Sunrise Sunset Calculator

How a sunrise time is actually calculated

Sunrise is not the moment the centre of the sun crosses the horizon. The standard definition used by the US National Oceanic and Atmospheric Administration is the moment the sun's upper edge appears, with the atmosphere bending the light around the curve of the Earth. Both effects are folded into a single number: the geometric zenith angle of 90.833 degrees, made up of 90 degrees for the horizon, about 0.267 degrees for the sun's apparent radius, and about 0.567 degrees for average refraction. Every mainstream sunrise table, including this one, starts from that convention.

From there the arithmetic is short. The tool converts your date into a day of the year and builds a fractional year angle, then evaluates two Fourier series that astronomers fitted to the sun's motion: the equation of time, which measures how far the real sun runs ahead of or behind clock noon, and the solar declination, which is how far north or south of the celestial equator the sun sits that day. With declination and your latitude, the hour angle for the 90.833 degree zenith falls out of one cosine formula, and that angle converts straight into minutes either side of solar noon.

Worked example: New York City, 20 March 2026

Enter latitude 40.71, longitude -74.01, and a UTC offset of -4 for Eastern Daylight Time. Day 79 of the year gives a declination close to zero, as you would expect at the March equinox, and an equation of time of roughly -7 minutes, meaning the real sun crosses the meridian about seven minutes after clock noon before the longitude correction. Solar noon lands at 13:04 EDT, because New York sits about 4 degrees west of the centre of its time zone and daylight saving pushes everything an hour later. Sunrise comes out at 07:01, sunset at 19:07, and day length at 12 hours 6 minutes. Civil dawn starts 06:34 and civil dusk ends 19:35, so there is roughly 27 minutes of usable light before the sun itself appears.

The equinox is not exactly a 12-hour day, which surprises people. Because sunrise is measured on the sun's upper edge and refraction lifts the image above its true position, day length exceeds 12 hours by six to eight minutes at mid-latitudes on the equinox. The date when day and night are truly equal, called the equilux, falls a few days earlier in spring and a few days later in autumn.

The twilight ladder

Once the sun is below the horizon, three thresholds matter. Civil twilight runs to 6 degrees below and is what this calculator reports as civil dawn and civil dusk; outdoor tasks are still possible and most jurisdictions tie headlight and navigation-light rules to it. Nautical twilight ends at 12 degrees, historically the last moment a navigator could take a star sight against a visible sea horizon. Astronomical twilight ends at 18 degrees, after which the sky contributes no measurable glow and faint galaxies come within reach. Above roughly 60 degrees of latitude in June, the sun never gets 6 degrees down at all, which is why the tool prints a continuous-twilight note instead of blank fields.

Who uses these numbers

Photographers plan around golden hour, the stretch while the sun is below about 6 degrees of elevation, and blue hour, which is the civil twilight window shown here. Runners and cyclists use civil dawn and dusk to decide when lights become a legal requirement. Muslim prayer times derive Fajr and Isha from twilight angles that vary by convention, typically 18 or 15 degrees, so the civil pair here acts as a sanity check rather than a substitute for a fiqh-specific table. Gardeners track day length because many plants flower on a photoperiod trigger rather than a temperature one, and solar owners compare day length against panel output to spot shading problems.

Limits worth knowing

Three things this calculator deliberately does not model. Elevation: standing 300 metres above the surrounding terrain gains you roughly 3 to 4 minutes of daylight at each end, and this tool assumes sea level. Horizon obstruction: a ridge 5 degrees high to the east delays visible sunrise by 20 minutes or more at mid-latitudes, far more than any algorithmic refinement. Local refraction: the 0.567 degree average can vary by a tenth of a degree in extreme temperature inversions, which is why polar sunrise tables carry explicit warnings.

The UTC offset field is a plain number rather than a time zone name, so daylight saving is on you. If your result is exactly one hour off, that is almost always the cause: New York is -5 in winter and -4 in summer, London is 0 and +1, Sydney is +10 and +11. The tool prefills the offset your browser is currently using, which is correct for today but not for a date on the other side of a clock change.