Find the speed needed to escape a planet or moon from its mass and radius, shown in m/s, km/h and km/s with the surface gravity for comparison.
kg
km
Results
Calculated
Escape velocity
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m/s
Escape velocity
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km/h
Escape velocity
—
km/s
Surface gravity
—
m/s² at this radius
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What escape velocity means
Escape velocity is the minimum speed at which an object must move, ignoring air drag and engine thrust, to coast away from a body's gravity and never fall back. It does not depend on the mass of the escaping object, only on the mass of the planet, moon or star and on how far from its center you start.
Use this calculator for astronomy and physics coursework, for comparing worlds (why rockets need about 11 km/s from Earth but only about 2.4 km/s from the Moon), or for checking whether a small body can hold an atmosphere. Pick a preset body or choose Custom and enter your own mass and radius.
The formula
vesc = √(2GM / r), where G = 6.6743 × 10-11 N·m²/kg², M is the mass in kg and r is the distance from the body's center in meters (the calculator takes km and converts). Surface gravity is g = GM / r². The speed of a circular orbit at the same radius is vesc / √2.
Worked example
For Earth, M = 5.972 × 1024 kg and r = 6,371 km = 6.371 × 106 m, which are the default inputs. GM = 6.6743 × 10-11 × 5.972 × 1024 = 3.986 × 1014. Then 2GM / r = 7.972 × 1014 / 6.371 × 106 = 1.251 × 108, and the square root is about 11,186 m/s, or 11.19 km/s. Multiplying by 3.6 gives roughly 40,270 km/h. Surface gravity is 3.986 × 1014 / (6.371 × 106)² = 9.82 m/s².
Common mistakes
Using altitude instead of radius. The radius is measured from the body's center, so add the body's radius to any height above the surface.
Entering mass in the wrong units. Mass must be in kilograms and radius in kilometers.
Treating it as a required launch speed. Real rockets never reach escape velocity at the ground; they keep thrusting and gain speed while climbing, and atmospheric drag adds losses.
Frequently Asked Questions
Does escape velocity depend on the mass of the rocket?
No. Only the mass of the body and the starting distance from its center matter. A satellite and a spacecraft need the same speed from the same point, ignoring thrust and drag.
Is escape velocity the same as orbital velocity?
No. Circular orbital speed at a given radius is escape velocity divided by the square root of two, about 7.9 km/s at Earth's surface. Going faster than that but below escape speed gives an elliptical orbit.
Why does the speed drop at higher altitude?
Because r is larger and gravity is weaker. Escape speed from 400 km above Earth is about 10.8 km/s instead of 11.2 km/s at the surface.
Can I use it for a black hole?
Only as a rough Newtonian estimate. Set the escape velocity equal to the speed of light to get the Schwarzschild radius, but this calculator does not include relativistic effects.
Practical Guide for Escape Velocity Calculator | Orbital Mechanics & Space Physics Tool
Escape Velocity Calculator | Orbital Mechanics & Space Physics Tool is most useful when the inputs reflect the situation you are actually planning around, not a best-case estimate. Treat the result as a decision aid: it gives you a structured way to compare assumptions, spot outliers, and decide what to verify next. For Physics work, the most important review lens is units, idealized assumptions, boundary conditions, measurement precision, and expected physical scale.
Start with a baseline run using values you can defend. Then change one assumption at a time and watch which output moves the most. If one input dominates the result, spend your verification time there first. If several inputs have similar influence, use a conservative scenario and an optimistic scenario to create a practical range instead of relying on a single exact number.
Before acting on the result, verify the output with dimensional analysis, known reference values, or a second formula when possible. This is especially important when the calculator supports a purchase, project plan, performance target, or operational decision. The calculator can make the math consistent, but the quality of the conclusion still depends on current data, clear units, and assumptions that match your real constraints.
When the output looks surprising, slow down and inspect each input in order. A small change in one high-leverage field can move the final number more than several low-leverage fields combined. For Escape Velocity Calculator | Orbital Mechanics & Space Physics Tool, that means you should first confirm the value with the greatest scale, then confirm the value with the greatest uncertainty, then rerun the calculator with conservative and optimistic assumptions. This sequence turns the calculator from a single answer into a practical decision range.
Review Checklist
Confirm every input uses the unit and time period requested by the calculator.
Run a low, expected, and high scenario so the answer has a useful range.
Check whether rounding or a missing decimal place changes the decision.
Update the calculation whenever the object, medium, force, distance, time, or measurement method changes.