Solar Altitude And Day Length Calculator

Solar Altitude Formula:

\[ \text{Altitude} = \arcsin(\sin(\delta) \sin(\phi) + \cos(\delta) \cos(\phi) \cos(HA)) \]

Solar Altitude:

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1. What is a Solar Altitude Calculator?

Definition: This calculator determines the sun's elevation angle above the horizon (altitude) at a specific location and time.

Purpose: Essential for solar panel placement, architecture, photography, and understanding daylight patterns.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Altitude} = \arcsin(\sin(\delta) \sin(\phi) + \cos(\delta) \cos(\phi) \cos(HA)) \]

Where:

\( \delta \) — Solar declination (Earth's axial tilt relative to the sun)
\( \phi \) — Observer's latitude
\( HA \) — Hour angle (time from solar noon)

Explanation: The formula combines the effects of Earth's tilt, location, and time of day to determine sun position.

3. Understanding the Inputs

Solar Declination: Varies from +23.45° (June solstice) to -23.45° (December solstice). 0° at equinoxes.

Latitude: Your location's angular distance from equator (-90° to +90°).

Hour Angle: 0° at solar noon, +15° per hour after noon, -15° per hour before noon.

4. Practical Applications

Solar Energy: Optimize solar panel tilt angles for maximum energy collection.

Architecture: Design buildings with proper shading and daylighting.

Photography: Plan golden hour and blue hour photography sessions.

5. Frequently Asked Questions (FAQ)

Q1: What is considered a "high" solar altitude?
A: Above 60° is high (summer midday), 30-60° is moderate, below 30° is low (winter/horizon).

Q2: How does solar altitude affect day length?
A: Higher maximum altitudes correlate with longer daylight hours.

Q3: What's the solar altitude at sunrise/sunset?
A: 0° (exactly at horizon), negative values indicate night time.

Q4: Where can I find current solar declination values?
A: Use our Solar Declination Calculator or astronomical tables.

Q5: How accurate is this calculation?
A: Very accurate for theoretical values, though atmospheric refraction can make the sun appear about 0.5° higher near horizons.