Hours of Daylight Calculator

Daylight Length Equation:

\[ DL = 2 \times \frac{\arccos(-\tan \phi \tan \delta) \times (180 / \pi)}{15} \]

Daylight Length (DL):

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1. What is the Daylight Length Equation?

The daylight length equation calculates the number of daylight hours at a given latitude on Earth for a specific solar declination angle. It's based on astronomical principles of Earth's rotation and axial tilt.

2. How Does the Calculator Work?

The calculator uses the daylight length equation:

\[ DL = 2 \times \frac{\arccos(-\tan \phi \tan \delta) \times (180 / \pi)}{15} \]

Where:

\( DL \) — Daylight length in hours
\( \phi \) — Latitude in degrees (-90 to 90)
\( \delta \) — Solar declination in degrees (-23.45 to 23.45)

Explanation: The equation accounts for the geometric relationship between the observer's latitude and the Sun's declination angle.

3. Importance of Daylight Calculation

Details: Daylight length affects agriculture, energy consumption, human circadian rhythms, and various ecological processes. Accurate calculation is essential for solar energy systems and astronomical observations.

4. Using the Calculator

Tips: Enter latitude between -90° (South Pole) to 90° (North Pole). Solar declination varies between -23.45° and 23.45° throughout the year (approximately ± Earth's axial tilt).

5. Frequently Asked Questions (FAQ)

Q1: What is solar declination?
A: Solar declination is the angle between the Sun's rays and Earth's equatorial plane, varying seasonally due to Earth's axial tilt.

Q2: How does latitude affect daylight hours?
A: Near the equator, daylight varies little throughout the year. At higher latitudes, variation increases, with continuous daylight or darkness near the poles during solstices.

Q3: What's the maximum possible daylight hours?
A: At the poles during summer solstice, daylight can last 24 hours. At the Arctic/Antarctic circles (66.56° latitude), maximum is 24 hours during respective summer solstices.

Q4: Why does the equation return 0 or 24 hours sometimes?
A: This indicates polar night (0 hours) or midnight sun (24 hours) when the Sun doesn't set or rise for that latitude and declination combination.

Q5: How accurate is this calculation?
A: It provides theoretical daylight length. Actual daylight may differ slightly due to atmospheric refraction and the Sun's angular diameter.