Equinox & Solstice Date Calculator
The Sun crosses four cardinal points on the ecliptic each year: longitude 0° = March (vernal) equinox, 90° = June solstice, 180° = September equinox, 270° = December solstice. At these instants the day–night balance reaches an equinox (equal length) or solstice (extreme length). Because Earth's orbit is elliptical, the four 90° segments are *not* equally long: the northern summer half-year (March–September equinox) is ~186.4 days, the winter half ~178.8 days. So fixed-date approximations like "spring equinox = 21 March" drift by up to two days; you need an astronomical formula for the exact instant. This tool uses Jean Meeus's *Astronomical Algorithms* Ch. 27 (polynomial mean + 24 periodic terms), accurate to ±4 minutes for years 1000–3000, and applies a ΔT (TT−UT1) correction to return UTC. Enter any year and the tool shows the four events in UTC and your browser's local time (Hong Kong = UTC+8).
Please enter a whole-number year between 1000 and 3000.
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March equinox (N. spring / S. autumn)
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June solstice (N. summer / S. winter)
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September equinox (N. autumn / S. spring)
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December solstice (N. winter / S. summer)
Season names are given from the Northern Hemisphere perspective; in the Southern Hemisphere the same instant is the opposite season. "Local time" follows your browser's timezone.
Formula
JDE₀ = a + b·Y + c·Y² + d·Y³ + e·Y⁴ (Y = (year − 2000)/1000; coefficients a..e from Meeus Table 27.A) ; T = (JDE₀ − 2451545.0)/36525 ; W = (35999.373·T − 2.47)° ; Δλ = 1 + 0.0334·cosW + 0.0007·cos2W ; S = Σ_{i=1..24} Aᵢ·cos(Bᵢ + Cᵢ·T)° ; JDE = JDE₀ + 0.00001·S ⁄ Δλ ; UTC = JDE − ΔT
- · Seasons are mirrored between hemispheres: a March equinox starts northern spring but southern autumn; a June solstice is the northern longest day but the southern shortest day. This tool labels seasons from the northern viewpoint.
- · An equinox or solstice is an *instant*, not a date. Depending on your timezone the same UTC instant can fall on the previous or next civil day — e.g. Hong Kong (UTC+8) records the date 8 hours ahead of UTC.
- · The four cardinal points correspond to four of the 24 Chinese solar terms (節氣): 春分 ≈ March equinox, 夏至 ≈ June solstice, 秋分 ≈ September equinox, 冬至 ≈ December solstice; the other 20 terms further subdivide the ecliptic into 15° steps.
- · Accuracy: Meeus's polynomial is ±4 minutes for AD 1000–3000; ΔT (TT−UT1) is approximated with the NASA Espenak/Meeus polynomial, accurate to a few seconds for 1900–2150.
- · Why does the date drift year-to-year? (1) The Gregorian calendar adds 1 leap day every 4 years (avg 365.25 days), but the astronomical tropical year is ~365.24219 days — a 11-minute mismatch; (2) Earth's orbit is elliptical so the four seasonal quarters are unequal. The result: equinox/solstice times drift earlier by ~5 h 48 min each year, then "snap back" a day in a leap year.
- · References: Jean Meeus, *Astronomical Algorithms* (Willmann-Bell, 2nd ed. 1998), Ch. 27; US Naval Observatory *Earth's Seasons* tables; NASA Eclipse Web Site ΔT polynomials.
Frequently asked
Is the spring equinox always on 21 March?
No. In the 21st century the (northern) spring equinox almost always falls on 19 or 20 March — 21 March has essentially disappeared. Two reasons: (1) the Gregorian calendar approximates the 365.2422-day tropical year with "+1 day every 4 years", which over-shoots by ~5 h 48 min per common year and gets clawed back on leap years, so the equinox time drifts earlier and then jumps; (2) the 1582 Gregorian reform was specifically designed to anchor the equinox near 20 March (for Easter computation), not 21 March. Concrete examples: 2000 → 20 Mar 07:35 UTC; 2008 → 20 Mar 05:48 UTC; 2020 → 20 Mar 03:50 UTC; 2024 → 20 Mar 03:06 UTC; 2028 → 20 Mar 02:17 UTC. The 2100 year (a non-leap centurial under the "minus 3 days per 400 years" rule) will jump back to late 20 March, and from 2100 onward the equinox will fall on 19 March more often than 20 March. "21 March" is a 19th–20th-century convention, not a present-day fact.
Is day and night really equal everywhere on an equinox?
*Close, but not exactly.* "Equinox" literally means *aequus + nox* (Latin: "equal night") and is defined as the instant the Sun's geometric centre crosses the celestial equator. Without an atmosphere and with a point-like Sun, day and night would be 12 h each globally on that date. In practice: (1) the Sun's disk is ~0.5° wide, so sunrise = upper limb first appears, sunset = upper limb disappears — that adds ~5 min of daylight; (2) atmospheric refraction lifts the apparent Sun above its true position when it's near the horizon, adding another ~6–8 min; (3) the effect grows with latitude. So on the actual equinox date the equator gets ~12 h 07 min of day, Hong Kong (22 °N) ~12 h 07 min, Beijing (40 °N) ~12 h 09 min, and at the poles you wait for the *equilux* (the day when sunrise-to-sunset really is 12 h) — usually 2–4 days *before* the equinox depending on latitude. For exact sunrise/sunset times use our Sunrise/Sunset calculator rather than the equinox instant.
Is the summer solstice the hottest day of the year? And the winter solstice the coldest?
No — that's *seasonal thermal lag*. The summer solstice (June 20–21) is the *longest day*, but Earth's surface and oceans don't hit peak temperature simultaneously: ocean thermal mass is huge, so it takes another 4–8 weeks for the surface to reach maximum, and the hottest stretch in the Northern Hemisphere typically falls in late July to early August (e.g. North America late July; East Asia late July through August; coastal areas later still). Likewise the winter solstice (Dec 21–22) is the shortest day, but the coldest stretch is usually late January to mid-February — exactly the reason the Chinese 立春 ("start of spring") solar term lands when it feels coldest. Hong Kong climatological means: warmest daily average ≈ 28–29 °C in late July; coldest daily average ≈ 15–16 °C in late January / early February. The solstice is an astronomical event, not a meteorological one — peak weather is 4–8 weeks behind.
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