Convert Tropical Years to Synodic Months
Convert Tropical Years (a_trop) to Synodic Months (syn.mo) instantly and accurately.
Conversion Formula
syn.mo = a_trop × 12.3682664
About Tropical Years
The tropical year = time from March equinox to the next = 365.24219 days = 31,556,925.2 s - the year that governs the seasons. The Gregorian 97/400 leap rule approximates it as 365.2425 days, leaving a residual drift of only ~26.8 s/year. The tropical year shortens ~0.53 s per century due to tidal deceleration. Persian Solar Hijri and Mayan Haab' calendars also approximate it. 1 a_trop ≈ 365.24219 d.
About Synodic Months
A synodic (lunar) month = new moon to new moon = 29.5306 days = 2,551,442.9 s. Longer than the sidereal month (27.32 d) because Earth advances ~27° in its orbit during that time; the Moon must travel further to realign with the Sun. Islamic Hijri, Hebrew lunisolar, and Chinese calendars are built on synodic months. Eclipses repeat via the Saros cycle (18 yr 11 d = 223 synodic months). 1 syn.mo ≈ 29.5306 d.
Quick Reference Table
| Tropical Years (a_trop) | Synodic Months (syn.mo) |
|---|---|
| 1 a_trop | 12.3683 syn.mo |
| 2 a_trop | 24.7365 syn.mo |
| 5 a_trop | 61.8413 syn.mo |
| 10 a_trop | 123.683 syn.mo |
| 25 a_trop | 309.207 syn.mo |
| 50 a_trop | 618.413 syn.mo |
| 100 a_trop | 1236.83 syn.mo |