Orbital Velocity Calculator - Circular Orbit Speed Tool

An orbital velocity calculator finds the speed an object must travel to stay in a circular orbit around a planet, moon, or star. It uses the central body's mass and the orbital radius, so you can read off the speed of a satellite, a space-station orbit, or a moon without solving the two-body equations by hand.

• • Use case: Satellite and space-station planning: confirm the speed of a low Earth orbit or a geostationary slot before a launch or rendezvous.
• • Use case: Physics coursework: check homework answers for circular-orbit speed from a given mass and radius.
• • Use case: Mission-design intuition: see how speed drops as you push an orbit farther from the central body.
• • Use case: Teaching the difference between orbital and escape speed for the same body.

For a perfectly circular orbit, the inward pull of gravity exactly supplies the centripetal force needed to keep the object turning. The speed that makes this balance work is the orbital velocity, and it depends only on the central body's mass and how far the orbit sits from the body's center. This orbital velocity calculator keeps that relationship in one place so you can compare bodies without rederiving it, and NASA's planetary fact sheets list the mass and radius of each body we use as presets, so the numbers match the standard reference figures (NASA planetary fact sheets).

Because the result scales with the square root of mass divided by radius, doubling the altitude does not halve the speed; the change is gentler. If you need the speed to leave the body entirely rather than circle it, the escape velocity calculator applies the related sqrt(2) relationship, and the gravitational force calculator shows the inward pull that the orbit must balance.

The calculator applies the classical circular-orbit relation and converts your altitude into a true orbital radius before taking the square root.

• orbital velocity: the speed needed for a circular orbit, reported in your chosen unit.
• gravitational constant: G, the CODATA recommended value (see citation below).
• central body mass: mass of the planet, moon, or star being orbited.
• orbital radius: distance from the body's center to the object, equal to the body radius R plus altitude h.

The gravitational parameter mu = G x M appears in many orbital formulas, so this orbital velocity calculator builds it internally and reuses it for the period as well. The gravitational constant G is the CODATA recommended value 6.67430 x 10^-11 m^3 kg^-1 s^-2 (NIST CODATA value of G).

When you select a preset body, the mass, radius, and surface gravity are filled in from NASA planetary fact sheets, so you can move from Earth to the Moon to Jupiter without looking up constants. Once you have the speed, the orbital period calculator turns the same radius into a lap time, and the Kepler's third law calculator connects period and radius across the solar system.

Four ideas explain why this orbital velocity calculator rests on a single formula that covers satellites, moons, and stations, and why that speed differs from escape speed.

The square-root dependence is the reason a small change in altitude near the surface has a larger fractional effect on speed than the same change far out.

Treating the bodies as point masses and ignoring atmosphere, oblateness, and other gravitating objects keeps the formula exact for introductory and mission-planning estimates.

Choose a preset or enter your own body, then set the altitude; the result updates as you type. For a lunar mission, pick the Moon and enter 100 km to get the roughly 1.63 km/s speed of a low lunar orbit, then raise the altitude to watch the speed fall the way the square-root law predicts.

1. 1 Step 1: Pick a central body from the preset list, or choose Custom to enter your own mass and radius.
2. 2 Step 2: Enter the altitude above the surface; use 0 for a surface-skimming orbit.
3. 3 Step 3: Choose the velocity output unit (m/s, km/s, mph, or ft/s); SI is used internally.
4. 4 Step 4: Read the orbital velocity, the km/s value, the orbital period in hours, and the angular velocity in rad/s.
5. 5 Step 5: Compare the period to a known orbit: about 1.5 hours for low Earth orbit, about 24 hours for geostationary.
6. 6 Step 6: Switch bodies or raise the altitude to see how speed falls with the square root of radius.

A student modeling the ISS enters Earth, altitude 400 km, and m/s output. The page returns 7,672 m/s with a period of 1.54 hours, matching the real station and confirming the formula before the student tackles a Hohmann transfer calculator move to a higher orbit.

These benefits matter when the orbit speed feeds a larger mechanics or mission problem.

• • Presets remove constant hunting: Earth, Moon, Mars, Jupiter, and Sun mass and radius come from NASA fact sheets, so you skip the lookup and avoid transcription errors.
• • Altitude-to-radius done for you: Typing altitude instead of center-to-center radius prevents the classic mistake of forgetting the body's own radius.
• • Period and angular velocity included: The same radius yields the orbital period and angular velocity, ready to drop into a follow-up calculation.
• • Unit-flexible output: m/s, km/s, mph, and ft/s cover textbook physics, engineering reports, and public-facing explanations from one entry.
• • Edge-aware validation: Zero or negative mass, zero radius, or negative altitude return a clear error instead of NaN or an imaginary number under the square root.
• • Quick escape-speed comparison: Seeing orbital velocity beside the escape figure for the same body clarifies why transfers need extra energy.

The single-form design works for a quick classroom check and for an early mission-sizing estimate without switching tools. Because the speed, period, and angular velocity all derive from one consistent radius, those numbers stay mutually consistent and line up with what you would read off a textbook orbit table for the same body.

The output depends on the inputs and on a few physics caveats that apply to every circular orbit.

• • The model assumes a circular orbit around a single point-mass body. Eccentric, multi-body, or atmosphere-affected orbits need a fuller simulation.
• • Preset radii are equatorial values; polar orbits around an oblate body see slightly different speeds than the formula returns.
• • The result is an ideal speed; real launches also need to account for inclination changes and drag losses not captured here.

For most teaching and early planning work the point-mass assumption is the right starting point. When the orbit is low enough to feel air drag or far enough to feel a second body, treat the value as an estimate. The acceleration due to gravity calculator shows how the local g that sets surface speed varies with the same mass and radius.

According to NASA's planetary fact sheets, the mass and radius values used as presets are the standard reference figures for each body.