Airmass Calculator
Airmass tells you how much atmosphere light from a star or planet passes through compared with looking straight up, which controls how much the object is dimmed and reddened. This calculator takes the object's altitude above the horizon and returns the zenith angle, the simple plane-parallel airmass (the secant of the zenith angle) and the Kasten-Young (1989) airmass, which corrects the secant for the curved atmosphere near the horizon. At the zenith both give 1; near the horizon the Kasten-Young value stays realistically finite while the plain secant blows up.
Airmass formula
zenith angle z = 90 - altitude
secant airmass = 1 / cos(z)
Kasten-Young = 1 / (cos(z) + 0.50572 * (96.07995 - z)^-1.6364)
The plane-parallel airmass is simply the secant of the zenith angle. The Kasten-Young (1989) relation adds an empirical term in the zenith angle (in degrees) so the airmass stays finite at the horizon, matching a standard atmosphere to better than one percent.
Airmass context
- Airmass is 1 at the zenith and rises toward the horizon, increasing extinction.
- Photometric reductions correct measured magnitudes for the airmass at observation.
- The plain secant model diverges at the horizon; the Kasten-Young relation does not.
- True horizon airmass is about 38, not infinite, because the atmosphere is curved.
- Enter altitude in degrees; the calculator derives the zenith angle for you.
Airmass: frequently asked questions
What is airmass in astronomy?
Airmass is the relative path length that light from a celestial object travels through Earth's atmosphere, compared to the path straight overhead. At the zenith the airmass is 1; nearer the horizon it grows, dimming and reddening the object. It is a key correction in photometry.
How is airmass calculated?
The simplest plane-parallel model gives airmass as the secant of the zenith angle, equal to one over the cosine of the zenith angle. This calculator computes that, and also the Kasten-Young (1989) relation, which corrects the secant for atmospheric curvature near the horizon.
What is the difference between altitude and zenith angle?
Altitude is the angle of the object above the horizon; zenith angle is measured from straight overhead. They sum to 90 degrees. Enter the altitude and the calculator converts it: zenith angle equals 90 degrees minus altitude.
Why does the secant model fail near the horizon?
The plane-parallel secant assumes a flat atmosphere, so it diverges to infinity at the horizon. Real atmosphere is curved, so the true airmass stays finite (around 38 at the horizon). The Kasten-Young relation adds empirical terms to match observations near the horizon.
Is the Kasten-Young relation exact?
It is a widely used empirical fit published by Kasten and Young in 1989 that closely matches a standard atmosphere. It is accurate to better than one percent down to the horizon for typical conditions, but real airmass varies slightly with the actual atmospheric profile.
Official sources
- NASA Astrophysics Data System: Kasten and Young (1989), Revised Optical Air Mass Tables.
- NASA Imagine the Universe: Astronomy Toolbox: Atmosphere and Extinction.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.