12h07m
Latitude · drag0.0°
90°SEquator90°N
- Daylight
- Civil twilight 6°
- Nautical 12°
- Astronomical 18°
- Night
1 Jan
Drag across the year · ← → keys
The length of a day is nothing but geometry: a tilted planet, a latitude and a date. Slide the bead along the meridian and the band of light swells from the flat ribbon of the equator into the midnight sun of the Arctic, then turns upside-down as you cross into the south. Every curve on this sheet is worked out from those two angles while you move.
12h07m
Every parallel from pole to pole, every day of the year. The twelve-hour contours pinch together at the equinoxes; refraction keeps them a few days apart, so day and night are never quite equal everywhere at once.
The same year bent into a circle, January at the top. Each day is one ray; its yellow length is its daylight.
cos ω = (sin h − sin φ sin δ) / (cos φ cos δ)ω hour angle of the sun at altitude h · φ latitude · δ solar declination
Simplifications. Sunrise and sunset are taken at a solar altitude of −0.83°, the standard allowance for refraction and the sun’s radius; there is no further atmospheric correction. Where the formula has no solution the sun either never sets or never rises.
Hours are local solar time, so noon always sits in the middle of the day. The equation of time and time zones are left out: they shift clock times but leave the length of the day untouched. The dot on the hairline reads this device’s clock.
Declination comes from the sun’s mean longitude and anomaly for the current year, laid on a 365-day axis, so dates may differ from an almanac by a day. Civil, nautical and astronomical twilight end with the sun 6°, 12° and 18° below the horizon.