Choose a calculation to estimate optical air mass from apparent zenith angle or from date and location, with optional surface-pressure adjustment. The secant and Kasten–Young models are approximations; air mass is dimensionless.

Estimate relative optical air mass from apparent solar zenith angle. This simple model becomes inaccurate near the horizon.

Angle from the local vertical to the apparent Sun. Use 0° overhead and less than 90°.

Air Mass Formula

The basic secant model uses the following formula. The Kasten–Young and date/location modes use a curved-atmosphere approximation and optional pressure correction, shown in their calculation details.

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?

Definition:

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?

Zenith angle is measured from the local vertical to the Sun at any elevation. Apparent zenith includes atmospheric refraction. The date/location mode estimates geometric zenith using NOAA’s seasonal equations, then applies a standard refraction correction before calculating air mass.

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