Circular speed
v = √(μ/r)
Circular speed depends on the central body's gravitational parameter and distance from its center.
Orbital Velocity Calculator
Calculate ideal circular-orbit speed and period from altitude above a selected central body.
Access: Free to use, no installation, and No account required.
Inputs
This page uses the ideal point-mass circular-orbit model. Atmospheric drag, J₂, third-body gravity, ephemerides, and finite burns are not included.
Results
Circular orbital velocity
The model uses v = √(μ/r) and T = 2π√(r³/μ), where r is measured from the central-body center, not from the surface.
Planning boundary
Use the full Orbital Mechanics Workbench or Orbital Mechanics Simulator when eccentricity, maneuvers, perturbations, transfer geometry, or trajectory propagation matter.
Engineering reference
Orbital Velocity Calculator: background and worked detail
Use the Orbital Velocity Calculator to calculate circular orbital speed, period, local gravity, angular rate, specific orbital energy, and angular momentum from altitude around a selected central body.
Circular orbital velocity from first principles
A circular orbit balances inward gravitational acceleration with centripetal acceleration. The entered altitude is converted to orbital radius by adding the central body's reference radius; orbital velocity then follows from the body's gravitational parameter μ.
The result is an ideal two-body circular-orbit state. Atmospheric drag, oblateness, third-body gravity, thrust, inclination, eccentricity, rotating reference frames, and navigation frames are outside this focused calculation.
Equations used by this calculator
Orbital period
T = 2π√(r³/μ)
Kepler's third-law form gives the circular orbit period.
Specific orbital energy
ε = −μ/(2r)
Bound circular orbits have negative specific mechanical energy.
400 km circular Earth orbit
Select Earth and enter 400 km altitude.
- Earth radius is added to the 400 km altitude to obtain orbital radius.
- Circular speed is about 7.67 km/s.
- The period is about 92.6 minutes.
Result: Local gravitational acceleration is about 8.68 m/s², showing that low-Earth-orbit weightlessness is caused by free fall rather than negligible gravity.
Validation checks
Known reference orbits give these checks an unambiguous expected value.
Higher orbit
Case: Increase altitude while keeping the central body fixed.
Expected: Circular speed should decrease while orbital period increases.
Surface-radius limit
Case: Compare 0 km altitude with a small positive altitude.
Expected: The small altitude increase should slightly reduce speed and gravity, with no discontinuity.
Two-body assumptions
Assumptions
- A point-mass two-body gravitational model.
- The selected body's gravitational parameter and reference radius are treated as constants.
- The orbit is circular at the entered radius.
Limitations
- Does not include atmospheric drag or body oblateness such as J2.
- Not a trajectory propagator or launch, rendezvous, station-keeping, or reentry model.
Orbital Velocity Calculator FAQ
Why is gravity still high in low Earth orbit?
Gravity at a few hundred kilometres altitude remains a large fraction of surface gravity. Orbiting objects feel weightless because they and their spacecraft are continuously falling together.
Do I enter altitude or distance from Earth's center?
Enter altitude above the selected body's reference surface. The calculator adds the body's radius internally.
Can this calculate an elliptical orbit?
This focused route is for circular orbits. The full Orbital Mechanics Workbench includes elliptical-orbit and additional maneuver analysis.
Where this calculation comes from
Shared with the Orbital Mechanics Workbench, which handles elliptical orbits, perturbations, and transfer planning.
Open the source workbench →Read calculation and source methodology →