What declination should I use?

Solar declination varies from +23.44° (June solstice) to -23.44° (December solstice). At equinoxes it is 0°, giving exactly 12 hours everywhere.

What happens at the Arctic Circle?

At 66.56° latitude, the formula gives 24 hours at summer solstice (midnight sun) and 0 hours at winter solstice (polar night).

No. This gives centre-of-disc sunrise to sunset. Civil twilight adds roughly 30-40 minutes of usable light at each end.

Estimate the number of daylight hours from your latitude and the Sun's declination using the hour-angle formula.

Latitude

Solar Declination

Daylight Hours

14.92 hrs

Night Hours9.08 hrs

Daylight Hours vs Latitude

The number of hours between sunrise and sunset depends on latitude and the Sun's declination (which changes through the year).

D = (2/15) × arccos(-tan(φ) × tan(δ)) hours

where φ = latitude and δ = solar declination (both in degrees, converted to radians for calculation).

Solar declination ranges from -23.44° (Dec solstice) to +23.44° (Jun solstice).

New York (40.7°N) at summer solstice (declination = 23.44°).