Sun Angle Calculator
Sun elevation and azimuth calculator for any location and time. Free solar position finder with sun path charts for solar energy, photography, and astronomy.
About This Calculator
The Sun Angle Calculator (also called a solar position calculator) computes the precise location of the Sun in the sky for any location on Earth at any given date and time. It returns two key values — the solar elevation angle (how high the Sun is above the horizon) and the solar azimuth angle (the compass direction of the Sun). Whether you are installing solar panels, planning a photography shoot, designing a building for passive solar heating, or simply curious about where the Sun is right now, this tool gives you instant, accurate results.
The calculator uses standard astronomical formulas. First, the solar declination is computed from the day of the year, ranging between -23.45° and +23.45° due to Earth axial tilt. Then the hour angle is derived from the local solar time, changing by 15° per hour. Using the latitude, declination, and hour angle, the elevation angle is found via α = arcsin(sinδ·sinφ + cosδ·cosφ·cosγ). The azimuth angle is computed from the same parameters and corrected for the time of day. The sun path chart shows the elevation angle plotted for every hour of the day, giving you a complete picture of the Sun arc at your location.
How to Use
Enter your latitude (positive for north, negative for south), select your date, enter the local time in 24-hour format, and choose your timezone offset from UTC. Click Calculate to see the Sun position. The chart tab lets you toggle between the computed angles and the full-day sun path visualization.
Regional Notes
India (IN): India spans latitudes from about 8°N to 37°N. The timezone is UTC+5:30 year-round with no daylight saving. At 28.6°N (New Delhi), the summer noon elevation reaches about 85° in June, while the winter noon elevation drops to about 38° in December.
United States (US): The US covers latitudes from about 19°N (Hawaii) to 71°N (Alaska). Timezones range from UTC-5 (Eastern) to UTC-8 (Pacific), plus Alaska and Hawaii. Daylight saving time shifts clocks forward by one hour from March to November. At 40.7°N (New York), the noon elevation ranges from about 26° in December to 73° in June.
United Kingdom (UK): The UK spans latitudes from about 50°N to 60°N. Timezone is UTC+0 (GMT) in winter and UTC+1 (BST) in summer. At 51.5°N (London), the Sun reaches only about 15° at noon in December but climbs to about 62° in June, with very long summer days and short winter days.
Frequently Asked Questions
What is the solar elevation angle?
The solar elevation angle measures how high the Sun is above the horizon. It ranges from -90° (below horizon at night) to +90° (directly overhead at the zenith). A 0° elevation means the Sun is at the horizon during sunrise or sunset.
What is the solar azimuth angle?
The solar azimuth angle tells you the compass direction of the Sun. It is measured clockwise from true north, ranging from 0° (north) through 90° (east), 180° (south), and 270° (west). Use this along with elevation to pinpoint the Sun exact location in the sky.
How is the Sun declination angle calculated?
The solar declination angle varies between -23.45° and +23.45° due to Earth axial tilt of 23.45°. It is approximated as -23.45° × cos(360/365 × (day + 10)), where day is the day of the year. The declination is 0° at the equinoxes and reaches its extremes at the solstices.
Why does the Sun path change with seasons?
The Sun path changes because Earth axis is tilted 23.45° relative to its orbital plane. In summer, the Sun rises earlier, sets later, and reaches a higher elevation at noon. In winter, it stays lower in the sky with shorter daylight hours. The effect is more pronounced at higher latitudes.
How accurate is this Sun angle calculator?
This calculator uses the standard solar position algorithm with the simplified declination formula, accurate to within about 1° for most locations and dates. For precise applications like solar tracking, use the NOAA solar calculator which accounts for atmospheric refraction and Earth orbital eccentricity.
Can I use this for solar panel angle optimization?
Yes. The optimal tilt angle for a fixed solar panel is roughly equal to your latitude for year-round production. For winter optimization, add 10-15° to the latitude; for summer, subtract 10-15°. Use the sun path chart to see the Sun elevation throughout the day at your location.
What is the hour angle in solar calculations?
The hour angle measures the angular distance of the Sun east or west of the local meridian. It changes by 15° per hour (360° per 24 hours). It is 0° at solar noon, negative in the morning, and positive in the afternoon. The hour angle is used alongside declination and latitude to compute elevation and azimuth.
How do I find the best time for golden hour photography?
Golden hour occurs when the Sun elevation is between 0° and about 6° above the horizon. Use the sun path chart to find times when the elevation falls in this range. At lower latitudes, golden hour is shorter; at higher latitudes, it can last much longer, especially near sunrise and sunset in summer.