Orbital Velocity Calculator
Enter the central body's mass in kilograms and the orbit radius in kilometres to find the speed of a circular orbit and how long one lap takes. The tool uses v = sqrt(GM/r) with a gravitational constant G of 6.674e-11, then finds the period from T = 2 x pi x r / v. A low Earth orbit works out near 7.67 km/s, which is why launch vehicles must reach that speed sideways, not just gain altitude.
How to use the orbital velocity calculator
- Enter the central body's mass in kilograms, or tap a preset like LEO satellite, Moon (Earth) or Geostationary.
- Enter the orbit radius in kilometres, measured from the centre of the central body rather than the surface.
- Read the circular orbital velocity in both km/s and m/s from the result cards.
- Read the orbital period in seconds for one complete lap.
- Use Copy to save the velocity and period as a single line of text.
Examples
Low Earth orbit satellite
mass = 5.972e24 kg, radius = 6771 km
v = 7.67232 km/s, period 5545.06 s (about 92 minutes)
Geostationary orbit
mass = 5.972e24 kg, radius = 42164 km
v = 3.07455 km/s, period 86166.7 s (about 23.9 hours)
The Moon around Earth
mass = 5.972e24 kg, radius = 384400 km
v = 1.01827 km/s, period 2371930 s (about 27.5 days)
Frequently asked questions
What is orbital velocity?
Orbital velocity is the speed a body needs to stay in a circular orbit at a given radius, where gravity exactly supplies the centripetal force. Too slow and it falls inward, too fast and it climbs to a higher or escape trajectory.
What is the orbital velocity formula?
For a circular orbit, v = sqrt(G x M / r), where G is the gravitational constant 6.674e-11 N m^2/kg^2, M is the central mass and r is the orbit radius measured from the centre.
How is the orbital period found from the velocity?
The period is the circumference divided by the speed, T = 2 x pi x r / v. It is the time the body takes to complete one full circular orbit, reported here in seconds.
Why is low Earth orbit about 7.7 km/s?
At roughly 400 km altitude the orbit radius is about 6771 km, and Earth's mass of 5.972e24 kg gives a circular speed near 7.67232 km/s with a period of about 5545 s, close to 92 minutes.
Is the radius the altitude or the distance from the centre?
It is the distance from the centre of the central body. For an Earth orbit at 400 km altitude you add Earth's radius of about 6371 km to get roughly 6771 km, which is the value to enter.
Does the orbiting body's own mass matter?
No, for a small body around a much larger one it cancels out. The circular speed depends only on the central mass and the orbit radius, not on the satellite's mass.
Does this handle elliptical orbits?
No. It solves the ideal circular case. A real elliptical orbit speeds up near periapsis and slows near apoapsis, so this gives the constant speed of the matching circular orbit.
Can I use solar masses or metres?
The on-page tool takes mass in kg and radius in km. The underlying API also accepts centralMassSolar in solar masses (1.989e30 kg each) and orbitalRadiusM in metres for programmatic use.
Does anything I enter leave my browser?
No. The calculation runs locally in JavaScript. Your mass and radius values are not uploaded or stored anywhere.
Learn more
- Circular Orbital Velocity Explained
How v = sqrt(GM/r) comes from balancing gravity and circular motion, and what it tells you about satellites and moons.
Related tools
Orbital Period Calculator
Calculate orbital period from Kepler's third law, T = 2 pi sqrt(a cubed / GM). Enter the semi-major axis and central mass to get seconds, days and years.
Escape Velocity Calculator
Calculate escape velocity from any planet, moon or star with v = sqrt(2GM/r). Pick Earth, Mars or Jupiter presets or enter mass and radius. Free tool.
Hohmann Transfer Calculator
Calculate Hohmann transfer delta-v between two circular orbits, plus the transfer time. Enter the central mass and both orbit radii to size each burn.
555 Timer Calculator
Calculate 555 timer astable frequency, period, high and low times and duty cycle from R1, R2 and the timing capacitor. Free oscillator design helper.
Absolute Humidity Calculator
Calculate absolute humidity in grams of water vapor per cubic meter from air temperature and relative humidity. Fast, free and works in your browser.
Allele Frequency Calculator
Find allele frequencies from genotype counts. Enter the number of AA, Aa and aa individuals to get the A and a allele frequencies and allele totals.