Calculator inputs
Formula used
The page estimates day length from the sunrise hour angle. A commonly used relation is:
Day length = (2 × H0) ÷ 15
where H0 is the sunrise hour angle in degrees. It is obtained from:
cos(H0) = [sin(h0) − sin(φ)sin(δ)] ÷ [cos(φ)cos(δ)]
- φ = observer latitude
- δ = solar declination for the selected date
- h0 = chosen solar altitude threshold
The default altitude angle of -0.833° approximates apparent sunrise and sunset by including atmospheric refraction and the Sun’s radius.
How to use this calculator
- Enter the calendar date you want to study.
- Type the latitude in decimal degrees.
- Keep -0.833° for standard sunrise and sunset estimates, or change the altitude angle for twilight studies.
- Select the declination model you prefer.
- Press Calculate day length to view the result block, chart, and export options.
- Download the generated result as CSV or PDF if needed.
Example data table
| Latitude | Date | Altitude angle | Approx. day length | Notes |
|---|---|---|---|---|
| 0.0° | March 20 | -0.833° | 12.11 h | Near equal day and night. |
| 40.7° N | June 21 | -0.833° | 15.05 h | Long summer daylight. |
| 40.7° N | December 21 | -0.833° | 9.24 h | Short winter daylight. |
| 65.0° N | June 21 | -0.833° | 21.11 h | Very long subpolar day. |
Why day length changes
Earth’s axis is tilted about 23.44°. As Earth orbits the Sun, that tilt changes the Sun’s apparent declination, which shifts sunrise and sunset times for each latitude. Locations near the equator stay close to 12 hours, while higher latitudes show stronger seasonal swings.
FAQs
1. What does this calculator measure?
It estimates the length of daytime between sunrise and sunset, or another chosen solar altitude threshold, using date, latitude, and a solar declination model.
2. Why is -0.833° used by default?
That angle is a standard apparent sunrise and sunset correction. It roughly accounts for atmospheric refraction and the visible solar disc radius near the horizon.
3. Does it give local clock sunrise time?
No. The listed sunrise and sunset are solar-time estimates centered on solar noon. Clock time also depends on longitude, time zone, and the equation of time.
4. What happens near the poles?
The formula can return continuous daylight or continuous darkness for part of the year. The page labels those cases as midnight sun or polar night.
5. Which declination model should I choose?
Both are useful approximations. Spencer is slightly more refined, while Cooper is simple and common for educational calculations and quick engineering estimates.
6. Can I use this for twilight duration studies?
Yes. Change the solar altitude angle to values like -6°, -12°, or -18° to study civil, nautical, or astronomical twilight thresholds.
7. Why does the equator stay near 12 hours?
The Sun’s daily path changes less there across the year, so sunrise and sunset remain relatively balanced compared with higher latitudes.
8. Is this suitable for precise observatory scheduling?
It is strong for planning and education, but precise observing work should also include longitude, time zone, elevation, refraction models, and ephemeris-based timing.