Calculators
Orbital Period Calculator
Calculate circular orbital period, speed, and frequency from central-body mass and orbital radius, privately in your browser.
Calculate the timing and speed of an ideal circular orbit.
For a circular orbit, speed v = √(GM/r), period T = 2πr/v = 2π√(r³/GM), and frequency f = 1/T. This calculator uses G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻². Enter the central-body mass M in kilograms and radius r in metres from its centre, not altitude above its surface. To use an altitude, first add the body’s radius. For M = 5.972 × 10²⁴ kg and r = 6.771 × 10⁶ m, the period is about 5545 seconds (92.4 minutes), and the speed is about 7672 m/s. The model assumes a negligible orbiting mass, a spherical central body or point mass, and Newtonian gravity. It excludes drag, other bodies, relativity, and elliptical orbits; for an elliptical orbit use the semi-major axis in the period formula, but this circular speed result does not apply. Check that the radius lies outside the body; the calculator does not know its physical size. Both inputs must be from 1e-12 to 1e40. Results use browser floating-point arithmetic rounded to 12 significant digits. All calculations stay on your device.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
How do you calculate orbital period?
T = 2π√(r³/GM), using radius in metres, central-body mass in kilograms, and G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻². The result is in seconds. Circular speed is √(GM/r), and frequency is 1/T.
Should I enter altitude or radius?
Enter distance from the central body’s centre. Add altitude above the surface to the body’s radius first, using metres for both. The calculator cannot check whether the orbit is inside the body.
What is an example near Earth?
A central mass of 5.972e24 kg and orbital radius of 6.771e6 m give roughly 5545 seconds per orbit, or 92.4 minutes, and a circular speed of 7672 m/s.
Which assumptions apply?
This models an ideal circular Newtonian orbit around a spherical body or point mass. The orbiting mass is negligible. Drag, other gravitating bodies, and relativistic effects are ignored. It is an educational model, not a flight planning tool.
Does this work for an elliptical orbit?
The period formula also works with the semi-major axis replacing radius, but the circular speed output does not describe speed along an elliptical orbit. This calculator labels its input and outputs for circular orbits.
What inputs can I use, and are they private?
Use positive numbers from 1e-12 to 1e40 in the stated SI units. Scientific notation is supported. Calculations and copy actions run locally in your browser.