Sun Angle Calculator

Our sun angle calculator helps you estimate the Sun's position in the sky regarding its elevation and azimuth angles.

Maximum elevation today57.8936°90° − |latitude − declination|, reached at solar noon

Sunrise04:15:34local clock time at UTC+0 — the moment the sun's UPPER LIMB clears the horizon, not its centre

Sunset19:58:37

Day length15 h 43 min943.04 minutes — 8 minutes for every degree of hour angle either side of noon

Night length8 h 17 min

Civil twilight begins03:33:34sun 6° below the horizon — bright enough to read outside

Civil twilight ends20:40:38the evening one lasts 42 minutes after sunset

Nautical twilight begins02:35:43sun 12° below the horizon — the horizon is still visible at sea

Nautical twilight ends21:38:29the evening one lasts 99.9 minutes after sunset

Astronomical twilight begins01:04:06sun 18° below the horizon — the sky is fully dark

Astronomical twilight ends23:10:06the evening one lasts 191.5 minutes after sunset

Solar noon12:07:06when the sun is due south and highest — this is 7.1 minutes AFTER clock noon, because clock time is a political convention and the sun keeps its own

Equation of time-6.584 minuteshow far apparent solar time runs ahead of mean solar time today. It swings between about −14 and +16 minutes over a year, from Earth's orbital eccentricity and axial tilt together — and it is why a sundial disagrees with a clock

Longitude correction-0.51 minutesfour minutes per degree from the zone meridian, because Earth turns 15° an hour

Solar declination19.401°the latitude where the sun is directly overhead today. It runs between ±23.44°, and those two extremes ARE the tropics

Sun elevation at that hour57.8633°above the horizon at 12:00 local

Sun azimuth at that hour176.854°clockwise from true north

Shortest shadow of a 1 m pole0.6275 mat solar noon — this is exactly how Eratosthenes measured the size of the Earth in 240 BC

Air mass at noon1.1806×how much atmosphere the light crosses against straight overhead — this is why the midday sun burns and the setting sun does not

The formula

cos θ_z = sin φ sin δ + cos φ cos δ cos H

Why the equinox is not twelve hours

Sunrise is defined as the moment the sun's upper limb touches the horizon, not its centre, which happens about 16 arcminutes early. Atmospheric refraction lifts the image by roughly another 34 arcminutes, so the geometric centre of the sun is about 0.833° below the horizon when sunrise is reported. Both effects lengthen the day at each end.

The result is that day length exceeds twelve hours at the equinox everywhere on Earth — by about seven minutes at the equator and more at higher latitudes, where the sun crosses the horizon at a shallower angle and so takes longer to do it. The dates of equal day and night, the equiluxes, fall a few days either side of the equinoxes rather than on them.

Clock noon is not solar noon

Two separate effects pull them apart. Longitude contributes four minutes for every degree away from the time zone's meridian, because Earth turns 15° an hour — at the western edge of a wide zone solar noon can fall well after one o'clock. The equation of time contributes up to another sixteen minutes, from the eccentricity of Earth's orbit and the tilt of its axis acting together.

That second term is why a sundial disagrees with a clock, and why the sun traces a figure of eight — the analemma — if photographed at the same clock time through a year. It is also why the earliest sunset and the shortest day are not the same date.

Polar day and night

Above the Arctic and below the Antarctic circle the sun's daily circle can lie entirely above or entirely below the horizon, and there is no sunrise to report. That is a real answer rather than a failure, and this calculator says so instead of returning an error.