Airmass Calculator (Atmospheric Extinction of Stars and the Sun)
How much atmosphere the light of a star or the Sun crosses at a given altitude above the horizon, and how much that dims it, using the Kasten–Young formula.
Results
The dashed line marks the value you entered.
What this tool does
Airmass is 1 straight overhead and grows as you look lower: 2 at 30° above the horizon, about 5.6 at 10° and nearly 38 at the horizon. The simple 1 ÷ cos z rule is fine above 30° but blows up at the horizon, where the curved atmosphere and refraction matter, so the Kasten–Young formula is used here. Astronomers observe at low airmass because each airmass costs about 0.2 magnitudes of light at a good site, rising with dust, humidity and shorter wavelengths.
Formula
X = 1 ÷ [ cos z + 0.50572 (96.07995° − z)^−1.6364 ] (Kasten and Young, 1989) · Δm = k X
Variables
| Symbol | Meaning | Unit |
|---|---|---|
alt | Altitude of the object above the horizon | ° |
k | Extinction coefficient (magnitudes per airmass; about 0.2 at a good low site) | mag |
X | Airmass (Kasten–Young) | — |
XS | Simple estimate, 1 ÷ cos(zenith angle) | — |
Z | Zenith angle | ° |
DM | Dimming by the atmosphere | mag |
TR | Share of the light that gets through | % |
Worked example
- Altitude of the object above the horizon30 °
- Extinction coefficient (magnitudes per airmass; about 0.2 at a good low site)0.2 mag
- Airmass (Kasten–Young)1.994
- Simple estimate, 1 ÷ cos(zenith angle)2.000
- Zenith angle60.0 °
- Dimming by the atmosphere0.399 mag
- Share of the light that gets through69.3 %
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.