Azimuth Angle Calculator
Find the solar azimuth altitude and declination using latitude longitude hour angle and day of year. Online sun position calculator for panels or navigation.
About This Calculator
The Azimuth Angle Calculator determines the exact position of the sun in the sky for any location on Earth and any day of the year. It computes three key metrics: the solar azimuth (horizontal direction measured clockwise from north), the solar altitude (elevation above the horizon), and the solar declination (the sun's angular distance from the equator). This tool is essential for solar panel installers optimizing panel tilt and orientation, navigators using the sun as a directional reference, astronomers planning observations, and architects designing buildings for passive solar heating.
The calculations use standard solar geometry formulas. Solar declination is computed using Cooper's equation: δ = 23.45° × sin(360/365 × (284 + N)) where N is the day of year. The solar elevation is derived from: sin(α) = sin(φ)×sin(δ) + cos(φ)×cos(δ)×cos(H) where φ is latitude and H is the hour angle. The solar azimuth is calculated using the atan2 function with the hour angle, latitude, and declination, then normalized to a 0–360° scale measured clockwise from north.
Regional Notes
India: Located between 8°N and 37°N, India experiences high solar altitude year-round. Summer solstice declination of +23.45° means the sun passes nearly overhead. Solar panels in India typically face south at a tilt angle equal to the latitude minus 10–15°.
United States: Spanning 25°N to 49°N, the US has significant seasonal variation in solar position. Northern states see winter sun altitudes below 25°, while southern states enjoy altitudes above 40° even in winter. Solar panel orientation varies from south-facing in most states to southwest-facing in some regions.
United Kingdom: Located between 50°N and 58°N, the UK has low solar altitudes especially in winter when the sun barely rises above 15° at noon. Solar panels are typically tilted at 30–40° facing south, though the abundant cloud cover reduces overall efficiency compared to sunnier climates.
Frequently Asked Questions
What is the solar azimuth angle?
The solar azimuth angle is the horizontal direction of the sun measured clockwise from true north. It ranges from 0° to 360°, where 0° is north, 90° is east, 180° is south, and 270° is west. Together with altitude, it describes the sun's exact position in the sky for any location and time.
How is the solar altitude angle calculated?
The solar altitude (elevation) angle is calculated using the formula: sin(altitude) = sin(latitude)×sin(declination) + cos(latitude)×cos(declination)×cos(hour angle). The declination depends on the day of year using Cooper's equation: declination = 23.45° × sin(360/365 × (284 + day)).
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 is 0° at solar noon, negative before noon, and positive after noon. Each hour equals 15° of hour angle. For example, 10:00 AM has an hour angle of -30° and 2:00 PM has +30°.
How does the day of year affect solar position?
The day of year determines the solar declination angle, which is the latitude where the sun is directly overhead at noon. On the summer solstice (day 172, June 21), declination is +23.45° and the sun is highest. On the winter solstice (day 355, December 21), declination is -23.45° and the sun is lowest.
Why is azimuth important for solar panel positioning?
Solar panels generate maximum energy when facing directly toward the sun. In the northern hemisphere, panels ideally face true south (180° azimuth), while in the southern hemisphere they face true north (0° azimuth). Tracking the sun's azimuth throughout the day can increase energy harvest by 25-35%.
How is this calculator useful for navigation?
In navigation, the sun's azimuth provides a directional reference when a compass is unavailable. By measuring the sun's position and knowing the local time and date, navigators can determine true north. This technique is used in orienteering, maritime navigation, and wilderness survival.
Can I use this calculator for any location worldwide?
Yes, this calculator works for any latitude and longitude on Earth. Enter positive latitudes for the northern hemisphere and negative for the southern hemisphere. Longitude is used for reference but does not directly affect the solar position formulas, which depend on latitude, day of year, and hour angle.
What is the solar declination angle?
Solar declination is the angle between the sun's rays and the Earth's equatorial plane. It varies between +23.45° at the summer solstice and -23.45° at the winter solstice due to Earth's 23.5° axial tilt. At the equinoxes, declination is 0° and the sun is directly above the equator.