AGL Light Intensity at Distance Calculator
Illuminance at the pilot's eye from a light of given intensity, at a distance, through fog or haze described by the meteorological optical range (MOR).
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
Open in the calculator with these values
About this calculator
This page calculates illuminance at the eye, illuminance in clear air, atmospheric transmissivity over the path and 1 more result from intensity toward the observer, distance to the light and meteorological optical range. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
This gives the light level at the eye only. Visual range needs an eye threshold for the background brightness you design for; take that from the method you follow (for example ICAO Doc 9328 for RVR). Not an operational RVR assessment.
Cross-check: 20 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | Not applicable: Allard’s law is an optical visibility relationship. This calculator is not an ICAO/DGCA RVR observation system or an approved RVR calculation; no AGL electrical standard governs the simplified illuminance-at-distance equation. |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 20 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Intensity toward the observer (cd) | 10,000 |
| Distance to the light | 300 m |
| Meteorological optical range (MOR) | 800 m |
- σ = ln 20 / MOR = 2.9957 / 800 = 3.7447 per km
- T = exp(−σ d) = exp(−1.1234) = 0.32517
- E = I × T / d² = 10,000 × 0.32517 / 300² = 0.03613 lux
Assumptions
- Point source seen head-on
- Uniform atmosphere along the path
- MOR is defined at 5% transmissivity (ln 20 = 2.9957)
This gives the light level at the eye only. Visual range needs an eye threshold for the background brightness you design for; take that from the method you follow (for example ICAO Doc 9328 for RVR). Not an operational RVR assessment.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Intensity toward the observer (cd) | (number) | greater than 0 | Example value. Use the isocandela data for the fitting and the viewing angle. |
| Distance to the light | m | greater than 0 m | |
| Meteorological optical range (MOR) | m | greater than 0 m | Path length that cuts a light beam to 5% (the standard MOR definition) |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Illuminance at the eye (lux) | (number) | Shown to 6 decimal places | |
| Illuminance in clear air (lux) | (number) | Shown to 6 decimal places | |
| Atmospheric transmissivity over the path (%) | (number) | Shown to 2 decimal places | |
| Extinction coefficient (per km) | (number) | Shown to 3 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with distance to the light
| Distance to the light (m) | Illuminance at the eye | Illuminance in clear air | Atmospheric transmissivity over the path |
|---|---|---|---|
| 30 | 9.930449 | 11.111111 | 89.37 |
| 75 | 1.342474 | 1.777778 | 75.51 |
| 150 | 0.25344 | 0.444444 | 57.02 |
| 300 | 0.03613 | 0.111111 | 32.52 |
| 600 | 0.002937 | 0.027778 | 10.57 |
| 1,200 | 0.000078 | 0.006944 | 1.12 |
| 3,000 | 1.469e-8 | 0.001111 | 0.0013 |
Other inputs are the same as in the worked example above.
Standards and further reading
- ICAO Annex 14, Volume I (aerodrome design and operations)
- ICAO Doc 9157, Part 5 (aerodrome design manual, electrical systems)
Photometric and circuit requirements come from the edition of Annex 14 and the regulator's rules that apply at your aerodrome, and from the fitting and regulator manufacturers' data. These are named as background reading. Elecmetric does not embed clause text or rating tables, and the reviewer record for this calculator is separate from this list.
Frequently asked questions
What do I need to enter?
Enter intensity toward the observer (cd), distance to the light and meteorological optical range (MOR). Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
Point source seen head-on. Uniform atmosphere along the path. MOR is defined at 5% transmissivity (ln 20 = 2.9957).
Which calculators should I use next?
Common next steps are AGL Brightness Step Current and Circuit Load, Candela, Lux and Distance (any two) and AGL Lamp Life at a Different Circuit Current. The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 20 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Point Illuminance Formulas: Point-by-point lighting formulas: the illuminance on a horizontal plane from a luminous intensity
- Lighting Formulas: Lux, Lumens and Candela: Lighting formulas for lux, lumens and candela: inverse square law
More Airport and AGL Engineering calculatorsAll engineering calculatorsAGL Light Intensity at Distance (Allard's Law) in Elecmetric