An equinox is an instant, defined by an angle
The four seasonal markers are not defined by weather, by day length or by a calendar date. Each is the instant at which the Sun's apparent geocentric longitude — its position measured along the ecliptic — reaches an exact multiple of 90°. The March equinox is longitude 0°, the June solstice 90°, the September equinox 180° and the December solstice 270°.
Because it is an instant rather than a day, the calendar date depends on where you are. A March equinox at 02:30 UT falls on the previous evening throughout the Americas, so northern spring can legitimately begin on 19 March in Los Angeles and 20 March in London in the same year. Both statements describe the same moment.
The dates drift within the calendar for a straightforward reason. The tropical year — equinox to equinox — is about 365.2422 days, while the Gregorian calendar year averages 365.2425 days. The two are close but not equal, so the equinox creeps slowly earlier over centuries, and each ordinary year of 365 days pushes it about six hours later until a leap day pulls it back. That is why March equinoxes cluster on the 20th now, fell mostly on the 21st a century ago, and will fall increasingly on the 19th.
The event names carry a hemisphere assumption that the astronomy does not. The June solstice is midsummer in the north and midwinter in the south, so this calculator names the events by month rather than by season, and reports the four intervals as “March equinox to June solstice” rather than “spring”.
The formula, one variable at a time
The calculation has two stages. First a fitted polynomial gives a mean instant: JDE₀ = a₀ + a₁Y + a₂Y² + a₃Y³ + a₄Y⁴, where Y = (year − 2000)/1000 and each event has its own five coefficients. For the March equinox the leading pair is 2451623.80984 + 365242.37404Y: the constant is the equinox nearest the year 2000 and the linear coefficient is a thousand tropical years.
Notice that the four linear coefficients differ slightly — 365242.37404 for March, 365241.62603 for June, 365242.01767 for September and 365242.74049 for December. That is not a rounding artefact. The interval between successive June solstices is genuinely a little shorter than the interval between successive March equinoxes, because the Earth's perihelion slowly precesses around the orbit and each event samples a different part of it.
Second, the mean instant is corrected. The periodic sum S = Σ A cos(B + C·T) has 24 terms, with T in Julian centuries from J2000. The largest term, amplitude 485 with argument 324.96° + 1934.136°T, is the 18.6-year nutation cycle driven by the regression of the lunar nodes. Others carry the periods of Jupiter, Venus and the Moon. The correction is divided by Δλ = 1 + 0.0334 cos W + 0.0007 cos 2W, which accounts for the Sun's apparent angular speed being faster in January than in July.
The total correction is typically a few tens of minutes — small against the polynomial, large against a user's expectations, and exactly the part that decides whether an equinox lands on the 19th or the 20th. Everything so far is in dynamical time, so ΔT is subtracted to reach Universal Time, using the same Espenak–Meeus polynomials as the next full moon calculator.
Worked example: the June solstice of 1962
This is Meeus's own example 27.a, which makes every intermediate value checkable.
- Scale the year. Y = (1962 − 2000)/1000 = −0.038.
- Evaluate the June polynomial. 2451716.56767 + 365241.62603 × (−0.038) + 0.00325Y² + 0.00888Y³ − 0.00030Y⁴. The linear term is −13,879.18179, and the higher terms together contribute under 0.000005, so JDE₀ = 2437837.38588.
- Julian centuries. T = (2437837.38588 − 2451545.0)/36525 = −0.3752940.
- Angular-speed factor. W = 35999.373 × (−0.3752940) − 2.47 = −13,512.82°, and Δλ = 1 + 0.0334 cos W + 0.0007 cos 2W = 0.96806.
- Periodic sum. Evaluating all 24 terms at that T gives S = 635.36, so the correction is 0.00001 × 635.36 / 0.96806 = +0.006563 days, about 9.45 minutes.
- True instant. 2437837.38588 + 0.006563 = JDE 2437837.39245, which is 1962 June 21 at 21h24m42s in dynamical time.
- Convert to Universal Time. ΔT for 1962 is about 34 seconds, so the event was at roughly 21:24:08 UT on 21 June 1962.
Now the season lengths for 2026. Running the four events gives JDE 2461120.1158, 2461212.8514, 2461306.5046 and 2461396.3690, and the March equinox of 2027 is at 2461485.3514. Subtracting consecutive pairs: 92.736, 93.653, 89.864 and 88.982 days. Their sum is 365.236 days — one equinoctial year, close to but not exactly the mean tropical year of 365.2422 days, because individual years vary by up to about twenty minutes.
Why the seasons are unequal
| Interval | Northern name | Southern name | Length (days) | Difference from 91.31 |
|---|---|---|---|---|
| March equinox → June solstice | Spring | Autumn | 92.74 | +1.43 |
| June solstice → September equinox | Summer | Winter | 93.65 | +2.34 |
| September equinox → December solstice | Autumn | Spring | 89.86 | −1.45 |
| December solstice → March equinox | Winter | Summer | 88.98 | −2.33 |
A circular orbit would give four equal quarters of 365.2422/4 = 91.31 days. The two intervals containing aphelion in early July are the long ones and the two containing perihelion in early January are the short ones, exactly as Kepler's second law requires.
How to read the result
Read the Universal Time first and the local time second. A date without a time is ambiguous by up to a day across the world, and disagreements between almanacs about which date an equinox fell on are almost always this and nothing else.
The instant is accurate to well under a minute in dynamical time across the fitted range, which is far better than anyone needs. In Universal Time the limit is ΔT: for the recent past it is measured and reliable, but for centuries ahead it is extrapolated and the uncertainty grows into minutes and eventually hours. The Julian Ephemeris Day is reported alongside precisely so the dynamical instant survives whatever ΔT turns out to be.
The season lengths are the most informative output on the page. Their inequality — nearly five days between the longest and the shortest — is a direct measurement of the eccentricity of the Earth's orbit. Because perihelion currently falls in early January, the Earth sweeps through the northern-winter half of its orbit fastest, making northern winter the shortest season and northern summer the longest.
That arrangement is not permanent. Perihelion precesses through the calendar with a period of about 21,000 years, so the pattern of long and short seasons slowly rotates: roughly 10,000 years from now the December solstice to March equinox interval will be the long one. The precession is one of the Milankovitch cycles, and it is measured through exactly this kind of calculation run backwards.
Assumptions and limits
- The polynomials are fitted to 1000–3000. Outside that range they diverge, and the calculator refuses the year rather than extrapolating.
- Dates before October 1582 are proleptic Gregorian. Contemporary records from those years used the Julian calendar, which by then ran about ten days behind.
- ΔT is modelled, not known, for the future. The dynamical instant is solid; the Universal Time reading degrades for distant years because the Earth's rotation slows unpredictably.
- The events are astronomical, not meteorological. Meteorological seasons start on the first of March, June, September and December and have no connection to the Sun's longitude.
- No daylight saving is applied. The local column adds exactly the offset you type.
- Equal day and night is not what an equinox means. Because sunrise is defined by the Sun's upper limb at the refracted horizon, the date on which day and night are truly equal falls a few days either side of the equinox and depends on latitude.
The equinox is not the day of equal day and night
The word means “equal night”, and the date it names is not the date it describes. Sunrise and sunset are defined by the Sun's upper limb at the horizon, with about 34 arcminutes of atmospheric refraction lifting its apparent position on top of 16 arcminutes of solar radius. That adds several minutes of daylight at each end, so at the equinox the day is 12 h 07 m long at the equator and slightly longer still at higher latitudes. The date of genuinely equal day and night, called the equilux, falls a few days before the March equinox and a few days after the September one, and its offset grows with latitude. The daylight hours calculator shows the effect directly, and the sunrise and sunset calculator explains where the 0.833° allowance comes from.
Related calculations and where these dates are used
The solstices set the extremes of the Sun's declination, which is the input to every solar-geometry calculation on this site: the solar declination calculator gives δ for any date, and the daylight hours calculator turns it into a day length. The equinoxes are where the day-over-day change in daylight is fastest, and the solstices where it is zero.
The March equinox is also a calendrical anchor. The date of Easter is defined against an ecclesiastical approximation of it, fixed at 21 March regardless of where the true equinox actually falls — the Easter date calculator works through the computus, and the divergence between the real and the ecclesiastical equinox is exactly the drift the Gregorian reform was designed to arrest, as the leap year calculator explains.
Several other calendars begin their year at the March equinox as computed rather than as approximated. The Iranian Solar Hijri calendar starts Nowruz on the day containing the equinox at Tehran's meridian, which makes the exact instant and the chosen longitude jointly decisive for the date — a rare case where a civil calendar depends directly on an astronomical computation of this kind, and where the local column on this page matters as much as the Universal Time one.
Key terms
- Apparent geocentric longitude
- The Sun's position along the ecliptic as seen from the centre of the Earth, corrected for aberration and nutation. Its exact multiples of 90° define the four events.
- Tropical year
- The interval between successive passages of the Sun through the same equinox, about 365.2422 days. Shorter than the sidereal year because of the precession of the equinoxes.
- Nutation
- A small nodding of the Earth's axis with an 18.6-year period, driven by the regression of the lunar nodes. It supplies the largest term of the periodic correction.
- Perihelion
- The point of the Earth's orbit closest to the Sun, currently reached in early January. Its position drifts through the calendar with a period of roughly 21,000 years.
- Equilux
- The date on which day and night are genuinely equal, a few days away from the equinox because of refraction and the Sun's angular radius.