Orbital Period Calculator
Find how long an object takes to complete an orbit.
Results update as you type.
How it works
The orbital period is the time an object takes to complete one full orbit, and this calculator finds it from the orbit's radius and the mass of the body being orbited. You enter the orbital radius, the distance from the center of the central body to the orbiting object, and the central body's mass, and it returns the period in seconds and hours. The calculation is Kepler's third law in its Newtonian form, which relates the period to the size of the orbit and the mass at its center through the gravitational constant. The most important pattern is that the period grows with the radius raised to the three-halves power, so a satellite twice as far out takes about 2.8 times as long to orbit, which is why distant planets have such long years. A more massive central body pulls harder and shortens the period. This formula assumes a small object in a circular orbit around a much more massive body, a good approximation for satellites around Earth, moons around planets, and planets around stars. To use it, remember the radius is measured from the center, so for a low Earth satellite you add Earth's radius to the altitude. Astronomers, aerospace engineers, and students use it to design orbits and understand celestial motion. Enter the orbital radius and central mass to compute the orbital period.
T = 2π·√(r³ / (G·M))
The orbital period comes from Kepler's third law: it equals two pi times the square root of the orbital radius cubed divided by the gravitational constant times the central body's mass. A larger orbit takes much longer, since the period grows with the radius to the three-halves power, while a more massive central body shortens it.
Source:Celestial mechanics (Kepler's third law)
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Worked example
How to use this calculator
- 1
Enter your values
Enter orbital radius and central body mass.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Orbital period updates instantly as you type — no button to press.
Frequently asked questions
What is orbital period?
Orbital period is the time it takes an object to complete one full revolution around another body. For a satellite it is how long one lap of Earth takes; for a planet it is the length of its year. It depends on the size of the orbit and the mass of the body being orbited.
How is orbital period calculated?
Using Kepler's third law: the period equals two pi times the square root of the orbital radius cubed divided by the gravitational constant times the central mass. Enter the radius from the center and the central body's mass, and the calculator returns the period. Distant orbits take much longer than close ones.
Why does a bigger orbit take so much longer?
The period grows with the orbital radius raised to the power of three-halves, a steep relationship. So an orbit twice as large has a period about 2.83 times as long. This is why the outer planets have years lasting decades or centuries while close-in satellites orbit in just hours.
What radius should I enter for a satellite?
Use the distance from the center of the central body, not the altitude above its surface. For an Earth satellite, add Earth's radius, about 6,371 kilometers, to the altitude. A satellite 600 kilometers up orbits at a radius of about 6,971 kilometers from Earth's center, which is the value to enter.
Does this work for any orbit?
It works well for a small object in a roughly circular orbit around a much more massive central body, which covers most satellites, moons, and planets. For highly elliptical orbits, use the semi-major axis as the radius. For two bodies of comparable mass, a more complete formula using their combined mass is needed.