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Airmass Calculator

Find the airmass at a given altitude.

Result

1.7434

How it is calculated

The tool uses the plane-parallel approximation X = 1 ÷ sin(h), where h is the altitude of the object above the horizon in degrees (0° at the horizon, 90° at the zenith). This equals the secant of the zenith angle, z = 90° − h. Straight up the result is 1.0000, and it increases as the object gets lower. The altitude must be greater than 0 and not greater than 90, so objects on or below the horizon give no result. The answer is shown with four decimals. The formula treats the atmosphere as flat layers, so near the horizon it overstates the real value and curvature-aware models should be used there.

Worked example

A star is 35° above the horizon. sin 35° = 0.5736, so the airmass is 1 ÷ 0.5736 = 1.7434. Its light travels through about 1.74 times as much air as it would at the zenith. For comparison, at 30° the airmass is exactly 2.0000, and at 60° it is 1.1547. An observer wanting low extinction would wait until the star is higher.

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Common mistakes

  • Entering the zenith angle instead of the altitude: the field is the angle above the horizon, so a star 20° from the zenith is entered as 70.
  • Using the result near the horizon as exact: at 5° the formula gives 11.4737, but the plane-parallel model overstates the value that low, so treat it as a rough figure.
  • Typing radians: the altitude is in degrees, so 0.61 (35° in radians) would be read as 0.61° and return no result or a huge airmass.
  • Entering a negative altitude for an object below the horizon: the formula only applies to objects above the horizon, so no airmass is returned.

About this calculator

The simple airmass formula X = 1/sin(altitude) — equivalently the secant of the zenith angle — estimates how much atmosphere starlight or sunlight passes through relative to looking straight up (X=1 at the zenith), under the simplifying assumption of a flat, plane-parallel atmosphere. It works well for altitudes above roughly 20°, but overestimates airmass near the horizon (it grows without limit at 0°), where more accurate models like Kasten–Young correct for the Earth's curvature.

Astronomers use airmass to correct photometric measurements for atmospheric extinction — dimming and reddening caused by scattering and absorption — and to schedule observations for when a target is highest (lowest airmass) and least affected by the atmosphere. It's a routine calculation in observatory planning software, amateur astrophotography, and any spectroscopy or photometry pipeline that needs to compare brightness measurements taken at different times of night.

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