Daylight Hours Calculator
Length of daylight at a latitude on a given day of the year, with the solar declination and noon sun height.
Results
What this tool does
Day number 172 is the June solstice and 355 the December one; 80 and 266 are the equinoxes, when every latitude gets twelve hours. The further from the equator, the wider the swing — which is the whole reason seasons exist. Valid between 66° north and south; inside the polar circles the sun can fail to set or rise at all.
Formula
δ = 23.45° sin(360(284+N)÷365) ; cos ω = −tan φ tan δ
Variables
| Symbol | Meaning | Unit |
|---|---|---|
la | Latitude | ° |
nd | Day of the year | — |
H | Hours of daylight | h |
DE | Solar declination | ° |
NI | Hours | h |
NO | Sun height at noon | ° |
Worked example
- Latitude38.7 °
- Day of the year172
- Hours of daylight14.7114 h
- Solar declination23.4498 °
- Hours9.2886 h
- Sun height at noon74.750 °
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.
Frequently asked questions
Why does this not match the sunrise time in my newspaper?
Published times usually define sunrise as the moment the sun's upper edge appears, and they correct for atmospheric refraction, which bends light over the horizon and adds several minutes at each end. This calculation treats the sun as a point at the geometric horizon, so it typically gives a shorter day by roughly six to ten minutes at mid latitudes, and much more near the poles.