Day Length Calculator
Daylight hours, night hours, and solar declination from latitude and date.
What it does
Day length swings with latitude and season: the equator holds near 12 hours year round while 40 N stretches to 14 h 51 min at the June solstice and shrinks near 9 h 20 min at December's. Past the polar circles the sun skips setting or rising for weeks.
The tool above takes latitude with a calendar date. It returns daylight hours with night hours and solar declination beside them.
The default of 40 N on 2026-06-21 gives 14 h 51 min day with 9 h 09 min night at +23.4 deg declination. The equator on March 20 gives 12 h 00 min, and 70 N on June 21 gives the full 24 h polar day.
The geometry follows federal solar calculation methods with published accuracy notes matching each caveat. Both place solstice declination near 23.44 degrees and warn refraction bends real horizons by minutes.
How to use
- Enter latitude: north positive, south negative.
- Pick any calendar date.
- Read daylight first for the date.
- Read night for the remainder.
- Compare solstices to feel the swing.
Formula
- N
- Day of year, 1 to 365.
- decl
- Solar declination swinging +-23.44 deg.
- H
- Half day hour angle from the cosine rule.
Research grade simplification without refraction or clock conversions: sunrise times need longitude and equation of time on top. Polar zones clamp to 24 or 0 hours honestly.
Worked example
Example: 40 N on June 21
Defaults: latitude 40, date 2026-06-21 (day 172).
- Declination: -23.44 x cos(360/365 x 182) = +23.4 deg.
- cosH: -tan(40) x tan(23.4) = -0.364.
- H: acos gives 111.3 deg, day = 2 x 111.3 / 15 = 14.84 h.
- Split: 14 h 51 min day with 9 h 09 min night.
- Tool shows 14 h 51 min, 9 h 09 min night, +23.4 deg solar declination.
Reference table
| Place / date | Daylight | Note |
|---|---|---|
| 40 N, June 21 | 14 h 51 min | Summer solstice |
| Equator, March 20 | 12 h 00 min | Equinox balance |
| 70 N, June 21 | 24 h 00 min | Polar day |
| 40 N, December 21 | 9 h 09 min | Winter solstice |
Limits
- Research simplification: refraction adds minutes at horizons.
- Clock sunrise needs longitude and time math too.
- No legal or certified use; observatories decide disputes.
- Southern seasons mirror with flipped dates.
Common mistakes
- Expecting clock times from a length tool.
- Forgetting south latitudes flip the seasons.
- Reading solstice as hottest day instead of longest.
- Ignoring refraction at real horizons.
- Assuming 12 hours everywhere on equinox exactly.
Try it yourself
Quick checks. Answers sit tucked under each question.
Equator on March 20?
12 h 00 min day with 12 h 00 min night.
70 N on June 21?
24 h 00 min: full polar day.
40 N on December 21?
9 h 09 min: the short end of the swing.
Questions
How long is today?
Enter latitude and date: 40 N on June 21 gives 14 h 51 min.
Why do days change length?
Tilted axis aims each hemisphere toward or away from the sun through the year.
What is solar declination?
The sun latitude overhead at noon, swinging +-23.44 deg with seasons.
When is the longest day?
Near June 21 north, December 21 south of the equator.
What is polar day?
Sun never setting inside the summer polar circle: 24 h of daylight.
Exact 12 hours on equinox?
Nearly: refraction and the sun disk add minutes around 12.