Visibility and Extinction Coefficient Calculator
Convert between meteorological visibility distance and atmospheric extinction coefficient using the Koschmieder equation.
🌁 What is Visibility and Extinction Coefficient?
Meteorological visibility is the greatest distance at which a large, dark object can just be distinguished from the sky at the horizon, a standardized way of reporting how far you can see through the atmosphere. It relates directly to the atmospheric extinction coefficient (sigma), which measures how quickly light intensity is scattered and absorbed per unit distance as it travels through the air. The Koschmieder equation, V = 3.912 / sigma, is the bridge between these two quantities.
Meteorologists, airport operators, and transportation agencies rely on this relationship constantly, to report visibility in aviation weather observations (METARs) that determine whether an airport can safely operate under visual or instrument flight rules, to issue dense fog advisories for highway safety, to interpret readings from automated transmissometers and forward-scatter visibility sensors installed along runways and roads, and to translate raw sensor extinction measurements into the plain-language visibility distance the public actually understands.
A common misconception is that visibility is measured directly with a tape measure or by eye alone. In practice, most official visibility readings come from an instrument that measures the extinction coefficient, either by transmitting a light beam over a known path or by measuring how much light nearby particles scatter, then converting that measurement to visibility using the Koschmieder equation. Another misconception is that visibility and extinction coefficient are linearly related. They are not: V and sigma are inversely proportional, so visibility falls off steeply once the extinction coefficient starts climbing.
This calculator converts freely between visibility distance and extinction coefficient in either direction, then classifies the result against the standard excellent-to-dense-fog visibility categories, so a raw sensor reading or a reported visibility becomes immediately interpretable.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Good Visibility Day
Extinction coefficient σ = 0.5 per km
Example 2 — Dense Fog
Visibility V = 0.15 km
Example 3 — Moderate Haze
Extinction coefficient σ = 2.0 per km
❓ Frequently Asked Questions
🔗 Related Calculators
What is the Koschmieder equation?
The Koschmieder equation, V = 3.912 / sigma, relates meteorological visibility (V) to the atmospheric extinction coefficient (sigma). The constant 3.912 comes from -ln(0.02), the standard convention that an object becomes indistinguishable from the horizon sky once its contrast drops to 2 percent.
How do you convert extinction coefficient to visibility?
Divide 3.912 by the extinction coefficient: V = 3.912 / sigma, with sigma in units of per kilometer and V in kilometers. For example, an extinction coefficient of 0.5 per km gives a visibility of 3.912 / 0.5 = 7.824 km.
How do you convert visibility to extinction coefficient?
Divide 3.912 by the visibility: sigma = 3.912 / V. For example, a visibility of 10 km corresponds to an extinction coefficient of 3.912 / 10 = 0.3912 per km.
Why is 3.912 the constant used in the Koschmieder equation?
3.912 equals -ln(0.02), derived from the convention that the human eye can just distinguish a large dark object from the horizon sky when its apparent contrast has dropped to 2 percent (a contrast threshold of 0.02) due to atmospheric scattering along the line of sight.
What visibility distance counts as fog versus haze?
Under the classification this calculator uses, visibility above 10 km is excellent, 4 to 10 km is good, 1 to 4 km is moderate haze, 0.2 to 1 km is fog or mist, and below 0.2 km is dense fog, following the general visibility categories used in aviation and surface weather reporting.
What is the atmospheric extinction coefficient?
The extinction coefficient (sigma) measures how quickly light intensity is attenuated per unit distance traveled through the atmosphere, combining scattering and absorption by air molecules, aerosols, water droplets, and other particles. It is the same physical quantity behind Beer's law of light attenuation.
Who developed the Koschmieder equation and when?
The German meteorologist Walter Koschmieder derived the equation relating visual range to the extinction coefficient in 1924, building on the physics of contrast perception against a bright background such as the sky. It remains the standard basis for how transmissometers and visibility sensors report meteorological visibility today.
How do modern visibility sensors measure the extinction coefficient?
Transmissometers measure how much a beam of light is attenuated over a known path length to derive sigma directly. Forward-scatter sensors instead measure light scattered by particles at a fixed angle and convert that to an equivalent extinction coefficient, then apply the same Koschmieder relation to report visibility.
Does the Koschmieder equation account for the type of obscuration (fog vs haze vs dust)?
No. The equation itself only relates extinction coefficient to visibility distance; it does not distinguish what is causing the extinction. Fog, haze, dust, smoke, and heavy precipitation can all produce the same extinction coefficient and therefore the same computed visibility, even though the underlying physical cause differs.
Why does visibility drop so sharply as the extinction coefficient rises?
Because V = 3.912 / sigma is an inverse relationship, not a linear one. Doubling the extinction coefficient halves the visibility, and the curve gets extremely steep at low sigma values, which is why visibility can fall from many kilometers to under a kilometer with only a modest increase in atmospheric particle loading.
Is meteorological visibility the same as the range at which you can physically see any object?
Not exactly. Meteorological visibility specifically refers to the distance at which a large, dark object can just be distinguished against the horizon sky under the standard 2 percent contrast threshold. Smaller, less contrasty, or artificially lit objects (like runway lights at night) can be seen at different distances even under the same atmospheric conditions.
How is this different from the Aerosol Optical Depth Calculator?
Aerosol optical depth integrates light attenuation through the entire vertical atmospheric column along a slanted sun path, while the Koschmieder visibility relation describes horizontal, near-surface light attenuation over the observer's direct line of sight. Both use the same underlying Beer's law physics, applied to different geometries and purposes.