Daylight Hours Calculator Latitude

Daylight Hours Formula:

\[ \text{Daylight Hours} = \frac{2}{15} \times \arccos(-\tan(\text{lat}) \times \tan(\text{decl})) \]

Daylight Hours:

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1. What is the Daylight Hours Calculator?

The Daylight Hours Calculator estimates the number of daylight hours at a specific latitude and solar declination angle. It uses astronomical formulas to calculate sunrise and sunset times, providing accurate daylight duration for any location on Earth.

2. How Does the Calculator Work?

The calculator uses the daylight hours formula:

\[ \text{Daylight Hours} = \frac{2}{15} \times \arccos(-\tan(\text{lat}) \times \tan(\text{decl})) \]

Where:

\( \text{lat} \) — Latitude in degrees (-90° to 90°)
\( \text{decl} \) — Solar declination in degrees (-23.45° to 23.45°)
\( \frac{2}{15} \) — Conversion factor from degrees to hours
\( \arccos \) — Inverse cosine function
\( \tan \) — Tangent function

Explanation: The formula calculates the hour angle of sunrise/sunset and converts it to time, accounting for the Earth's axial tilt and geographic position.

3. Importance of Daylight Hours Calculation

Details: Accurate daylight hours calculation is essential for agriculture, solar energy planning, architectural design, tourism, and understanding seasonal variations in different geographic regions.

4. Using the Calculator

Tips: Enter latitude between -90° (South Pole) and 90° (North Pole), and solar declination between -23.45° and 23.45° (Earth's axial tilt limits). All values must be valid numeric inputs.

5. Frequently Asked Questions (FAQ)

Q1: What is solar declination?
A: Solar declination is the angle between the rays of the sun and the plane of the Earth's equator. It varies throughout the year due to Earth's axial tilt.

Q2: How does latitude affect daylight hours?
A: Higher latitudes experience greater seasonal variation in daylight hours, with polar regions having 24-hour daylight in summer and 24-hour darkness in winter.

Q3: What are typical declination values?
A: Declination ranges from +23.45° at summer solstice (June 21) to -23.45° at winter solstice (December 21), and 0° at equinoxes.

Q4: Why use arccos in the formula?
A: The arccos function calculates the hour angle when the sun is at the horizon, which determines sunrise and sunset times.

Q5: Are there limitations to this calculation?
A: This formula provides theoretical maximum daylight and doesn't account for atmospheric refraction, terrain, or local horizon obstructions.