodies in the table.
Escape velocity and orbital velocity formulas
| Quantity | Formula | Earth (surface) |
|---|---|---|
| Escape velocity | ve = √(2GM / r) | 11.19 km/s |
| Circular orbital velocity | vo = √(GM / r) = ve / √2 | 7.91 km/s |
| Surface gravity | g = GM / R² | 9.82 m/s² (not counting rotation) |
| Orbital period | T = 2π √(r³ / GM) | 84.3 min (at the surface) |
G = 6.6743 × 10⁻¹¹ N·m²/kg². Earth: M = 5.9722 × 10²⁴ kg, mean radius 6,371 km.
Escape velocities in the Solar System
| Body | Escape velocity |
|---|---|
| Sun | 617.7 km/s |
| Jupiter | 60.2 km/s |
| Saturn | 36.1 km/s |
| Neptune | 23.6 km/s |
| Uranus | 21.4 km/s |
| Earth | 11.19 km/s |
| Venus | 10.36 km/s |
| Mars | 5.03 km/s |
| Mercury | 4.25 km/s |
| Moon | 2.38 km/s |
| Pluto | 1.21 km/s |
Values are for the mean radius, without atmosphere or rotation. Planets with no solid surface use the 1-bar level radius.
Frequently asked questions
What is the escape velocity formula?
v = √(2GM / r), where G = 6.6743 × 10⁻¹¹ N·m²/kg² is the gravitational constant, M the mass of the body and r the distance from its centre. It is the speed at which kinetic energy equals the gravitational binding energy.
What is Earth's escape velocity?
About 11.19 km/s (40,270 km/h or 25,020 mph) from the surface, ignoring air resistance and Earth's rotation.
What is the escape velocity of the Moon and Mars?
About 2.38 km/s for the Moon and about 5.03 km/s for Mars, from the surface.
How is escape velocity related to orbital velocity?
At the same distance, escape velocity is √2 (about 1.414) times the circular orbital velocity. Near Earth's surface the orbital velocity is about 7.9 km/s and the escape velocity about 11.2 km/s.
Does escape velocity depend on the mass of the rocket?
No. The mass of the escaping object cancels out, so a pebble and a spacecraft need the same speed. Heavier rockets just need more energy to reach it.
Why is escape velocity lower at higher altitude?
Because r is larger, so gravity is weaker. From the ISS altitude of about 408 km, Earth's escape velocity drops to about 10.84 km/s.
Do rockets actually travel at escape velocity?
Not necessarily. Escape velocity is for an unpowered object launched once. Rockets keep thrusting, so they can leave slowly, but in practice deep-space probes are boosted to near escape speed and use Earth's rotation and gravity assists to save fuel.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.
Related tools
Pendulum Period CalculatorPendulum period and frequency from length and gravity, or length from period.Time Dilation CalculatorLorentz factor, dilated time and length contraction from speed and proper time.Gravitational Force CalculatorNewton's law of gravitation F = Gm₁m₂/r² for any two masses, with planet presets.Free Fall CalculatorFall time and impact velocity from a height, or height from time or speed, with a chart and table.Speed Distance Time CalculatorSolve for speed, distance or travel time and get your arrival time.Half Life CalculatorSolve radioactive decay for amount left, half-life, time or initial amount, with a curve.Kinetic Energy CalculatorSolve KE = ½mv² and PE = mgh for energy, mass, speed or height, with unit conversions.Projectile Motion CalculatorRange, max height, flight time and impact speed of a projectile, with an animated trajectory.Meeting Cost CalculatorWork out what a meeting really costs from attendees and salaries, with a live cost ticker.Velocity CalculatorSolve v = d/t and a = Δv/t for any variable, plus a SUVAT solver for any three kinematics values.Torque CalculatorSolve τ = r·F·sin θ for torque, force, lever arm or angle, and convert torque to power at any rpm.Wavelength Frequency CalculatorConvert frequency to wavelength and back for light, radio or sound, with photon energy and band.Acceleration CalculatorAcceleration from velocity change and time, distance and time, or force and mass.Force CalculatorSolve F = ma for force, mass or acceleration, plus weight on every planet.Density CalculatorSolve density, mass or volume with unit conversion and a table of common material densities.Momentum CalculatorCalculate momentum (p = mv), mass, velocity, impulse and momentum change with unit conversion.Potential Energy CalculatorGravitational PE = mgh and spring PE = ½kx²: solve for energy, mass, height, k or stretch.Power CalculatorCalculate power from work and time, force and velocity, or volts and amps, in W, kW and hp.PPI CalculatorPixel density (PPI), dot pitch and retina viewing distance from resolution and screen size.Download Time CalculatorHow long a file takes to download at your internet speed, or the speed you need.Pressure CalculatorSolve P = F/A for pressure, force or area in Pa, kPa, bar, psi and atm.Work CalculatorSolve W = F·d·cos θ for work, force, distance or angle in J, kWh and ft-lb.Hooke's Law CalculatorSolve F = kx for spring force, spring constant or extension, plus stored spring energy.Centripetal Force CalculatorCentripetal force and acceleration from mass, radius and speed or RPM: F = mv²/r.Speed of Sound CalculatorSpeed of sound from air temperature or medium, and distance from an echo or thunder delay.Doppler Effect CalculatorObserved frequency from source and observer speeds, or source speed from a pitch shift.Specific Heat CalculatorSolve Q = mcΔT for heat energy, mass, specific heat or temperature change, with materials.Decibel CalculatorAdd dB levels, convert power or voltage ratios to dB, and find sound level at a distance.Bernoulli Equation CalculatorSolve Bernoulli's equation for pressure, velocity or height, with pipe continuity and flow.Buoyancy CalculatorBuoyant force from fluid density, volume and gravity, with a float or sink check.Friction Force CalculatorStatic and kinetic friction from material presets, normal force or mass and incline angle.Inclined Plane CalculatorForces, acceleration and push force for a mass on a slope with friction.Light Travel Time CalculatorHow long light or radio takes to reach the Moon, Sun, Mars, Voyager 1 or any distance.E=mc2 CalculatorConvert mass to energy and back with E=mc², in joules, kWh, eV and tons of TNT.Orbital Period CalculatorOrbital period from central mass and semi-major axis with Kepler's third law and presets.Photon Energy CalculatorPhoton energy in eV and joules from wavelength or frequency, with momentum and color.Snell's Law CalculatorRefraction angle, critical angle and total internal reflection from n₁, n₂ and the angle.Speeds and Feeds CalculatorSpindle RPM and feed rate (mm/min, in/min) from tool size, flutes, surface speed and chip load.Coulomb's Law CalculatorElectrostatic force between two charges, attractive or repulsive; solve for charge or distance.Cpk CalculatorCp, Cpk, Pp, Ppk and ppm out of spec from your data or mean and standard deviation.Crosswind Component CalculatorCrosswind and headwind/tailwind components for any runway and wind, with gusts and a diagram.Drag Force CalculatorAerodynamic or hydrodynamic drag force and power from Cd, frontal area, speed and density.E85 Blend CalculatorHow many gallons of E85 and gas to add to hit a target ethanol blend like E30 or E50.Elastic Collision CalculatorGet final velocities after a 1D elastic collision, with momentum and kinetic energy checks.G-Force CalculatorCalculate g-force from turn speed and radius, a speed change over time, or any acceleration.Heat Transfer CalculatorConduction heat flow in W and BTU/h through one or more layers, with R-value and U-value.Helium Balloon Lift CalculatorHow much a helium balloon lifts in grams and how many balloons you need for a payload.Hydrostatic Pressure CalculatorGauge and absolute pressure at any depth in water, seawater, oil or a custom fluid.Impact Force CalculatorAverage impact force and g-force from mass, drop height or speed, and stopping distance/time.Impulse CalculatorFind impulse from force × time or momentum change, or solve for average force or time.Inverse Square Law CalculatorFind light, sound or radiation intensity at a new distance, or the distance for a target.Lever CalculatorEffort force, load or arm length for class 1, 2 and 3 levers, with mechanical advantage.Lightning Distance CalculatorTap at the flash and again at the thunder to see how far away lightning struck, in miles and km.Magnetic Declination CalculatorFind magnetic declination, inclination and field strength for any place and date (WMM2025).Map Radius ToolDraw circles of any radius around points on a map, with multiple rings and a share link.MTBF CalculatorMTBF, failure rate, availability and mission reliability from operating hours and failures.Pipe Pressure Drop CalculatorDarcy-Weisbach pressure drop and head loss with Reynolds number and Colebrook friction factor.Refrigerant PT ChartPressure-temperature chart for R-410A, R-32, R-454B, R-22, R-134a, R-404A and more.Reynolds Number CalculatorReynolds number and laminar, transitional or turbulent regime for pipes, ducts, plates and spheres.RMS Voltage CalculatorConvert peak, peak-to-peak, RMS and average voltage for sine, square and triangle waves.Spring Rate CalculatorCompression spring rate from wire size, coil diameter, coils and material, plus solid height.Standard Atmosphere (ISA) CalculatorISA 1976 temperature, pressure, density, speed of sound and viscosity at any altitude to 86 km.Steam Table CalculatorSaturated and superheated steam properties: enthalpy, entropy, volume and quality (IAPWS-IF97).Superheat and Subcooling CalculatorFind superheat, subcooling and target values from gauge pressures and line temperatures.Thermal Expansion CalculatorLinear, area or volume expansion from size, temperature change and material coefficient.Top of Descent CalculatorWhen to start descending: distance and time to top of descent, required fpm, 3-degree rule.True Airspeed CalculatorTrue airspeed, Mach number and density altitude from IAS/CAS, pressure altitude and OAT.Valve Cv CalculatorSize a valve: required Cv or Kv for liquid, gas or steam, or flow and pressure drop from Cv.