Daylight Calculator

Calculate the approximate hours of daylight for any latitude and day of the year using solar declination and hour angle geometry.

DAYLIGHT HOURS
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Solar Declination
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Hour Angle
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Night Hours
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Sunrise Approx
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What is Daylight Duration?

Daylight duration is the length of time between sunrise and sunset on a given day at a specific location. It varies throughout the year due to the tilt of Earth's rotational axis (23.44 degrees) relative to its orbital plane around the Sun. This axial tilt causes the Sun's declination angle to change over the course of a year, resulting in longer days in summer and shorter days in winter for locations away from the equator.

At the equator, daylight remains nearly constant at about 12 hours year-round. As you move toward the poles, the seasonal variation increases dramatically. Above the Arctic Circle (66.56 degrees N) and below the Antarctic Circle, there are periods of continuous daylight (midnight sun) and continuous darkness (polar night) lasting from days to months depending on how close you are to the poles.

The Formula

δ = 23.44 × sin(360/365 × (284 + N))
ω = arccos(-tan(φ) × tan(δ))
Daylight Hours = 2ω / 15

Where δ is the solar declination, N is the day of year, φ is the latitude, and ω is the hour angle at sunrise/sunset. The factor of 15 converts degrees to hours (360 degrees / 24 hours = 15 degrees/hour).

Seasonal Variation

  • Summer Solstice (~June 21): Maximum daylight in Northern Hemisphere, minimum in Southern
  • Winter Solstice (~Dec 21): Minimum daylight in Northern Hemisphere, maximum in Southern
  • Equinoxes (~Mar 20, Sep 22): Nearly equal day and night everywhere on Earth
  • Polar regions: Experience 24-hour daylight or darkness near solstices

Daylight by Latitude (Summer Solstice)

LatitudeLocation ExampleJune 21 Daylight
Quito, Ecuador~12h 7m
30°NCairo, Egypt~14h 0m
45°NMinneapolis, USA~15h 37m
60°NHelsinki, Finland~18h 50m
66.5°NArctic Circle~24h 0m

Frequently Asked Questions

Why is daylight not exactly 12 hours at the equinox?

Atmospheric refraction bends sunlight around the curvature of the Earth, making the Sun visible even when it is geometrically below the horizon. This adds about 6-8 minutes of extra daylight. Additionally, sunrise and sunset are defined by when the upper limb (top edge) of the Sun crosses the horizon, not the center.

What latitude has the most daylight variation?

The Arctic and Antarctic Circles (66.56 degrees) mark the boundary where at least one day has 24 hours of daylight and one day has 0 hours. The variation increases as you move poleward until the poles experience 6 months of continuous daylight and 6 months of darkness.

Does altitude affect daylight hours?

Yes, higher altitudes can slightly increase daylight because the observer can see further around the curvature of the Earth. A mountain summit may experience a few extra minutes of daylight compared to sea level at the same latitude.