1. What Is Daylight Hours Calculation?

The daylight hours calculation determines the duration of daylight at a specific location on Earth for a given date. It uses astronomical formulas based on latitude and solar declination to predict sunrise and sunset times.

2. How Does The Calculator Work?

The calculator uses the daylight hours formula:

Where:

• \( lat \) — Latitude in radians
• \( decl \) — Solar declination in radians
• \( \arccos \) — Inverse cosine function
• \( \tan \) — Tangent function

Explanation: The formula calculates the hour angle of sunrise/sunset and converts it to hours of daylight. The division by 15 converts from degrees to hours (15 degrees per hour).

3. Importance Of Daylight Calculation

Details: Daylight duration calculations are essential for agriculture, solar energy planning, architectural design, tourism, and understanding seasonal variations in different geographical locations.

4. Using The Calculator

Tips: Enter latitude and declination values in radians. Remember to convert from degrees to radians if necessary (degrees × π/180). Ensure inputs are within valid mathematical ranges for trigonometric functions.

5. Frequently Asked Questions (FAQ)

Q1: How do I convert degrees to radians?
A: Multiply degrees by π/180 (approximately 0.0174533). For example, 45 degrees = 45 × π/180 = 0.7854 radians.

Q2: 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.

Q3: Why does daylight duration vary?
A: Daylight duration varies due to Earth's axial tilt (23.5°), latitude, and time of year, causing seasonal changes in day length.

Q4: What are typical daylight hours?
A: At equator: ~12 hours year-round. At poles: 0-24 hours depending on season. Mid-latitudes: 8-16 hours seasonally.

Q5: When is the calculation invalid?
A: The calculation fails when |tan(lat)×tan(decl)| > 1, indicating polar day (24h daylight) or polar night (0h daylight) conditions.