Table of Contents
What Is Sun Angle?
The sun angle, or solar elevation angle, is the angle between the sun's position and the horizontal plane at a given location and time. When the sun is at the horizon, the elevation is 0 degrees; when directly overhead, it is 90 degrees. The solar azimuth angle indicates the compass direction of the sun measured from true north.
Solar position depends on three main factors: the observer's latitude, the day of the year (which determines solar declination), and the time of day (which determines the hour angle). These parameters allow precise calculation of where the sun appears in the sky at any moment.
Solar Position Formulas
where δ is solar declination and n is the day of year.
where α is solar elevation, φ is latitude, and h is the hour angle (15° per hour from solar noon).
Seasonal Solar Angles
| Date | Declination | Noon Elevation (40°N) |
|---|---|---|
| March Equinox | 0° | 50.0° |
| June Solstice | +23.45° | 73.45° |
| Sept Equinox | 0° | 50.0° |
| Dec Solstice | -23.45° | 26.55° |
Practical Applications
- Solar panel installation: Optimal tilt angle equals latitude for annual energy, adjusted seasonally.
- Architecture: Building orientation and window placement for passive solar heating.
- Agriculture: Predicting shadow lengths for crop spacing and greenhouse design.
- Photography: Planning golden hour and blue hour shoots based on solar altitude.
Frequently Asked Questions
What is the maximum sun angle at my latitude?
The maximum solar elevation at any latitude occurs at solar noon on the summer solstice. The formula is: max elevation = 90° - latitude + 23.45°. For 40°N, the maximum is 73.45°.
Why does the sun angle matter for solar panels?
Solar panels produce maximum power when sunlight strikes them perpendicularly. By knowing the sun angle throughout the year, you can set the panel tilt for maximum annual energy capture or adjust it seasonally for better performance.
How accurate is this calculator?
This calculator uses the standard solar position equations which are accurate to within about 1 degree. For higher precision (needed for solar tracking systems), atmospheric refraction correction and the equation of time should be applied.