Point source to workplaneLive ray distance, plane, and current lux
Unit Converters
Illuminance Reference Table Calculator
Estimate direct illuminance on a plane from a point-source approximation, convert the result, and inspect how inverse-square distance and oblique incidence change the workplane value.
POINT-SOURCE PHOTOMETRY
Relate luminous intensity, distance, angle, and workplane illuminance
Use this reference when a source can reasonably be treated as a point and its candela value is known in the workplane direction. The model supports preliminary geometry checks, not a complete room-lighting design.
Validity: distance is measured from the photometric center; angle is between the incoming ray and the receiving plane normal. Reflections and beam distribution are excluded.
Illuminance—
Foot-candle equivalent—
Incident luminous flux—
Cosine factor—
Distance—
Directional intensity—
LIGHT-CONE GEOMETRY
See the ray path and receiving plane
The cone emphasizes geometric spreading; the center ray and plane show distance and incidence. The table then isolates the inverse-square effect at exact distance multiples.
| Distance | Illuminance | Foot-candles | Relative to current |
|---|
HOW TO USE
Set up the geometry before reading lux
- Obtain luminous intensity in candela for the direction toward the workplane, not total lumens.
- Measure distance from the luminaire photometric center to the evaluation point.
- Measure incidence angle from the plane normal; zero degrees means perpendicular arrival.
- Enter receiving area only when incident lumens over that idealized area are useful.
- Compare the distance table with the live cone, then decide whether a point-source approximation is defensible.
PHOTOMETRY FUNDAMENTALS
Six quantities have different roles
CALCULATION METHOD
Apply geometric spreading before unit conversion
E = Iv cosθ / r²Efc = Elx / 10.7639104167Φincident = E × AIv is candela, θ degrees from normal, r metres, E lux, A square metres, and Φ lumens.
INVERSE-SQUARE BEHAVIOR
Doubling distance reduces direct illuminance to one quarter
The same directional intensity crosses a surface whose relevant area grows with distance squared. This relationship is the reason mounting-height errors can dominate preliminary estimates. It applies to point geometry; an extended line or panel source near the plane does not follow the same simple form.
COSINE RESPONSE
Oblique light spreads over more receiving area
The cosine factor belongs to the receiving geometry. At 60° from normal, cosθ is 0.5, so the direct illuminance is half the normal-incidence value at the same distance and intensity. A real meter also needs adequate cosine response; instrument error is not corrected here.
POINT-SOURCE LIMIT
Large luminaires and reflective rooms require another model
When source dimensions are not small relative to distance, integrate the luminous distribution or use photometric software. Walls, ceilings, task surfaces, glazing, and inter-reflections can add substantial indirect illuminance. The direct point estimate should never be presented as a complete maintained-lighting result.
DETAILED CALCULATION PROCESS
Default 800 cd example
| Symbol | Meaning | Default | Unit |
|---|---|---|---|
| Iv | Directional intensity | 800 | cd |
| r | Distance | 2 | m |
| θ | Incidence angle | 0 | degree |
| A | Area | 12 | m² |
- Convert 0° to radians for the cosine evaluation.
- cos(0°) = 1.0000.
- Square distance: 2² = 4 m².
- Direct illuminance: 800 cd × 1 ÷ 4 m² = 200 lx.
- Foot-candles: 200 ÷ 10.7639104167 = 18.5806 fc.
- Uniform-equivalent incident flux: 200 lx × 12 m² = 2,400 lm.
- At 4 m, the same geometry gives 50 lx.
- Reverse check: 50 × (4/2)² = 200 lx.
RESULT INTERPRETATION
Lux is local to the selected point and plane
A high result can arise from strong directional intensity, short distance, or near-normal incidence. Zero candela produces zero direct illuminance. Results near zero at steep angles do not prove darkness because indirect light is excluded. Incident lumens assume uniformity and should not be confused with source lumens.
MEASUREMENT EVIDENCE
Retain the photometric direction and geometry
Record luminaire file or intensity table, vertical and horizontal angles, mounting coordinates, photometric center, workplane height, receiving normal, meter location, ambient-light subtraction, lamp output state, temperature, and maintenance condition.
LIMITS AND EXCLUSIONS
What the reference does not establish
- No beam distribution or cutoff curve is integrated.
- No inter-reflection or daylight contribution is added.
- No glare, uniformity, color quality, or flicker is assessed.
- No maintenance factor or lumen depreciation is applied.
- The area result assumes the point lux is uniform over the entered area.
WORKED DECISION CASES
Geometry changes the interpretation
Task light
A compact source is far enough from a small task point that point geometry is reasonable. The distance table shows whether raising the luminaire would push the direct component below a project target.
Luminous ceiling panel
The panel is large and close to the workplane. The point-source approximation understates its extended geometry; use zonal or numerical photometric calculation instead.
TECHNICAL GLOSSARY
Photometric terms
- Candela
- SI unit of luminous intensity.
- Lux
- Lumen per square metre.
- Lumen
- SI unit of luminous flux.
- Workplane
- Plane where illuminance is evaluated.
- Photometric center
- Reference point for luminaire geometry.
- Cosine law
- Reduction caused by oblique incidence.
- Inverse-square law
- Distance-squared reduction for point geometry.
- Foot-candle
- Lumen per square foot.
IMPORTANT NOTE
Use a luminaire distribution when the source is directional
A single candela value is valid only for its stated direction. Do not substitute total lumens or a peak candela value for the direction toward the workplane.
Frequently asked questions
Why not enter lumens?
Total flux does not identify the directional intensity reaching the point.
Is lux equal to lumens?
No. Lux is lumens per square metre.
Can angle exceed 90°?
No direct light reaches the front face in this model.
Why is area not in the lux formula?
Lux is already flux per area at the point.
Does 1 fc equal 10 lx?
Approximately, but the page uses 10.7639104167 lx per fc.
Can reflections increase measured lux?
Yes; this direct model excludes them.
Does the model include maintenance?
No. Apply an approved maintenance method separately.
When is the point assumption unsafe?
When source dimensions are not small relative to distance.
AUTHORITATIVE BASIS