Enter the observer's latitude, the moon's declination, and the hour angle into the calculator to determine the moon elevation.

Moon Elevation Formula

The following formula is used to calculate the moon elevation. 

E = arccos((sin(L) * sin(D)) + (cos(L) * cos(D) * cos(H)))

Variables:

  • E is the moon elevation (degrees)
  • L is the observer's latitude (degrees)
  • D is the moon's declination (degrees)
  • H is the hour angle, which is the time since the moon crossed the observer's meridian, expressed in degrees (15 degrees per hour)

To calculate the moon elevation, first calculate the sine of the observer's latitude and the sine of the moon's declination. Multiply these two values together. Then, calculate the cosine of the observer's latitude and the cosine of the moon's declination. Multiply these two values together, then multiply the result by the cosine of the hour angle. Add the two results together, then calculate the arccosine of the result to get the moon elevation.

What is a Moon Elevation?

Moon elevation refers to the angle between the observer's horizon and the moon. It is measured in degrees, with 0 degrees indicating that the moon is on the observer's horizon and 90 degrees indicating that the moon is directly overhead. The moon's elevation changes throughout the night due to the rotation of the Earth.

How to Calculate Moon Elevation?

The following steps outline how to calculate the Moon Elevation using the given formula:

  1. First, determine the observer's latitude (L) in degrees.
  2. Next, determine the moon's declination (D) in degrees.
  3. Next, determine the hour angle (H) in degrees.
  4. Using the formula E = arccos((sin(L) * sin(D)) + (cos(L) * cos(D) * cos(H))), substitute the values of L, D, and H into the formula.
  5. Finally, calculate the Moon Elevation (E) in degrees.
  6. After inserting the variables and calculating the result, check your answer with a scientific calculator or online tool.

Example Problem:

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

Observer's latitude (L) = 45 degrees

Moon's declination (D) = 20 degrees

Hour angle (H) = 30 degrees