If you know an orbit’s radius and the mass of the object it orbits, you can compute the orbital period (how long one full revolution takes). This guide explains the exact formula used and helps you avoid unit mistakes.
Use the calculator above to input values, switch units, and get the period instantly. Then use the examples and FAQ to verify your results.
What Is Orbital Period?
Orbital period is the time required for a body to complete one full orbit around another object. For satellites, planets, and moons, it depends mainly on the orbital size (radius) and the central mass (the body being orbited).
In physics, orbital period is tied to gravity and the geometry of the orbit. For most practical cases, you can model the orbit using Newtonian gravity and treat it as a circular orbit to get a very useful estimate.
Orbital Period Formula (Circular Orbit)
For a circular orbit, the orbital period is:
T = 2π · √( r³ / (G·M) )
- T = orbital period (time for one revolution)
- r = orbital radius (distance from the center of the central mass)
- G = gravitational constant, 6.67430 × 10⁻¹¹ m³/(kg·s²)
- M = mass of the central object (e.g., planet or star)
This formula comes from balancing the required centripetal acceleration with gravitational force. The key idea is that larger orbits take longer because the distance term uses r³.
Variables and Units You Must Get Right
The calculator uses consistent SI units internally. You can enter values in common units, but the math requires the correct conversion.
- Orbital radius (r): meters (m), kilometers (km), or astronomical units (AU)
- Central mass (M): kilograms (kg), solar masses (M☉), or Earth masses (M⊕)
- Output period (T): seconds, minutes, hours, days, or years
If you accidentally enter altitude above the surface instead of distance from the center, your period will be wrong. For satellites around a planet, you typically use:
r = planet radius + altitude
How the Calculator Computes the Result
The Orbital Period Calculator performs these steps:
- Converts inputs (radius and mass) into SI units.
- Computes r³ and the denominator G·M.
- Applies T = 2π · √( r³ / (G·M) ).
- Converts the final period into your selected time units.
Because it uses the same constants every time, results are consistent and repeatable.
Practical Example 1: A Satellite Around Earth
Imagine a satellite in a circular orbit at a radius of 7,000 km from Earth’s center. Earth’s mass is about 5.972 × 10²⁴ kg.
Plugging these values into the Orbital Period Calculator gives a period of roughly about 97 minutes (order-of-magnitude check). Real satellites may differ slightly due to non-circular orbits and atmospheric drag, but the calculation is a strong first estimate.
- Radius: 7,000 km
- Central mass: Earth mass
- Expected output: minutes (≈ 97 min for low Earth orbit)
Practical Example 2: Earth’s Orbit Around the Sun
For planets, you can use the same approach. Earth orbits the Sun at about 1 AU. The central mass is the Sun’s mass, about 1.989 × 10³⁰ kg.
The calculator will return a period close to 1 year. Small differences come from the fact that planetary orbits are not perfectly circular and from how you define the “radius” (semi-major axis vs. instantaneous distance).
- Radius: 1 AU
- Central mass: solar mass
- Expected output: years (≈ 1 year)
Common Mistakes (And How to Avoid Them)
- Using altitude instead of orbital radius: remember r = R + h.
- Mixing units: the calculator handles conversions, but you must select the correct input type.
- Assuming exact circular orbits: the formula is for circular orbits; elliptical orbits need more advanced treatment.
- Using the wrong central mass: orbiting a moon means the moon is the central mass, not the planet.
Frequently Asked Questions
What inputs do I need for an Orbital Period Calculator?
You need two values: the orbital radius (distance from the center of the central body) and the central mass (mass of the object being orbited). Select your units for each input, then choose the time unit you want for the output.
Does the orbital period calculator work for elliptical orbits?
This calculator uses the circular-orbit form of the orbital period equation. For many real cases, it still gives a useful estimate when you use the orbit’s semi-major axis as the radius. For precise results on elliptical orbits, you need the full Kepler-based method.
Should I enter altitude or orbital radius?
Enter orbital radius, not altitude. Orbital radius is measured from the center of the central body. For low Earth orbit, use r = Earth radius + altitude. If you enter only altitude, your computed period will be too small.
Why do orbits farther away take longer?
Orbital period scales with r³ inside a square root, meaning T grows rapidly as radius increases. Double the orbital radius and the period increases by more than a factor of two. This comes directly from how gravity weakens with distance.
What units are supported by the calculator?
The calculator accepts common radius units (meters, kilometers, and AU) and central mass units (kilograms, solar masses, and Earth masses). It outputs the orbital period in selectable time units like seconds, minutes, hours, days, and years.
Next Steps
Use the calculator to compute orbital period for your scenario, then validate your input choices: radius measured from the center and the correct central mass. If you’re working with spacecraft or planets on real missions, consider elliptical corrections for higher accuracy.
When you’re ready, try changing only one variable at a time (radius or mass) to see how sensitive orbital period is to distance and gravity.