What this calculator does
Equinoxes and solstices are moments, not whole days. At the March equinox the sun crosses the equator heading north; at the June solstice it reaches its farthest point north; and so on. This calculator gives the exact minute of all four for any year from 1000 to 3000, in Coordinated Universal Time (UTC) and in the time zone you choose. Because they're instants, the local date can differ: the 2026 September equinox is on September 23 in UTC but still September 22 in the Americas.
How it's calculated
It uses the method in chapter 27 of Jean Meeus's Astronomical Algorithms. First, a polynomial in Y = (year − 2000) ÷ 1000 gives a mean time JDE₀ as a Julian Ephemeris Day. Then 24 periodic terms correct it for the pull of the Moon and planets:
W = 35999.373° × T − 2.47°
Δλ = 1 + 0.0334 cos W + 0.0007 cos 2W
S = Σ A cos(B + C × T) over 24 terms
JDE = JDE₀ + 0.00001 × S ÷ Δλ
JDE is in Terrestrial Time, a uniform atomic time scale. Clocks follow Earth's rotation, which is slightly irregular, so the calculator subtracts ΔT (about 75 seconds in 2026) using the Espenak–Meeus polynomials published by NASA. The result is UTC, and your browser's time zone rules turn it into local time.
Worked example: June solstice 2026
Y = 0.026, so JDE₀ = 2461212.84995. Then T = 0.264691, Δλ = 0.96818 and S = 144.83, giving JDE = 2461212.85145. That is June 21, 2026 at 8:26:05 Terrestrial Time; minus ΔT of about 75 seconds, it's about 8:24:49 UTC, or 4:25 AM in New York (EDT). The Naval Observatory lists 08:24.
Accuracy: checked against the U.S. Naval Observatory
| Event | This calculator (UTC) | USNO (UTC) |
|---|---|---|
| March equinox 1800 | Mar 20, 20:12 | Mar 20, 20:12 |
| December solstice 1800 | Dec 22, 00:16 | Dec 22, 00:16 |
| March equinox 2000 | Mar 20, 07:35 | Mar 20, 07:35 |
| December solstice 2000 | Dec 21, 13:38 | Dec 21, 13:37 |
| June solstice 2024 | Jun 20, 20:51 | Jun 20, 20:51 |
| September equinox 2024 | Sep 22, 12:44 | Sep 22, 12:44 |
| March equinox 2026 | Mar 20, 14:45 | Mar 20, 14:46 |
| June solstice 2026 | Jun 21, 08:25 | Jun 21, 08:24 |
| September equinox 2026 | Sep 23, 00:05 | Sep 23, 00:05 |
| December solstice 2026 | Dec 21, 20:50 | Dec 21, 20:50 |
| March equinox 2100 | Mar 20, 13:03 | Mar 20, 13:05 |
From 1800 to 2026, every time we tested was within 1 minute of the Naval Observatory, and most matched exactly. By 2100 the gap grows to about 2 minutes, mostly because nobody can know ΔT that far ahead. Before 1800 and after 2100, expect errors of a few minutes, growing for the most distant years.
Limitations
- Calendars. Dates use the Gregorian calendar, extended backward before 1582. For earlier years the result also shows the Julian calendar date people used then.
- Astronomical vs. meteorological seasons. Weather services count seasons by whole months (for example, summer is June, July and August). This calculator gives the astronomical start of each season.
- Old time zones. Local times for past centuries use your browser's time zone history, which falls back to local mean time before standard time existed.
Sources
- Jean Meeus, Astronomical Algorithms, 2nd edition (Willmann-Bell, 1998), chapter 27, "Equinoxes and Solstices"
- U.S. Naval Observatory: Earth's seasons, equinoxes, solstices, perihelion and aphelion
- NASA Eclipse Web Site: Polynomial expressions for Delta T (Espenak and Meeus)