Day Length Calculator

Work out day length instantly with clear inputs, formula shown and shareable results.

About Day Length Calculator

Day length follows from the sunrise hour angle, whose cosine is -tan(latitude) tan(declination). At 51.5 degrees north on the June solstice, declination is about 23.4 degrees and the hour angle 122 degrees, giving 16 hours 22 minutes of daylight. The formula ignores refraction and the Sun's disc, which add roughly six minutes.

Formulas

Sunrise hour angle

cos(H) = -tan(latitude) x tan(declination)

Day length

hours = 2H / 15

Worked example

With the default values below, Day Length Calculator returns Day Length of 16.404. Change any input above and every figure here is recalculated in your browser.

Inputs used

Latitudeaccepts -66–66 deg: 51.5 deg
Date: 2026-06-21

Results

Day Length: 16.404 h
Day Length As Hours And Minutes: 16h 24m
Solar Declination: 23.44 deg
Sunrise Hour Angle: 123.03 deg

Step by step

1Values used
2Sunrise hour angle
3Day length
4Day Length= 16.404 h
5Day Length As Hours And Minutes= 16h 24m
6Solar Declination= 23.44 deg
7Sunrise Hour Angle= 123.03 deg

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why is the calculated day slightly shorter than published sunrise to sunset?

Because official times allow for atmospheric refraction and use the upper limb of the Sun, adding about three minutes at each end.

What happens above the Arctic Circle?

The cosine exceeds one in magnitude, meaning permanent day or night. The calculator limits latitude to 66 degrees for that reason.