Lumen, Lux, Candela & Foot-Candle Converter
The geometry-aware photometric converter
Lumens, lux, candelas, and foot-candles describe different parts of the same lighting problem. Lumens measure total visible-light output, candela measures how strongly it is aimed in a direction, and lux or foot-candles measure how much arrives on a surface. A truthful conversion therefore needs one missing piece of geometry: illuminated area, beam solid angle, or throw distance. This page asks for that piece instead of pretending the units convert by a fixed multiplier.
Unit references: the BIPM practical realization of the candela and derived photometric units and the NIST light-unit conversion table. NIST gives 1 foot-candle = 10.76391 lux.
Which conversion route should you use?
| Known | Wanted | Geometry required | Ideal formula |
|---|---|---|---|
| Lumens | Lux / foot-candles | Illuminated area | illuminance = lumens ÷ area |
| Lux / foot-candles | Lumens | Illuminated area | lumens = illuminance × area |
| Lumens | Candela | Beam solid angle | candela = lumens ÷ steradians |
| Candela | Lumens | Beam solid angle | lumens = candela × steradians |
| Candela | Lux / foot-candles | Distance | lux = candela ÷ distance² |
| Candela + target lux | Throw distance | Normal incidence | distance = √(candela ÷ lux) |
Core formulas
Illuminance is flux per receiving area. One lux is one lumen per square metre; one foot-candle is one lumen per square foot:
A conical beam with full beam angle θ occupies the solid angle below. Half the full beam angle belongs inside the cosine:
Under the ideal uniform-beam assumption, luminous intensity is I = Φ ÷ Ω. At a perpendicular target far enough away for a point-source approximation, centre illuminance follows E = I ÷ d². A circular beam's diameter at that plane is 2d tan(θ/2).
Plain-text formulas: lux = lumens / squareMetres; footCandles = lumens / squareFeet; lux = footCandles × 10.76391; steradians = 2π × (1 − cos(beamAngle / 2)); candela = lumens / steradians; luxOnAxis = candela / distanceMetres².
Worked example: why the beam angle matters
Take a 1,000 lm lamp with a 30° full beam angle. The ideal cone occupies about 0.214 steradians, so intensity is 1,000 ÷ 0.214 ≈ 4,671 cd. At 5 m, the on-axis estimate is 4,671 ÷ 25 ≈ 187 lux, or 17.4 fc. Widen the same 1,000 lm to 60° and the cone grows to about 0.842 sr. Intensity falls to about 1,188 cd and the 5 m centre estimate falls to 47.5 lux. The lumens did not change; only their directional concentration did.
The 30° beam also draws a circle roughly 2.68 m across at 5 m. Dividing all 1,000 lumens by that flat circle gives an ideal average of about 177 lux. That is close to, but not exactly the same as, the 187 lux centre calculation because a cone's solid angle lives on a sphere while the footprint lies on a flat plane. The difference grows for very wide beams.
What the numbers do—and do not—mean
- Lumens are total flux: useful for lamp output, but not enough to predict brightness at a particular spot.
- Candela is directional: fixture data often reports peak candela, not a uniform value across the beam.
- Beam angle needs a definition: manufacturers commonly define it at a percentage of peak intensity; field angle and spill can be wider.
- Lux and foot-candles are illuminance: they describe incident light, not surface luminance or perceived brightness after reflectance.
- Real installations lose light: optics, dirt, tilt, obstruction, reflectance, and nonuniform distributions all move the measured result.
Use this calculator for unit conversion, rough fixture comparison, photography setup, and first-pass throw planning. For compliance, safety-critical workplaces, horticulture, sports lighting, roadway design, or final fixture placement, use manufacturer IES/LDT photometric files and verify the installed result with a calibrated meter.
Frequently asked questions
Can I convert lumens straight to lux?
Only after supplying the receiving area. A 1,000 lm source spread over 1 m² gives an ideal 1,000 lux; the same flux spread over 10 m² gives 100 lux.
How many lux are in a foot-candle?
One foot-candle is 10.76391 lux. Divide lux by 10.76391 to get foot-candles, or multiply foot-candles by 10.76391 to get lux.
Is candela the same as candlepower?
Candela is the SI unit of luminous intensity. “Candlepower” is often used informally for candela, but older historical candlepower definitions were not always identical, so use the stated unit on the datasheet.
Should I use beam angle or field angle?
Use the full angle associated with the lumens or intensity definition you are modelling. If a manufacturer provides both, beam angle usually describes the brighter core while field angle includes more spill. An IES distribution is better than either single angle.
Why are average beam lux and on-axis lux different?
Average beam lux divides assumed captured lumens by a flat circular footprint. On-axis lux uses candela and inverse-square distance. The geometries agree closely for narrow cones but diverge for wide beams, and real beam intensity is rarely uniform.
Mini-game: Lux Landing
You are calibrating a light meter on a dark stage. Each round gives a spotlight's candela and a target lux reading. Slide the meter nearer or farther until the live reading matches the target, then lock it in. The game is the inverse-square law in motion: double the distance and the reading falls to one quarter.
Start a run, move the slider or use ←/→, and lock eight readings before time expires.
The game uses ideal on-axis illuminance: lux = candela ÷ metres². It is optional and does not change the converter result.