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Escape Velocity Calculator

Calculates escape velocity and orbital velocity for any planet or moon, or for a body of your own mass and radius.

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Optional. Set both this and the radius to override the body above.
Enter your figures and press Calculate.
In short Escape velocity is the speed at which an object's kinetic energy exactly equals the gravitational energy binding it, so it can coast away and never fall back: v = √(2GM/r). From Earth's surface that is 11.186 km/s, or about 40,300 km/h. The circular orbital velocity at the same radius is 7.910 km/s, and the ratio between them is exactly √2 — not approximately. Escaping needs twice the kinetic energy of circling, and energy goes as v², so the speed ratio is the square root of two. The page prints that ratio so you can watch two separate calculations produce one exact relationship. Escape velocity does not depend on the mass of the thing escaping: a pebble and a rocket need the same speed. What differs is the fuel needed to reach it. And no rocket actually launches at this speed — a rocket climbs under continuous thrust and never needs it in one go, which is why the figure matters for asteroid impacts and for whether a planet can hold on to an atmosphere rather than for spaceflight. This page stores only two numbers per body, GM and a mean radius; surface gravity, escape velocity and orbital velocity are all derived, so the table cannot quietly disagree with itself.

How to use the Escape Velocity Calculator

  1. Enter your figures in the input fields.
  2. The result updates as you type, together with the full working.
  3. Check the breakdown table to see exactly how the number was reached.

About the Escape Velocity Calculator

Escape and orbital velocity for any body, derived from its GM and radius.

What people use it for

  • Comparing the gravity wells of different planets.
  • Astronomy and physics homework.
  • Working out escape velocity for a made-up body.

Details

Earth11.186 km/s
The Moon2.376 km/s
Mars5.027 km/s
Escape ÷ orbital velocityexactly √2, for every body
Derived surface gravity of Earth9.820 m/s², not the defined 9.80665

The maths behind it

This tool uses v = √(2GM ÷ r), which is exactly √2 times the circular orbital velocity √(GM ÷ r) at the same radius. Every intermediate value is shown on screen, so the result can be checked by hand.

Only GM and a mean radius are stored for each body. Surface gravity, escape velocity and orbital velocity are all computed from those two, and the √2 ratio between the last two is printed as a check.

Where this tool stops

Every body is treated as a non-rotating sphere with no atmosphere. Rotation genuinely helps a launch — going east from near the equator is worth a few hundred metres per second, which is why launch sites cluster there — and for the oblate giants the mean radius differs materially from the equatorial one.

Frequently asked questions

Does escape velocity depend on what is escaping?
No. The mass of the escaping object cancels out entirely, so a pebble and a spacecraft need the same speed. Only the fuel required to reach it differs.
Do rockets reach escape velocity?
Not usually, and they do not need to. Escape velocity is what a projectile with no engine would need in a single push. A rocket thrusts continuously and can leave at any speed given enough fuel.
Why is the derived surface gravity not 9.80665?
Because 9.80665 is a DEFINED conventional value for weights and measures, not a measurement of Earth. A perfect sphere of Earth's GM and mean radius gives 9.820, and the real value varies with latitude, altitude and rotation.
Why does this differ from the quoted figure for Jupiter?
Reference tables quote Jupiter and Saturn at their EQUATORIAL radius, which is thousands of kilometres larger than the mean radius used consistently here. Both are correct about different radii, and the page says so on those two bodies.
Does the Escape Velocity Calculator cost anything?
No charge and no sign-up. There is no free tier to run out of because there is no paid tier — inputtesthub.com is funded by advertising rather than by metering the tool.
Is my data uploaded anywhere?
No. The Escape Velocity Calculator runs entirely in your browser using JavaScript. Because the work happens locally, the tool also keeps working if your connection drops, and closing the tab is all it takes to discard everything.
Can I check the maths myself?
It uses v = √(2GM ÷ r), which is exactly √2 times the circular orbital velocity √(GM ÷ r) at the same radius. The full working is printed under the result, so you can follow every step rather than trusting a black box.
Can you show an example?
Enter Earth and the Escape Velocity Calculator returns 11.186 km/s, orbital 7.910 km/s.
What do people use the Escape Velocity Calculator for most?
In practice it gets used for three things: comparing the gravity wells of different planets. Astronomy and physics homework. Working out escape velocity for a made-up body. It is built for exactly those cases rather than being a general-purpose tool with this bolted on.
When is the Escape Velocity Calculator not the right tool?
Every body is treated as a non-rotating sphere with no atmosphere. Rotation genuinely helps a launch — going east from near the equator is worth a few hundred metres per second, which is why launch sites cluster there — and for the oblate giants the mean radius differs materially from the equatorial one. Knowing where a tool stops being trustworthy matters more than the cases where it works.
Which values should I know?
Earth is 11.186 km/s. The Moon is 2.376 km/s. Mars is 5.027 km/s. These are printed on the page itself, so you do not have to take them on trust.
Can I rely on this for exact work?
The calculation runs in double precision and the result is shown to ten significant figures, so converting a value and converting it back returns the original. What is displayed is rounded for readability; what is copied is not.

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