Synodic Period Calculator

Summary

The synodic period is the time between successive identical configurations of a body as observed from Earth — for example, one full moon to the next, or one opposition of Mars to the next. This calculator converts between synodic and sidereal periods using the standard formula 1/P_syn = |1/P_sid - 1/P_earth|. It supports both inner bodies (faster than Earth) and outer bodies (slower than Earth), and can solve in either direction.

How it works

1. Choose whether you are solving for the synodic period or the sidereal period.
2. Enter the known period in days.
3. For synodic-from-sidereal mode, also specify whether the body is inner (orbit inside Earth's) or outer.
4. Click Calculate to instantly see the result with the full formula breakdown.
5. Use the presets to load well-known planets or the Moon with one click.

Use cases

• Find how often Mars reaches opposition as seen from Earth.
• Determine the synodic month length (lunar cycle) from the Moon's sidereal period.
• Convert a measured synodic period back to a body's true orbital period.
• Verify textbook values for planetary synodic periods.
• Explore hypothetical orbital periods for exoplanets.
• Teach the difference between synodic and sidereal periods interactively.

Frequently Asked Questions