Daylight Hours Calculator
Exploring how solar geometry controls daylength
The number of hours between sunrise and sunset—known as the photoperiod—shifts throughout the year because Earth’s axis is tilted by approximately 23.45° relative to its orbital plane. As our planet orbits the Sun, this tilt causes each hemisphere to lean toward or away from the Sun at different times, stretching or shortening the span of daylight. Gardeners track photoperiod to plan planting dates, ecologists examine it to study animal migrations, and energy planners use it to anticipate seasonal solar production swings.
Photoperiod calculations begin with the solar declination angle \(\delta\), which specifies the latitude where the Sun is directly overhead at solar noon. A widely used approximation in degrees is:
Once \(\delta\) is known, the sunrise hour angle \(h_s\) satisfies the relationship:
where \(φ\) is the latitude in radians. Converting the angular distance from degrees to hours yields the photoperiod \(N\):
The 2/15 factor reflects Earth’s rotation rate of 15° per hour. When the cosine argument exceeds ±1—typical near the poles during solstices —the calculation indicates polar day (24 hours) or polar night (0 hours). The calculator accounts for those limits by constraining the argument and clearly reporting the permanent daylight state.
| Latitude | Daylight hours | Seasonal context |
|---|---|---|
| 0° (Equator) | 12.1 | Nearly equal day and night year-round |
| 30° N | 14.4 | Subtropical cities with warm, long summer evenings |
| 50° N | 16.4 | High-latitude regions like central Canada or northern Europe |
| 66.5° N | 24.0 | Arctic Circle experiencing midnight sun |
Shifts in daylight influence agriculture, renewable energy design, wildlife behavior, and even human circadian health. Cold-climate planners use long winter nights to forecast heating demand, while architects orient buildings to capture or avoid summer sun. Pairing the calculator’s outputs with real observations—such as sunrise clocks or solar production logs—sharpens intuition about seasonal rhythms.
Continue exploring seasonal planning
Extend this analysis with the Solar Declination Angle Calculator, the Solar-Powered IoT Sensor Duty Cycle Calculator, and the Solar Panel Cleaning Calculator to translate photoperiod insights into energy production, sensor uptime, and maintenance strategies.