Orbital Velocity Calculator
Calculate circular orbital velocity and orbital period from mass and radius.
Check Orbital Velocity Calculator
Formula result
Check before you use it
What the numbers show
The answer shows the tangential speed needed for an ideal circular orbit and the corresponding time for one trip around the central body.
Use orbital velocity calculator for low-orbit estimates, satellite homework, moon-orbit comparisons, spaceflight intuition, and circular-orbit baselines.
Larger orbital radius lowers orbital speed but usually increases orbital period strongly.
Copy-ready formula handoff
Use this after solving the live calculator result, then paste the answer into a lab note, homework check, or engineering review.
v = sqrt(G * M / r), T = 2*pi*r / v
- Orbital velocity: Ideal circular-orbit speed around the central body.
- Central mass: Mass of the planet, moon, star, or other body being orbited.
- Orbital radius: Center-to-center distance from the central body to the orbiting object, not altitude above the surface.
- Orbital period: Time for one full ideal circular orbit at that radius.
- The orbit is treated as circular.
- The orbiting mass is assumed negligible compared with the central mass.
- Entering altitude above the surface instead of orbital radius measured from the central body center.
- Using the satellite mass in place of the central body mass; circular speed depends on M, not the small orbiting mass.
Orbital Velocity Calculator result: [paste the solved value from the calculator above]. Formula used: v = sqrt(G * M / r), T = 2*pi*r / v Inputs checked: Orbital velocity, Central mass, Orbital radius, Orbital period. Assumptions: The orbit is treated as circular. The orbiting mass is assumed negligible compared with the central mass. Worked example: 400 km low Earth orbit. Add Earth radius and altitude: r = 6.371e6 m + 400000 m = 6.771e6 m. Apply v = sqrt(GM/r) with M = 5.972e24 kg and G = 6.67430e-11 N*m^2/kg^2. The circular speed is about 7670 m/s, and T = 2*pi*r/v is about 5546 s, or 92.4 min. Next check: Entering altitude above the surface instead of orbital radius measured from the central body center.
Equation context
Built for low-orbit estimates, satellite homework, moon-orbit comparisons, spaceflight intuition, and circular-orbit baselines. This page pairs the live calculator with the governing formula, variable glossary, and a worked example so the result is easier to trust and reuse.
Quick entry points
Use the calculator to verify arithmetic after you set up the formula yourself.
Change one input at a time to see which variable is driving the result.
Review the formula notes before using the answer in a lab or design check.
Variables to track
Ideal circular-orbit speed around the central body. Unit: m/s.
Mass of the planet, moon, star, or other body being orbited. Unit: kg.
Center-to-center distance from the central body to the orbiting object, not altitude above the surface. Unit: m.
Time for one full ideal circular orbit at that radius. Unit: s.
Formula method and unit assumptions
Formula and example
Worked example
400 km low Earth orbit
- 1Add Earth radius and altitude: r = 6.371e6 m + 400000 m = 6.771e6 m.
- 2Apply v = sqrt(GM/r) with M = 5.972e24 kg and G = 6.67430e-11 N*m^2/kg^2.
- 3The circular speed is about 7670 m/s, and T = 2*pi*r/v is about 5546 s, or 92.4 min.
The altitude alone is not the orbit radius; using the center-to-center radius is what makes the orbital speed physically meaningful.
Assumptions
Common mistakes
Related formula checks
Equation context and next checks
Formula and variable setup for Orbital Velocity Calculator
Calculate circular orbital velocity and orbital period from mass and radius. The page is designed to help you move from the known values to the correct formula without rebuilding the derivation every time.
For orbital velocity calculator, the safest workflow is to confirm the unit system first, then map each symbol to the physical quantity in your problem statement before solving.
- v: Orbital velocity (m/s) - Ideal circular-orbit speed around the central body.
- M: Central mass (kg) - Mass of the planet, moon, star, or other body being orbited.
- r: Orbital radius (m) - Center-to-center distance from the central body to the orbiting object, not altitude above the surface.
- T: Orbital period (s) - Time for one full ideal circular orbit at that radius.
How to read the result
The answer shows the tangential speed needed for an ideal circular orbit and the corresponding time for one trip around the central body.
This tool is especially useful for low-orbit estimates, satellite homework, moon-orbit comparisons, spaceflight intuition, and circular-orbit baselines. The output becomes more trustworthy when you compare nearby cases instead of relying on one single run.
- Orbital speed
- Orbital period
- Useful for low-orbit comparisons
Assumptions and limits
The calculator applies the standard textbook relation for this topic, which makes it a strong first-pass answer but not always a full real-world model.
Before you use the result in a lab, design review, or report, check whether the simplified assumptions still match the physical system you care about.
- The orbit is treated as circular.
- The orbiting mass is assumed negligible compared with the central mass.
- Atmospheric drag and non-spherical gravity effects are ignored.
- Maneuvers, inclination changes, perturbations, and elliptical-orbit speed variation are outside this circular baseline.
Quick glossary
Ideal circular-orbit speed around the central body.
Mass of the planet, moon, star, or other body being orbited.
Center-to-center distance from the central body to the orbiting object, not altitude above the surface.
A simplified physics model that omits secondary effects so the first-order relationship is easier to inspect.
Formula checks before using the result
Formula questions
Checks before using the result
When should I use the orbital velocity calculator?
Use orbital velocity calculator for low-orbit estimates, satellite homework, moon-orbit comparisons, spaceflight intuition, and circular-orbit baselines, especially when the governing formula is already known and the main need is a fast, transparent calculation.
What is the main thing the orbital velocity calculator tells me?
The answer shows the tangential speed needed for an ideal circular orbit and the corresponding time for one trip around the central body.
What can make the orbital velocity calculator answer inaccurate?
The answer is exact for the formula and assumptions on the page, but it can drift when the real system violates those assumptions. Common limits include The orbit is treated as circular. The orbiting mass is assumed negligible compared with the central mass. Atmospheric drag and non-spherical gravity effects are ignored. Maneuvers, inclination changes, perturbations, and elliptical-orbit speed variation are outside this circular baseline.
Formula references and related examples
Formula Basis