Daylight Hours Calculator
What this daylight hours calculator does
This calculator estimates the number of daylight hours (photoperiod) between sunrise and sunset for any latitude and day of the year. It uses standard solar geometry to approximate how long the Sun stays above the ideal horizon, assuming a clear, unobstructed view of the sky.
You can use the results to compare seasons, understand how daylight changes with latitude, or get a first-pass estimate for planning gardening, outdoor work, or solar energy production. For precise legal sunrise/sunset times at a specific address, you should still rely on an astronomical or weather service.
How the daylight calculation works
The calculation is based on the tilt of Earth’s axis (about 23.45°) and Earth’s position in its orbit. Two angles are central to the model:
- Latitude : your location north (positive) or south (negative) of the Equator, in degrees.
- Solar declination : the latitude where the Sun is directly overhead at solar noon on a given day.
A commonly used approximation for solar declination in degrees, as a function of day-of-year (1–366), is:
This captures the yearly swing of the Sun’s apparent path: is positive when the Sun is north of the Equator (Northern Hemisphere summer) and negative when it is south (Northern Hemisphere winter).
Once is known, we find the sunrise hour angle , which represents the angular distance the Earth rotates between solar noon and sunrise (or sunset). In an idealized model:
The hour angle is measured in degrees. If we convert this rotation to time, we obtain the photoperiod , the total hours of daylight:
The factor appears because:
- Earth rotates about 15° per hour (360°/24 h).
- Daylength includes the time from sunrise to solar noon and from solar noon to sunset, so the hour angle is doubled.
Near the poles, the expression can fall outside the range . In that case, the model predicts either continuous day (24 hours of sun above the horizon) or continuous night (0 hours of sun). The calculator detects these conditions and reports 24 h or 0 h accordingly.
Interpreting the results
The output is the idealized number of daylight hours for your chosen latitude and day-of-year. Some ways to interpret the value:
- Short days (e.g., 8–10 hours) usually mean winter in your hemisphere, with limited time for outdoor work and reduced solar energy production.
- Moderate days (around 12 hours) occur near the equinoxes, when day and night are roughly equal worldwide.
- Long days (15+ hours) indicate summer at mid to high latitudes, often helpful for crops, outdoor activities, and solar generation.
- 24 hours indicates continuous daylight (midnight sun), while 0 hours indicates polar night.
Remember that this is a geometric model at sea level with a flat horizon. Real-world sunrise and sunset can differ by several minutes because of refraction, terrain, and atmospheric conditions.
Worked example: mid-latitude city in summer
Suppose you want to estimate the daylight hours in Berlin, Germany (about 52.5° N) on the June solstice (around day-of-year ).
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Set the inputs.
- Latitude (positive for the Northern Hemisphere).
- Day-of-year .
-
Estimate solar declination.
Around the June solstice, is close to +23.45°. Using the formula above gives a value within a fraction of a degree of this. -
Compute the cosine of the sunrise hour angle.
Convert and to radians internally, then evaluate . For 52.5° and 23.45°, this product is between −1 and 1, so there is a normal sunrise and sunset rather than polar day or night. -
Find the hour angle and convert to time.
Taking and applying , we obtain roughly 16.5 hours of daylight.
A typical astronomy table for Berlin confirms that late June daylight is about 16.5–16.8 hours, showing that this simple model provides a good first approximation.
Typical daylight by latitude and season
The table below compares idealized daylight lengths at the June and December solstices for different latitudes. Values are rounded and may differ slightly from the calculator output because of rounding and model choices.
| Latitude | June solstice daylight (h) | December solstice daylight (h) | Seasonal context |
|---|---|---|---|
| 0° (Equator) | ≈ 12.1 | ≈ 12.1 | Nearly equal day and night all year |
| 30° N | ≈ 14.4 | ≈ 9.8 | Subtropical locations with noticeable seasons |
| 50° N | ≈ 16.4 | ≈ 7.9 | High-latitude regions with long summer days and short winter days |
| 66.5° N (Arctic Circle) | 24.0 | 0.0 | Experiencing midnight sun in summer and polar night in winter |
| 35° S | ≈ 9.7 | ≈ 14.5 | Southern mid-latitudes with seasons opposite to the Northern Hemisphere |
Use the calculator to reproduce or refine these values for specific days close to the solstices, or to explore intermediate dates such as the equinoxes (around days 80 and 264).
Practical uses and planning examples
Because daylight hours change predictably through the year, this calculator can support a range of planning tasks:
- Agriculture and gardening: Compare spring and summer daylengths to choose planting dates for long-day or short-day crops, or to schedule irrigation and field work in available light.
- Solar energy and off-grid systems: Estimate seasonal variation in potential solar generation, or combine with panel and battery models to size systems for the darkest part of the year.
- Outdoor work and events: Plan construction shifts, outdoor classes, or events when there is enough natural light without relying heavily on artificial lighting.
- Ecology and biology: Photoperiod influences animal migration, breeding cycles, and plant phenology. Researchers often use daylength as a key environmental driver.
For more detailed solar-angle analysis, you can pair this calculator with a solar declination or solar altitude tool to examine how high the Sun gets in the sky for the same dates and locations.
Assumptions and limitations
The model behind this calculator uses several simplifying assumptions. These make it fast and easy to use but also explain why it may not match official sunrise/sunset times exactly.
- Spherical Earth with no terrain: Mountains, hills, buildings, and trees are ignored. Real horizons that are higher or lower than the ideal sea-level horizon will shift sunrise and sunset by minutes or more.
- No atmospheric refraction: The bending of light in the atmosphere lets you see the Sun slightly before it is geometrically above the horizon. Official sunrise/sunset definitions account for this; this calculator does not.
- Idealized Sun size and definition of sunrise: The Sun is treated as a point, and sunrise/sunset are defined when the center of the Sun reaches the horizon. Many almanacs define events when the upper limb of the Sun touches the horizon instead.
- Day-of-year treatment: The input runs from 1 to 366 so you can represent leap years. The mapping between calendar dates and is approximate in this simple model, especially near leap days.
- Latitude range and polar regions: The formulas are intended for latitudes between about 0° and 66.5°, but the calculator also handles higher latitudes by detecting polar day and night. Near the Arctic and Antarctic Circles, small changes in or can flip between 0, very short, very long, or 24-hour daylight.
- No time zones or clock times: The output is a duration in hours, not local clock times for sunrise and sunset. Time zones, daylight saving time, and your longitude within the time zone are outside the scope of this tool.
Because of these assumptions, use the results for educational, comparative, or preliminary planning purposes rather than for safety-critical navigation or legal timekeeping.
Related tools for deeper solar analysis
If you want to go further, consider pairing this daylight hours result with other calculators:
- Solar Declination Angle Calculator: Explore how the Sun’s declination changes through the year and how it relates to seasons at different latitudes.
- Solar-Powered IoT Sensor Duty Cycle Calculator: Translate available daylight into estimated device uptime based on panel size, load, and storage.
- Solar Panel Cleaning Calculator: Estimate how soiling and cleaning schedules might affect energy yield, using your seasonal daylight profile as context.
FAQs about daylight length and accuracy
Why are days longer in summer and shorter in winter?
Because Earth’s axis is tilted about 23.45°, your hemisphere leans toward the Sun in its summer and away from the Sun in its winter. When you lean toward the Sun, its apparent path crosses the sky higher and for a longer time, producing longer days. When you lean away, the path is lower and shorter, producing short winter days.
How does latitude affect daylength?
Near the Equator, daylength stays close to 12 hours all year. As you move toward the poles, the seasonal swing increases: summers bring very long days, and winters bring very short days. Above the Arctic and Antarctic Circles, you can experience 24-hour daylight in summer and 24-hour darkness in winter.
Why doesn’t this match my weather app exactly?
Weather and astronomical services include effects such as atmospheric refraction, the finite size of the Sun, local elevation, and detailed Earth-orbit models. This calculator uses a simpler geometric approach that is usually within a few minutes of those values but not identical.
Can I use this for solar energy planning?
Yes, as a starting point. The calculator tells you how daylight duration changes with season and latitude, which is important for estimating seasonal solar production. For system design, you should combine this with local irradiance data, panel specifications, shading analysis, and, if possible, long-term measurements from your site.