Visibility in Fog Calculator
Fog reduces visibility because suspended water droplets scatter and absorb light, dimming distant objects until they vanish into the haze. The Koschmieder relationship links the meteorological visibility (the distance at which a black object against the horizon just becomes indistinguishable) to the atmospheric extinction coefficient, a measure of how strongly the air attenuates light per unit distance. This tool applies that relationship to convert an extinction coefficient into visibility, in metres and kilometres. Enter the extinction coefficient in inverse metres; a thicker fog has a higher coefficient and a shorter visibility. The contrast threshold used in the standard formula is also user-editable.
Koschmieder visibility formula
visibility (m) = -ln(contrast threshold) / extinction coefficient
with the standard 0.02 threshold: visibility = 3.912 / extinction coefficient
The Koschmieder relationship states that visibility equals the natural logarithm of the contrast threshold divided by the extinction coefficient, with a sign that makes it positive. Using the World Meteorological Organization's standard contrast threshold of 0.02, the negative logarithm is 3.912, giving the familiar form visibility = 3.912 divided by the extinction coefficient. A higher extinction coefficient means denser fog and shorter visibility.
Worked example
An extinction coefficient of 0.05 per metre is entered with the standard contrast threshold of 0.02. The negative natural log of 0.02 is 3.912, so visibility = 3.912 / 0.05 = 78.24 metres, or 0.08 km. That is dense fog. A lighter mist with a coefficient of 0.005 would give 782.40 metres of visibility, and a coefficient of 0.0039 gives about 1,000 metres, the conventional upper limit of fog.
Frequently asked questions
What is the Koschmieder relationship?
It is the standard physical relationship between meteorological visibility and the atmospheric extinction coefficient. It assumes a black target viewed against the horizon sky and a fixed contrast threshold at which the eye can no longer distinguish the target. Visibility equals the negative natural logarithm of that threshold divided by the extinction coefficient.
What contrast threshold should I use?
The World Meteorological Organization adopts a contrast threshold of 0.02 for meteorological optical range, which gives the constant 3.912 in the simplified formula. Some aviation and road applications use 0.05, which yields a constant of about 3.0. The threshold is a user-editable input so you can match the standard you need.
What extinction coefficient corresponds to fog?
Fog is conventionally defined as visibility below 1,000 metres, which corresponds to an extinction coefficient above about 0.0039 per metre at the 0.02 threshold. Dense fog with visibility under 200 metres implies a coefficient above roughly 0.02 per metre. Higher coefficients mean thicker fog and shorter sight distances.
Does this account for daylight or object colour?
The basic Koschmieder formula assumes a black object against the horizon in daylight, which defines meteorological optical range. Real targets are not perfectly black, and at night visibility depends on light sources rather than contrast, so other models apply. This calculator gives the standard daytime meteorological visibility.
Official sources
- World Meteorological Organization: Guide to Instruments and Methods of Observation.
- NOAA National Weather Service: fog and visibility.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.