Synodic Period Calculator
Find how often two orbiting bodies return to the same relative configuration (conjunction or opposition) from their sidereal periods.
Period units
2.1353 years
- 1
Difference |P1 − P2|
|365.256 − 686.98| = 321.724 - 2
Product P1 × P2
365.256 × 686.98 = 250,923.567 - 3
Synodic period S (days)
250,923.567 ÷ 321.724 = 779.93
How does this calculator work?
The synodic period is how often two bodies return to the same alignment. From sidereal periods P1 and P2, compute S = P1·P2 / |P1 − P2|, or equivalently 1/S = |1/P1 − 1/P2|. For Earth (365.26 d) and Mars (686.98 d) this gives about 779.9 days between oppositions, roughly 2.14 years.
Formula
How this is calculated
The synodic period is the time between successive identical alignments of two bodies as seen from one another (for example, Earth and a planet returning to opposition or conjunction). It differs from the sidereal period, which is one full orbit relative to the fixed stars.
Enter the two sidereal orbital periods P1 and P2 in the same unit (days or years). The faster body laps the slower one, and the rate at which their angular positions diverge is the difference of their angular speeds: 1/S = |1/P1 − 1/P2|. Solving for S gives S = P1·P2 / |P1 − P2|. The result is reported in both days and years using 1 year = 365.25 days for conversion.
Assumptions: circular, coplanar, uniform orbits and constant periods. If the two periods are equal the bodies never change configuration and the synodic period is infinite, so the calculator requires two different positive values. Very close periods produce a very large synodic period, which is expected.
Frequently asked questions
The sidereal period is one full orbit relative to the distant stars. The synodic period is the time to return to the same alignment relative to another body (such as Earth), which is what you observe as repeating oppositions or conjunctions.
If P1 equals P2 the bodies orbit in lockstep and never change their relative angle, so 1/S = 0 and the synodic period is infinite. The formula requires |P1 − P2| > 0.
No. Both P1 and P2 must use the same unit. Pick days or years for the inputs; the calculator then reports the synodic period in both days and years.
Also known as
TG we-Calculate Editorial Team. (2026). Synodic Period Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/synodic-period-calculator
TG we-Calculate Editorial Team. "Synodic Period Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/synodic-period-calculator.
TG we-Calculate Editorial Team, "Synodic Period Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/synodic-period-calculator
@misc{wecalculate_synodic_period_calculator, title = {Synodic Period Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/synodic-period-calculator}}, year = {2026}, note = {TG we-Calculate} }
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