Enter the solar declination angle, latitude of the location, and the hour angle into the calculator to determine the solar azimuth angle.

Solar Azimuth Formula

The following formula is used to calculate the solar azimuth angle.

A = cos^{-1}[(sin(δ) - sin(φ) * cos(h)) / (cos(φ) * sin(h))]


  • A is the solar azimuth angle (degrees) δ is the solar declination angle (degrees) φ is the latitude of the location (degrees) h is the hour angle (degrees)

To calculate the solar azimuth angle, subtract the product of the sine of the latitude and the cosine of the hour angle from the sine of the solar declination angle. Divide the result by the product of the cosine of the latitude and the sine of the hour angle. Finally, find the inverse cosine of the quotient to get the solar azimuth angle.

What is a Solar Azimuth?

A Solar Azimuth is a measurement used in astronomy to determine the direction of the sun or other celestial bodies from the observer’s standpoint on the earth’s surface. It is calculated in degrees, with the north direction set as zero degrees, and increases clockwise towards the east. The azimuth indicates the sun’s position in relation to true north at a specific time and location. It is a crucial component in solar tracking systems and solar energy studies.

How to Calculate Solar Azimuth?

The following steps outline how to calculate the Solar Azimuth Angle.

  1. First, determine the solar declination angle (δ) in degrees.
  2. Next, determine the latitude of the location (φ) in degrees.
  3. Next, determine the hour angle (h) in degrees.
  4. Next, calculate the numerator of the formula: sin(δ) – sin(φ) * cos(h).
  5. Next, calculate the denominator of the formula: cos(φ) * sin(h).
  6. Finally, calculate the Solar Azimuth Angle using the formula: A = cos^-1[(sin(δ) – sin(φ) * cos(h)) / (cos(φ) * sin(h))].
  7. After inserting the values of the variables and calculating the result, check your answer with a calculator or online tool.

Example Problem:

Use the following variables as an example problem to test your knowledge:

solar declination angle (δ) = 23

latitude of the location (φ) = 40

hour angle (h) = 60