What Light Is Measured In, and Why the Units Confuse People

Why this matters

A customer says the space is dark. Your meter says it is over the number in the specification. Both of you are right, and the reason is that the meter and the customer are not looking at the same quantity. Light is described by four separate measurements that get quoted as if they were interchangeable, and only one of the four is what a person actually sees. Quote the wrong one to a specifier and you lose the argument. Design a retrofit against the wrong one and you deliver a space that measures better and reads worse, which is the single most common outcome in lighting work.

The four quantities differ by what they are divided by

That is the whole taxonomy. Each quantity takes the one before it and divides by something.

The one that matters for the argument with the customer is the last row. The eye responds to luminance. Nothing in the visual system measures illuminance; the retina sees surfaces, and a surface's brightness is its luminance. Illuminance is the quantity we measure because it is easy to measure, portable, and specifiable, not because it is the quantity anyone perceives.

What each unit refuses to tell you

• A lumen figure refuses to say where the light went. Two luminaires rated at the same total flux can put nothing on the task and everything on the ceiling. Flux is a property of the source alone. The delivered-lux card owns the map from one to the other.
• A candela figure refuses to say how far away you are. Candela is per solid angle, and a solid angle is a direction with no distance in it. The same 480 cd produces a different illuminance at every distance, which is the inverse-square card's subject.
• An illuminance figure refuses to say what the surface looks like. A white paper at 0.80 reflectance and a dark walnut counter at 0.12, both at 30 fc, differ by a factor of about seven in how bright they appear, because that is the ratio of their reflectances.
• A luminance figure refuses to say how much light was delivered. A bright surface may be a highly reflective surface in modest light or a dark surface in punishing light, and the luminance alone cannot separate the two.

Every complaint that survives a passing meter reading lives in one of those four refusals.

The bridge from what arrives to what is seen

For a matte, diffusing (Lambertian) surface, the two sides connect cleanly:

• US units: L (fL) = E (fc) x rho, where rho is reflectance.
• SI units: L (cd/m2) = E (lux) x rho / pi.

The pi is not a fudge; it is what appears when flux leaving a diffuse surface into a full hemisphere is expressed per steradian. The held-constant condition is matte diffusion. On a gloss surface the relationship fails outright, because a specular reflection returns an image of the source at something close to the source's own luminance, which can be three orders of magnitude above the diffuse value. That is why a matte desk and a laminated one under identical illuminance are not the same visual problem.

Footcandles and lux are one quantity in two unit systems

One footcandle is one lumen per square foot, and one lux is one lumen per square meter, so 1 fc = 10.764 lx. The shop habit of multiplying by ten runs 7.1 percent low on the lux figure, and it errs in one direction only: converting footcandles to lux by ten always understates. On a job where the specification is written in lux and your meter reads footcandles, that habit alone can move a marginal reading across the acceptance line in the direction that flatters you.

Luminance carries the same split. One foot-lambert is 3.426 cd/m2. Foot-lamberts and candela per square meter are the same quantity, and mixing them within one calculation is the fastest way to be off by a factor of three and a half.

Where a footcandle number came from decides how much force it has

A footcandle target arrives from one of two places and they are not the same kind of thing.

• A code minimum. For construction work, 29 CFR 1926.56(a) and its Table D-3 set enforceable floors: 5 foot-candles for general construction area lighting, 3 foot-candles for general construction areas including excavation, waste areas and accessways, and 30 foot-candles for offices and first aid stations. These are floors for the work to proceed, not design values. Separately, 29 CFR 1910.303(g)(1) requires illumination for working spaces about service equipment, switchboards, panelboards and motor control centers installed indoors and states no footcandle value at all, so a requirement can exist with no number attached.
• A recommended practice. An IES recommended illuminance, in the edition your specification or your employer's standard names, binds only through that specification, contract or programme and never on its own. It is written as a design target with a plane, a height and a maintained basis attached, which is what makes it far above the OSHA floor for the same activity.

Say which one you are quoting, every time. "The code minimum is 5 fc and the specification calls for a recommended maintained level well above it" is a sentence that keeps you out of trouble in both directions.

Worked example: one luminaire described four ways

A recessed downlight. Its photometric test report gives 2,000 lumens total output and 480 candela at nadir (straight down). The aperture is round, 0.80 ft across, so its area is pi x (0.40 ft)^2 = 0.50 ft2. It is mounted 8.0 ft above a 2.5 ft work plane. The desktop reflectance is 0.30.

Flux, 2,000 lm. Total output. It says nothing about the desk.

Intensity, 480 cd at nadir. Worth a sanity check: a perfectly cosine (Lambertian) distribution putting out 2,000 lm would show 2000 / pi = 637 cd at nadir. The printed 480 cd is below that, which tells you this distribution is broader than cosine: more of its flux leaves at high angles. It sits between the 637 cd a cosine distribution would show and the 318 cd a uniform hemisphere would show, which is a spread downlight rather than a spot. Whether it also peaks off-nadir is a question for the candela table, not for these two numbers. That is a real read you can take off two numbers.

Illuminance, directly under the fixture. E = I / d^2 = 480 / (8.0)^2 = 7.5 fc, horizontal, at the 2.5 ft work plane, initial. Initial because it comes straight off the photometric file with no light loss factors applied; converting that to a maintained figure is a re-basing, not an addition, and the maintained-illuminance card owns it. In SI that is 7.5 x 10.764 = 80.7 lux. The times-ten habit would have printed 75 lux, which is 5.7 lux low, or 7.1 percent of 80.7.

Luminance of the desk. L = 7.5 fc x 0.30 = 2.25 fL, which is 2.25 x 3.426 = 7.7 cd/m2.

Luminance of the fixture aperture. 480 cd / 0.50 ft2 = 960 cd/ft2, and 1 cd/ft2 is 10.764 cd/m2, so 10,333 cd/m2.

Now the payload. The desk the customer is trying to read is at 7.7 cd/m2. The aperture sitting in their upper field of view is at 10,333 cd/m2, a ratio of about 1,340 to 1. Nothing in the 7.5 fc reading contains that ratio, and the meter cannot see it, because a cosine-corrected cell on a horizontal plane sums arriving flux and discards direction. What to do about that ratio belongs to the glare card; the point here is only that the quantity driving the complaint was never in the number you measured.

Checking your own figures

Run these against your own arithmetic, printing the value beside the criterion.

• Point-source treatment. The inverse-square card puts the working boundary at five times the maximum luminous dimension. Here: 5 x 0.80 ft = 4.0 ft required, 8.0 ft used, so the treatment stands.
• Initial versus maintained. The 7.5 fc figure contains zero light loss factors, so it may not be compared against a maintained target. Stated, not assumed.
• Plane and height printed. Horizontal, 2.5 ft above finished floor. An illuminance value without both is not a measurement.
• Unit conversion direction. 7.5 fc x 10.764 = 80.7 lux against the rounded 75 lux, a 7.1 percent shortfall, and it runs low every time rather than sometimes high.
• Lambertian bridge used only where it holds. The 2.25 fL applies to the matte desktop at rho = 0.30. It was not applied to the aperture, whose luminance came from candela divided by aperture area instead.
• The two candela figures agree. 480 cd printed against 637 cd for a cosine distribution of the same 2,000 lm, so the distribution is wider than cosine, which is consistent with a spread downlight rather than a spot.

If you cannot print a figure next to one of those lines, you have not checked it, you have asserted it.

References

• 29 CFR 1926.56(a) and Table D-3, minimum illumination intensities for construction work areas
• 29 CFR 1910.303(g)(1), illumination required for working spaces about indoor service equipment, switchboards, panelboards and motor control centers
• IES recommended practice for the space type in question, in the edition named by your specification or employer standard, which is where design target levels live
• Manufacturer photometric test report for the specific luminaire, which is the only source for its flux, intensity distribution and aperture dimensions
• See related: Why Lumens and Lux Are Not Interchangeable; What the Inverse Square Law Does to a Lighting Layout; What Glare Is and the Two Kinds That Matter