Enter the zenith angle in degrees into the calculator to determine the total air mass.

Air Mass Formula

The following formula is used to calculate an air mass.

AM = 1 / Cos (ZA)
  • Where AM is the air mass
  • ZA is the zenith angle

To calculate air mass, divide the value of 1 by the cosine of the zenith angle.

What is an air mass?


In this context, the air mass is a measure of how much atmosphere sunlight has to travel through to reach a point. It’s measured as a ratio of the amount of atmosphere relative to the amount of atmosphere sunlight has to travel through when it is directly overhead.

For example, 1.25 air masses would be 25% more air mass than directly above.

What is a zenith angle?

A zenith angle is a measure of the angle from the surface to the line of the sun in the sky. It is measured only at sea level.

How to calculate air mass?

Example Problem:

The following example outlines how to calculate the amount of air sunlight needs to travel through, aka. the air mass.

First, determine the zenith angle. In this example, the zenith angle is measured to be 30 degrees.

Next, the final and last step is to use the formula above to calculate the air mass.

AM = 1 / Cos (ZA)

AM = 1 / Cos (30)

AM = 1.1547