Solar Azimuth & Sun Path Calculator
Calculate solar azimuth angle, solar elevation/zenith angle, solar noon time, and day length for any latitude and day of the year using astronomical algorithms.
Astronomical Solar Coordinates
Solar Azimuth & Sun Path Calculator - Elevation, Solar Noon & Declination: Free Solar Azimuth & Sun Path Calculator tool: calculate solar azimuth angle, solar elevation/zenith angle, solar noon time, and day length for any.
How to Use the Solar Azimuth & Sun Path Calculator - Elevation, Solar Noon & Declination
Enter Geographic Latitude & Longitude
Specify coordinates in decimal degrees (e.g. 37.77° N, -122.42° W).
Input Target Calendar Date & Local Time
Select any day of the year (solstice, equinox, or today) and target clock time.
Specify Local Time Zone UTC Offset
Enter standard or daylight savings UTC offset (e.g. -5 for EST, -4 for EDT, -7 for PDT).
Analyze Elevation, Azimuth & Solar Noon Time
Review sun height above the horizon, compass azimuth bearing, and exact solar noon.
Engineering Guide: Principles & Formula Details
Understanding the astronomical geometry of the sun path is fundamental to maximizing photovoltaic solar panel energy harvest and minimizing inter-row shadow casting. The position of the sun in the sky at any given second is completely described by two spherical angular coordinates: the Solar Elevation angle (alpha) and the Solar Azimuth angle (phi). The elevation angle measures the vertical angle between the sun and the local horizontal plane, while the azimuth angle measures the compass bearing of the sun along the horizon relative to true North.
Solar noon represents the exact astronomical instant when the sun crosses the local celestial meridian and reaches its highest elevation of the day. Because standard clock time is grouped into broad artificial time zones spanning 15 degrees of longitude each, and because Earth elliptical orbit causes the planet to speed up and slow down throughout the year (described by the Equation of Time), solar noon rarely coincides exactly with 12:00 PM on the clock. It typically occurs between 11:45 AM and 12:45 PM.
Earth 23.44-degree axial tilt creates the annual cycle of solar declination (delta), which shifts from +23.44° on the summer solstice (June 21) to -23.44° on the winter solstice (December 21). At the equinoxes in March and September, declination is zero. This seasonal variation causes the sun midday elevation to swing by 46.88 degrees between summer and winter, which dictates the minimum spacing required between solar panel ground-mount rows to prevent winter self-shading.
For fixed-tilt photovoltaic arrays, orienting panels to true solar azimuth (180° due South in the Northern Hemisphere, or 0° due North in the Southern Hemisphere) delivers the highest cumulative annual kilowatt-hour production. However, in regions with time-of-use (TOU) billing where utilities charge premium rates between 4 PM and 9 PM, rotating arrays slightly west of south (azimuth 210° to 240°) sacrifices minor morning production in exchange for high-value peak afternoon solar output.
Key Engineering Features & Advantages
NOAA Algorithm Precision
Implements official NOAA and Spencer solar astronomical trigonometric position algorithms.
Exact Compass Bearing
Provides solar azimuth degrees clockwise from true North for site compass alignment.
Solar Noon Calculation
Identifies the precise minute when the sun peaks for midday solar testing and calibrations.
Seasonal Declination Tracking
Tracks Earth axial tilt from +23.45° summer solstice to -23.45° winter solstice.
Inter-Row Shading Sizing
Essential for calculating winter solstice row-to-row spacing on commercial solar arrays.
Global Coordinate Support
Accurately computes sun trajectories for any latitude on Earth (-90° to +90°).
Frequently Asked Questions
Solar elevation is the angle of the sun above the horizontal ground plane (0° at horizon, 90° directly overhead). Solar zenith angle is the angle between the sun and the vertical zenith (straight up). Elevation and zenith are complementary: Elevation = 90° - Zenith.
Solar noon differs from 12:00 PM because of two factors: (1) Longitude offset: time zones are wide, and clock time only matches solar time at the exact center meridian; (2) Equation of Time: Earth elliptical orbit and axial tilt cause the sun to be up to 16 minutes fast or 14 minutes slow.
In the Northern Hemisphere, 180° (due South) is the standard azimuth for maximum total annual energy production. In the Southern Hemisphere, 0° (due North) is optimal. Facing panels 210° to 230° (Southwest) can increase afternoon production under time-of-use tariffs.
By standard astronomical convention: 0° is North, 90° is East, 180° is South, and 270° is West.