Illuminance Converter

Lumens describe the lamp, lux the room

“How many lux is 1000 lumens?” is one of the most-asked lighting questions and it has no answer, in the same way that “how fast is 60 miles?” has none. A lumen counts the light a lamp emits in total. A lux counts the light landing on one square metre of something. Between them sits the area, and the area is not a detail — it is half the conversion.

The same lamp is daylight-bright and street-lit-dim depending on nothing but the floor plan. This is why bulbs are sold in lumens — a property of the product, true wherever you take it — while lighting standards are written in lux, because what a standard actually cares about is the light reaching the desk.

The practical consequence when specifying: a target of 500 lx over a 12 m² office needs 6000 lumens arriving at the working plane. Buying a single 6000-lumen fitting will not achieve it, because a real installation loses light to the fitting, to the walls and to the lamp’s decline with age. Lighting designers apply a utilisation and a maintenance factor for exactly this, and between them they commonly account for a third or more of the output.

This converter reports the plain average, and says so. It is the right number for sanity-checking a specification and the wrong number to sign a compliance certificate against.

Candela is a direction, not a total

Torch manufacturers quote candela. Bulb manufacturers quote lumens. Both are measuring light and neither is being evasive, but the two numbers answer different questions and the gap between them is enormous.

A candela is luminous intensity — brightness in one particular direction, per unit of solid angle. To get a total you multiply by the solid angle the light actually goes into, and that is set by the beam. A cone of full angle θ subtends Ω = 2π(1 − cos(θ/2)) steradians, which is where the half angle appears and where most of the arithmetic errors live.

One candela is 526 times the total light omnidirectionally that it is in a 10° spot. That is the whole reason a torch advertising a six-figure candela number can be less useful indoors than a modest lamp: the candela figure is concentrated intensity, and concentration is exactly what a room does not want.

Two of the entries are exact rather than rounded, which is a useful check on any tool doing this arithmetic. At 120° the half angle is 60°, cos 60° is one half, and the solid angle is exactly π. At 360° the cosine is −1 and the answer is exactly 4π, the whole sphere. A calculator that misses those two landings is using the full angle where the half angle belongs.

One honest limitation: a beam angle is defined to the points where intensity has fallen to half its centre value, so light carries on past the stated cone and the intensity is not uniform inside it. Treating the beam as a clean cone of constant intensity is an approximation — good enough to compare fittings, not good enough to predict a measurement.

Nits belong to the surface

A nit is a candela per square metre, and it is the unit phone and television specifications are written in. It describes light leaving a surface towards the eye. Lux describes light arriving. Those are different physical quantities, and no factor converts one to the other.

What bridges them is the surface. For a diffusely reflecting one the relation is L = ρE/π, where ρ is the reflectance. The π is not a fudge factor: it is what comes out of integrating the cosine-weighted radiance over the hemisphere the surface scatters into.

Identical light, and a twelve-fold range in what the eye actually receives. This is the reason a road looks dark under a lamp that makes the pavement beside it look bright, and the reason photographers meter off a grey card rather than off whatever happens to be in front of them.

It also explains a specification that confuses people: a screen rated at 1000 nits is not comparable to a room lit to 1000 lux. The screen emits its own light, so its luminance does not depend on a reflectance at all — which is precisely why it stays readable in sunlight that would wash out printed paper.

The reflectance figures above are typical published values for the named materials rather than measurements of any particular sample, and few real surfaces are perfectly diffuse. Gloss paint, water and polished stone send light in preferred directions, so a single luminance figure understates them at some viewing angles and overstates them at others.

Why distance costs so much

Light from a point source spreads over a sphere, and a sphere’s area goes as the square of its radius. So illuminance falls as 1/d². Doubling the distance does not halve the light — it quarters it.

The practical readings of this are worth stating plainly. Raising a workshop light from two metres to three costs more than half the light on the bench. Moving a desk lamp from an arm’s length to twice that leaves a quarter. And a floodlight advertised on its output at ten metres is being described at a hundredth of its one-metre intensity, which is a fair way to quote it and an easy one to misread.

The law holds for a point source, and a source counts as a point when it is small relative to the distance — the usual rule of thumb is five times its largest dimension. Close to a long fluorescent tube or a large panel the falloff is gentler than 1/d², which is one of the reasons large-area fittings feel more even than their raw numbers suggest.

The foot-candle factor is exact

A foot-candle is one lumen per square foot. A lux is one lumen per square metre. Since 1959 a foot has been defined as exactly 0.3048 metres, so a square foot is exactly 0.09290304 m² and the conversion is exactly its reciprocal: 10.763910416709722 lux to the foot-candle. There is nothing measured about it.

A great many charts and rules of thumb round that to ten. It is a tempting simplification and it costs more than it looks: using ten under-reports the true figure by 7.1%. On a 500 lx target that is 35 lux — enough to move a specification from compliant to not.

The rounding also travels in one direction only, which makes it worse than a symmetric error. Converting foot-candles to lux with the factor ten always gives a number that is too small, so a room designed that way is always under-lit rather than sometimes over.

The rest of the family is straightforward once the foot-candle is pinned down. A kilolux is a thousand lux. A phot, occasionally still seen on older instruments, is one lumen per square centimetre and therefore exactly ten thousand lux. And “lumens per square foot” is not a separate unit at all — it is the foot-candle written out rather than named, which is worth knowing because seeing both in one specification suggests a conversion has already happened somewhere.

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Sources and methodology

The three facts this page turns on are definitional rather than empirical. The candela is an SI base unit and the lumen and lux are derived from it, which is why a solid angle and an area appear in those conversions and cannot be dropped. The foot is exactly 0.3048 m by international agreement, which makes the foot-candle factor exact. And the illuminance/luminance distinction is set out in the international lighting vocabulary, along with the Lambertian relation that connects them once a reflectance is known.

• SI Brochure, 9th edition — the candela and the derived photometric unitsBureau International des Poids et Mesures · verified 2026-09-07 · The candela as an SI base unit and the definitions of the lumen (cd·sr) and the lux (lm/m²) derived from it — the reason a solid angle and an area are part of those conversions rather than optional extras
• International yard and pound agreement (1959) — the foot as exactly 0.3048 mNational Institute of Standards and Technology · verified 2026-09-07 · That a square foot is exactly 0.09290304 m², which makes the foot-candle to lux factor exact rather than measured — 10.763910416709722, where the widely used 10 is 7.1% low
• CIE S 017 — International Lighting VocabularyInternational Commission on Illumination · verified 2026-09-07 · The distinction between illuminance (light arriving at a surface) and luminance (light leaving it towards the observer), and the Lambertian relation L = ρE/π that connects them only once a reflectance is known