Sun Angle Calculator
Calculate solar elevation and azimuth angles for any location and time using astronomical formulas
Calculate Sun Position
North positive, South negative (-90° to 90°)
East positive, West negative (-180° to 180°)
Select the date for calculation
24-hour format local time
Solar Position Results
Calculation Details
Day of Year: 0
Solar Declination: 0.00°
Hour Angle: 0.18°
Local Solar Time: 12.01 hours
Sun Status: Below horizon (Not visible)
Solar Position Analysis
Solar Position Formulas
Solar Elevation Angle (α)
α = sin⁻¹[sin δ sin φ + cos δ cos φ cos γ]
Solar Azimuth Angle (β)
β = cos⁻¹[(sin δ cos φ - cos δ sin φ cos γ) / cos α]
Variables
- α: Solar elevation angle
- β: Solar azimuth angle
- δ: Solar declination angle
- φ: Latitude of observer
- γ: Hour angle
Additional Formulas
- δ = -23.45° × cos[360°/365 × (d + 10)]
- γ = 15° × (T - 12)
- d = day of year
- T = local solar time (hours)
Quick Location Selection
Sun Path Information
Angle Interpretation
Elevation Angle
Twilight Phases
Understanding Solar Position Calculations
What are Solar Angles?
Solar angles describe the position of the Sun in the sky relative to an observer on Earth. The two primary angles are elevation (altitude) and azimuth, which together precisely define the Sun's location using spherical coordinates.
Key Components
- •Solar Declination: Earth's tilt causes seasonal variation (-23.45° to +23.45°)
- •Hour Angle: Earth's rotation relative to solar noon
- •Latitude: Observer's position north or south of equator
- •Atmospheric Refraction: Light bending affects apparent position
Applications
- 1Solar Panel Design: Optimize orientation and tilt angles for maximum energy capture
- 2Architecture: Design building orientation and window placement for natural lighting
- 3Photography: Plan optimal lighting conditions and golden hour timing
- 4Agriculture: Understand crop sun exposure and growing conditions
- 5Navigation: Traditional celestial navigation and orientation
Note: These calculations use simplified models suitable for most practical applications. Professional astronomical software may use more complex algorithms for higher precision.
Seasonal Sun Path Variations
Winter Solstice
December 21: Lowest sun path in Northern Hemisphere. Sun declination at -23.45°. Shortest day and longest shadows.
Equinoxes
March/September 21: Sun crosses celestial equator. Declination = 0°. Day and night equal length worldwide.
Summer Solstice
June 21: Highest sun path in Northern Hemisphere. Sun declination at +23.45°. Longest day and shortest shadows.