Air Mass Calculator
Light from a star low in the sky passes through far more air than light from overhead. Enter the altitude to see the air mass and how much the star is dimmed.
Air mass
How much air the light passes through, and how much it dims.
90° is straight overhead, 0° the horizon.
Per air mass, V band. About 0.15 at a dry mountain site, 0.3 or more in hazy city air.
Air mass (Kasten and Young)
1.413
At 45.0° altitude, a zenith angle of 45.0°. Overhead is 1.
- Plane-parallel, sec z
- 1.414
- Extinction
- 0.28 mag
- Light lost
- 22.9%
| Altitude | Air mass | Dimming | Light lost |
|---|---|---|---|
| 90° | 1.00 | 0.20 mag | 17% |
| 60° | 1.15 | 0.23 mag | 19% |
| 45° | 1.41 | 0.28 mag | 23% |
| 30° | 1.99 | 0.40 mag | 31% |
| 20° | 2.90 | 0.58 mag | 41% |
| 10° | 5.59 | 1.12 mag | 64% |
| 5° | 10.31 | 2.06 mag | 85% |
Extinction changes with wavelength, dust and humidity. Measure it on the night for precise photometry.
How this is calculated
- 1
Zenith angle
The zenith angle z is 90° minus the altitude, so an object halfway up the sky at 45° altitude has z = 45°.
- 2
Plane-parallel air mass
Treating the atmosphere as a flat slab gives X = sec z = 1 / cos z. It is accurate high in the sky but runs to infinity at the horizon.
- 3
Kasten and Young (1989)
Allowing for the Earth's curvature, X = 1 / (cos z + 0.50572 (96.07995 − z)^−1.6364), with z in degrees. It gives about 38 at the horizon.
- 4
Extinction
The dimming in magnitudes is k × X, where k is the extinction coefficient. The fraction of light lost is 1 − 10^(−0.4 k X).
Frequently asked questions
What is air mass in astronomy?
The length of the path light takes through the atmosphere, relative to the path straight up. It is 1 overhead, 2 at 30° altitude and about 38 at the horizon.
What is a typical extinction coefficient?
In the visual (V) band about 0.12 to 0.15 magnitudes per air mass at a high, dry observatory, 0.2 at a decent rural site and 0.3 or more in hazy or dusty air. Blue light is dimmed more than red.
Why use Kasten and Young instead of sec z?
sec z assumes a flat atmosphere, which works well above about 30° altitude but overstates the air mass near the horizon. Kasten and Young follows the curved atmosphere and stays accurate down to the horizon.
Why do stars twinkle more near the horizon?
Their light passes through several times more turbulent air, so it is bent and scattered more. The same extra air also dims and reddens them, which is why the setting Sun looks orange.