Day Length

Length of daylight, sunrise and sunset in local solar time for any latitude and date, polar day and polar night.

What to find:

the day length on any date

the day length on an equinox or solstice

Coordinates in degrees: 55.75, 55°45′, 55 45 21, 55°45′ N; southern latitude and western longitude with a minus sign or the letters S / W.

The day length calculator finds the length of daylight and the sunrise and sunset times in local solar time for any latitude and date, and detects polar day and polar night.

How it works

cos ω = −tan φ · tan δ, T = ^2ω/_15° h

ω is the sunset hour angle — how many degrees the Earth turns from noon to sunset, and δ is the solar declination on that day. If cos ω ≤ −1, the Sun does not set (polar day); if cos ω ≥ 1, it does not rise (polar night).

On the equinoxes day and night are equal (12 h) at all latitudes. The closer to a pole, the more the day length changes over the year; beyond the polar circles (66.6°) there are polar day and polar night.

The calculation uses the center of the Sun's disk without atmospheric refraction, so the real day is a few minutes longer.

Example. Saint Petersburg, 59.9° N, June 21: cos ω = −tan 59.9° · tan 23.44° ≈ −0.749, ω ≈ 138.5°, T ≈ 18 h 28 min.