Fog Visibility Distance Calculator
Introduction: How Fog Visibility Is Lost Across Distance
In this fog visibility calculator, the starting point is a simple but important idea: fog makes distant objects harder to distinguish by scattering and absorbing light before it reaches your eyes. Tiny droplets suspended near the ground turn the air into a light-scattering layer, so a sign, shoreline, runway light, or vehicle gradually loses contrast against its background. Once that contrast falls below the eye’s detection threshold, the object effectively disappears from view even though it is still physically present.
This loss of contrast defines meteorological visibility, which is the greatest distance at which a large, dark object can just be seen against the horizon sky. On this page, that means the calculator is estimating a real-world sight range for foggy, misty, or hazy conditions rather than a generic distance value.
Drivers, pilots, mariners, and outdoor planners use visibility estimates to judge whether a route is still reasonable, whether conditions are improving, or whether a delay is the safer option. A common operational benchmark is visibility below about 1 km, but dense ground fog can reduce sight range far below that and create sudden local differences over short distances.
Koschmieder’s Law and the Fog Visibility Formula
Koschmieder’s law gives this fog visibility calculator a compact way to convert atmospheric clarity into an estimate of how far you can see. It links visibility to the extinction coefficient, which describes how strongly the air attenuates light per unit distance through scattering and absorption.
The basic form of Koschmieder’s law for visibility V is:
V = 3.912 / β
where:
- V is the meteorological visibility (in kilometres), and
- β (beta) is the extinction coefficient (in 1/km).
The constant 3.912 comes from assuming that the minimum contrast the average human eye can detect is about 2%. In mathematical terms, it is derived from the natural logarithm of 1/0.02. A more formal expression of the relationship between contrast and distance uses an exponential decay model:
Here C is the contrast after travelling distance x through the atmosphere, C0 is the initial contrast at the source, β is the extinction coefficient, and e is the base of natural logarithms. Setting C equal to the threshold contrast of the human eye and solving for x yields the familiar visibility formula.
Typical values of β vary widely:
- Clean, dry air: β ≈ 0.02–0.05 1/km (very long visibility, tens of kilometres or more)
- Haze or light pollution: β ≈ 0.1–0.3 1/km
- Dense fog or heavy pollution: β > 0.3 1/km (visibility can drop below 1 km, sometimes to tens of metres)
Relative humidity is closely linked to fog formation because moist air is more likely to reach saturation and condense into droplets. However, humidity alone does not fully determine β; droplet number, size, and additional aerosols (such as smoke or dust) all matter as well.
How This Fog Visibility Calculator Works
This fog visibility calculator uses the extinction coefficient as the quantity that drives the distance result, while relative humidity serves as context for how likely foggy conditions are. You provide:
- Relative humidity (%): a general indicator of how close the air is to saturation. Higher values (often > 90%) commonly accompany fog or mist.
- Extinction coefficient (1/km): a measure of how strongly the atmosphere reduces light per kilometre. This is the primary input used in the visibility formula.
The calculator then uses the relationship V = 3.912 / β to estimate visibility in kilometres, optionally presenting the result in metres as well for very low-visibility situations.
Finding or estimating β:
- If you have access to instrument data (e.g., from a visibility sensor, transmissometer, or a detailed weather report), you may be given β directly or a related parameter that can be converted.
- If you only know an approximate visibility from a nearby weather station, you can invert Koschmieder’s law: β ≈ 3.912 / V.
- When no measurements are available, you can use typical ranges such as those in the comparison table below as rough guidance.
Worked Example: Estimating Visibility in Morning Fog
This fog visibility example uses a humid early-morning situation where the air feels nearly saturated, with a reported relative humidity of 95%. Local weather information suggests a hazy layer rather than clean air, and you estimate an extinction coefficient of β = 0.3 1/km.
Using Koschmieder’s law:
V = 3.912 / 0.3 ≈ 13.0 km
In other words, under the simplified assumptions used by the calculator, a large dark object would still be distinguishable from the horizon sky at roughly 13 km. That does not mean every road, field, or harbor view will feel equally clear, because fog often varies near the ground, around trees and buildings, or in pockets over water and low terrain.
If you instead estimate a denser fog with β = 1.0 1/km, then:
V = 3.912 / 1.0 ≈ 3.9 km
And for more extreme conditions such as heavy ground fog, β can exceed 2 1/km, pushing the theoretical visibility below 2 km and making practical driving visibility much shorter in the places that matter most.
Reference Table: Extinction Coefficient, Fog Visibility, and Conditions
The fog visibility calculator’s table below links the extinction coefficient to the approximate sight range returned by the formula and to the kind of atmospheric conditions those values often describe. These are illustrative, not strict thresholds.
| Extinction coefficient β (1/km) | Approx. visibility V (km) | Typical description |
|---|---|---|
| 0.02 | ≈ 195 km | Exceptionally clear, dry air (mountain or polar regions) |
| 0.05 | ≈ 78 km | Very clear air, distant landmarks easily visible |
| 0.10 | ≈ 39 km | Light haze; long-distance views still good |
| 0.20 | ≈ 20 km | Moderate haze; distant hills appear washed out |
| 0.50 | ≈ 7.8 km | Mist or light fog; reduced contrast, especially at night |
| 1.00 | ≈ 3.9 km | Dense haze or fog; markedly reduced visibility |
| 2.00 | ≈ 2.0 km | Very dense fog; visibility potentially down to hundreds of metres |
Assumptions and Limitations for Fog Visibility Estimates
Fog visibility estimates are only approximate because the atmosphere rarely behaves like the simple model used in this calculator. The result is useful for planning and comparison, but it should not be treated as a direct measurement of what every driver, pilot, or lookout will experience on the ground.
- Single extinction coefficient: The calculation assumes a single, constant β value along the entire line of sight. Real fog layers often vary with height, terrain, and distance.
- Horizontally uniform conditions: Koschmieder’s law assumes that the atmosphere has uniform properties. In practice, fog can form patches, banks, and layers, leading to sharp visibility changes over short distances.
- Fixed contrast threshold: The 3.912 constant is based on an average human contrast threshold of 2%. Individual eyesight, lighting conditions, and object properties can significantly change the actual detection distance.
- Idealised geometry: The formula is derived for a large, dark object against the horizon sky. Real-world objects may be smaller, lighter, moving, or illuminated in ways that deviate from this ideal.
- Humidity as a proxy: Relative humidity is included as a helpful context variable, but it is not a complete predictor of β. Two situations with the same humidity can have very different visibilities depending on aerosols, droplet sizes, and temperature structure.
- Rapidly changing conditions: Fog and low cloud can form, deepen, or dissipate quickly due to wind, solar heating, or changes in air mass. Any estimate is only valid for the conditions at the time of input.
How to use this fog visibility estimate safely
Use this fog visibility calculator to compare how changes in extinction coefficient affect sight range, to interpret a weather report, or to build intuition about why two damp mornings can feel very different at the roadside.
Do not use the results as your only source of information for operating vehicles, aircraft, or vessels. Visibility estimates from this tool are for informational and educational purposes only and are not a substitute for:
- official weather forecasts and visibility reports,
- aviation, marine, or road authority guidance, and
- local regulations and safety procedures.
Always follow official guidance and err on the side of caution when fog or poor visibility is present, especially when visibility is changing between a sheltered road, open water, or an exposed airport approach.
Arcade Mini-Game: Fog Visibility Distance Calculator Calibration Run
Use this quick arcade run to practice separating useful scenario inputs from common planning mistakes before you rely on the calculator output.
Start the game, then use your pointer or arrow keys to catch useful inputs and avoid bad assumptions.
Status messages will appear here.