How is the length of a day calculated?

From two inputs, latitude and the day of the year. The day of the year sets the sun declination through a standard cosine formula, and the declination combined with the latitude gives the hour angle of sunrise. Doubling that hour angle and converting to time yields the number of daylight hours. It is straightforward trigonometry used by every astronomical almanac.

Why is the answer called geometric daylight?

Because it measures the time the centre of the sun is above the true horizon, ignoring atmospheric refraction and the size of the sun disc. Refraction bends sunlight so the sun appears to rise a little early and set a little late, which is why real sunrise-to-sunset is usually a few minutes longer than the geometric figure.

What happens at very high latitudes?

Near the poles the sun can stay above or below the horizon all day. When that happens the formula returns 24 hours of polar day or 0 hours of polar night rather than a normal sunrise and sunset, which is exactly what places inside the Arctic and Antarctic circles experience around the solstices.

Do I need my longitude or time zone?

Not for the length of the day. Day length depends only on latitude and date. Longitude and time zone shift the clock times of sunrise and sunset but do not change how many hours of daylight there are, so they are not needed here.

What is the Daylight Hours Calculator?

Calculate how many hours of daylight a place gets on any date from its latitude, using the standard astronomical sunrise equation. Shows the day length plus the longest and shortest days of the year. It runs free in your browser on Gera Tools, with nothing uploaded.

Daylight Hours Calculator

Name: Daylight Hours Calculator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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How long is the day where you are

The number of daylight hours a place receives depends on just two things — how far it sits from the equator and where the Earth is in its orbit. This calculator takes a latitude and a date and returns the length of the day using the same sunrise equation that powers astronomical almanacs. Enter your latitude, pick a date, and see the hours and minutes of daylight instantly.

The astronomy behind it

Each day of the year corresponds to a solar declination, the angle of the sun above or below the celestial equator, which swings between about plus and minus 23.44 degrees over the year. Combine that declination with your latitude and a little trigonometry gives the hour angle at which the sun crosses the horizon. Double it, convert from degrees to time, and you have the day length. The figure is geometric, meaning it tracks the centre of the sun and leaves out the few minutes that atmospheric refraction adds at each end.

Longest and shortest days

Alongside the date you choose, the tool shows the longest and shortest days of the year for your latitude — the values around the June and December solstices. The gap between them widens the further you travel from the equator, from almost nothing at the tropics to full polar day and night inside the polar circles. It is a quick way to see just how much the seasons swing where you live.