What formula does this calculator use?

It implements the NOAA Solar Calculator algorithm, which is itself a practical version of Jean Meeus's "Astronomical Algorithms". The Julian Day Number is computed with the Fliegel–Van Flandern integer formula, then the sun's ecliptic longitude, right ascension, and declination are derived from the Julian centuries since J2000.0, and finally the hour angle is solved from the standard spherical-trigonometry relation — cos(H) = (cos(zenith) - sin(lat)*sin(dec)) / (cos(lat)*cos(dec)) — to place sunrise and sunset on either side of solar noon.

Why are times given in UTC and not my local time?

UTC is the universal reference that is unambiguous regardless of time zone or daylight-saving rules. To convert to your local time, simply add your UTC offset. For example, if you are in Paris (UTC+2 in summer), add 2 hours to every time shown.

How accurate are the results?

For latitudes between roughly -65 deg and +65 deg the algorithm is accurate to within about one minute of the true time. Closer to the poles the sun skims the horizon at a shallow angle, stretching any small angular error into a larger time error. For extreme polar latitudes, expect an accuracy of a few minutes.

What does solar noon mean, and why does it differ from 12:00?

Solar noon is the moment the sun reaches its highest point in the sky — its meridian transit. It equals 12:00 local solar time by definition, but it rarely coincides with noon on your clock for two reasons: your location is probably not exactly on your time-zone's central meridian, and the equation of time shifts solar time by up to about 16 minutes depending on the time of year due to the eccentricity of Earth's orbit and the obliquity of the ecliptic.

What is the equation of time, and why does it matter?

The equation of time is the difference between apparent solar time (as read by a sundial) and mean solar time (as kept by a clock). It ranges from about -14 minutes in February to +16 minutes in November. The calculator reports it so you can understand why solar noon is not always at your midday, and it is baked into the solar-noon calculation automatically.

What happens at extreme latitudes like the Arctic or Antarctic?

Near the poles, the sun can stay continuously above the horizon for weeks (midnight sun / polar day) or continuously below it (polar night). When that occurs the hour-angle formula has no solution — cos(H) falls outside the range -1 to 1 — and the calculator reports a polar-condition message instead of times. Roughly speaking, polar day occurs in summer for latitudes above about 66.5 deg (or below -66.5 deg in the southern hemisphere).

Is any data sent to a server?

No. Every calculation runs entirely inside your browser using JavaScript. No coordinates, dates, or results are ever transmitted to any server.

Sunrise & Sunset Calculator

A sunrise and sunset calculator that works entirely in your browser using a published astronomical algorithm. Enter any latitude, longitude, and date and the tool returns the exact UTC times for sunrise, solar noon, and sunset, together with the total daylight duration, the sun’s declination, and the equation of time — all with no network request and no API key required.

How it works

The calculation follows the NOAA Solar Calculator method, a practical distillation of Jean Meeus’s Astronomical Algorithms. The steps are:

Julian Day Number — the date is converted to a continuous count of days since noon UTC on 1 January 4713 BC using the Fliegel–Van Flandern integer formula.
Julian centuries since J2000.0 — expressed as n / 36525 where n is the day offset from 1.5 January 2000.
Solar position — the sun’s mean longitude, mean anomaly, equation of centre, true longitude, apparent longitude, obliquity of the ecliptic, and finally right ascension and declination (delta) are derived from polynomial fits to the orbital elements.
Equation of time — a trigonometric expression that quantifies the difference between apparent solar time (sundial) and mean solar time (clock), in minutes.
Solar noon — noon_UTC = (720 - 4 * longitude - eqT) / 60 hours, where longitude is in degrees and eqT is the equation of time in minutes.
Hour angle — the key formula is:

cos(H) = (cos(zenith) - sin(lat) * sin(dec)) / (cos(lat) * cos(dec))

For standard sunrise/sunset the zenith is 90.833 degrees, which already accounts for atmospheric refraction (about 0.5 deg) and the semi-diameter of the solar disc (about 0.25 deg). Sunrise occurs at noon - H/15 hours UTC; sunset at noon + H/15.
Polar conditions — when cos(H) falls outside the range (-1, 1) the sun never crosses the horizon and no time exists; the calculator reports this state explicitly.

Worked example: London, midsummer

For 21 June 2026 at latitude 51.5074 N, longitude -0.1278 E (London):

Sunrise: approximately 03:43 UTC (04:43 BST, UTC+1)
Solar noon: approximately 12:01 UTC
Sunset: approximately 20:21 UTC (21:21 BST)
Daylight duration: roughly 16 h 38 m
Solar declination: +23.4 deg (sun at its northernmost point, summer solstice)

Compare with 21 December 2026 (winter solstice):

Sunrise: approximately 08:03 UTC
Sunset: approximately 15:57 UTC
Daylight duration: only about 7 h 54 m

The dramatic swing from nearly 17 hours to under 8 hours of daylight across the year illustrates why latitude has such a large effect on seasons at temperate and polar locations.

Formula note

The zenith value of 90.833 deg is a standard convention that bakes in:

0.5833 deg for atmospheric refraction at the horizon (air bends sunlight slightly upward, so you see the sun rise a little before it geometrically clears the horizon)
The remaining 0.25 deg accounts for the solar disc radius

If you wanted astronomical sunrise (geometric centre of the sun on the mathematical horizon, no refraction), you would use a zenith of exactly 90 deg instead.

The equation of time means that the earliest sunrise and latest sunset do not fall exactly on the solstice — the earliest UK sunset occurs around 12 December, a week or two before the December solstice, precisely because of this effect.