Who needs this?
Light gets measured at the bulb and at the surface. These people end up converting between the two:
- Bulb shoppersThe old 60 W bulb burned out, and the LED boxes only list lumens and a much smaller wattage.
- Homeowners and remodelersA kitchen plan calls for a certain light level on the counters, and the fixtures are sold by lumens.
- Electricians and lighting designersSpecs written to metric standards give lux, while US drawings and meters often use foot-candles.
- PhotographersMoving a light half a meter changes the exposure more than most people expect.
- Indoor gardenersPlant guides quote foot-candles, phone meter apps read lux, and grow-light makers use yet another measure.
- StudentsPhysics problems on point sources and the inverse-square law use candelas, lumens and lux together.
Light out vs light landing
Think of a garden sprinkler. The total water it sprays per minute is fixed, like a bulb's lumens. How wet the lawn gets depends on where you stand: right next to the sprinkler the grass gets soaked, ten steps away it gets a light mist. That wetness per patch of lawn is lux (or foot-candles). Same sprinkler, very different results depending on the area the water lands on.
- Lumens (lm) measure the total visible light a source puts out, in all directions. It's the big number on a bulb box.
- Lux (lx) measures light arriving at a surface: one lumen per square meter. A light meter reads lux.
- Foot-candles (fc) are the same idea per square foot: one lumen per square foot. A square foot is exactly 0.09290304 m², so 1 fc is about 10.764 lx.
- Candelas (cd) measure how strong a light is in one particular direction. A plain candle gives roughly one candela, which is where the name comes from. Spotlights and flashlights are often rated this way.
Watts are not brightness
Watts measure the power a bulb draws, not the light it gives. An old 60 W incandescent bulb gave about 800 lumens. An LED that gives the same 800 lm uses roughly 9 to 10 W. That's why US bulb boxes now lead with lumens on a "Lighting Facts" label. The energy vs power guide explains what the watts do cost you.
The inverse-square law
For a small light (a bare bulb, a camera flash) the light spreads out as it travels. At twice the distance, the same light covers a patch twice as wide and twice as tall, so four times the area. Each square meter gets a quarter as much. At three times the distance it gets a ninth.
The math is short: lux = candelas ÷ distance² (in meters). A 100 cd lamp gives 100 lx at 1 m, 25 lx at 2 m and about 11 lx at 3 m. It holds when the light is small compared with the distance.
How bright is "bright"?
Your eyes adjust so well that the real numbers surprise people. Full summer sun can reach about 100,000 lx. An overcast day is roughly 1,000 to 10,000 lx. Lighting standards for offices (the IES recommendations in North America and EN 12464-1 in Europe) land in the range of about 300 to 500 lx on the desk. A full moon gives well under 1 lx.
Color is a separate number
A bulb's color temperature is given in kelvins: about 2700 K is the warm, yellowish light of a classic living-room lamp, and 5000 to 6500 K looks like daylight. It describes the color of the light, not how much there is, so a 2700 K and a 5000 K bulb can both put out 800 lm. The temperature guide explains the kelvin itself.
Converting, step by step
Lumens to lux
There's no lumens-to-lux converter, because you need one more number: the area the light falls on. If the light spreads evenly, divide:
- Find the area
2 m × 1 m = 2 m² - Divide lumens by area
800 lm ÷ 2 m² = 400 lx
In feet, the same division gives foot-candles: 800 lm over 20 ft² is 40 fc. Walls, ceilings and shades soak up some of it, so treat this as the most a meter could read.
Lux and foot-candles
These two convert directly with one factor.
- Foot-candles to lux
50 × 10.764 = 538.2 lx - Lux to foot-candles
500 × 0.09290304 = 46.45 fc
Need the floor area first? This gives it in square feet and square meters:
Length: 20 ftWidth: 20 ftHow many: 1
Real situations, worked out
Look for about 800 lumens on the box and ignore the wattage. An LED at that output draws around 9 W. Burned 4 hours a day for a year, the old bulb used 87.6 kWh and the LED about 13.1 kWh, for the same light on the table.
60 W incandescent ≈ 800 lm ≈ 9–10 W LEDEach fixture is rated 4,000 lm, so 16,000 lm in all. The garage is 20 × 20 ft, or 400 ft². 16,000 ÷ 400 = 40 fc, and 40 × 10.764 is about 431 lx. Some light lands on walls, but that's office territory, plenty for a workbench.
16,000 lm over 400 ft² ≈ 40 fc ≈ 431 lx (at best)The photographer wants one stop more light, which means twice as much. Under the inverse-square law that's the old distance divided by √2 (about 1.41): 2 ÷ 1.41 is about 1.41 m. At that distance the meter reads about 800 lx.
move from 2 m to about 1.4 m for double the lightThe phone meter app reads in lux. 200 × 10.764 is about 2,153 lx, so a spot that reads 2,500 lx clears the bar. Grow-light makers often quote PPFD instead, in micromoles of photons per square meter per second. That's a different measure (it counts the light plants use, not the light eyes see), and there's no single factor that turns it into lux.
200 fc ≈ 2,153 lxDoing it in your head
One foot-candle is about 10 lux. Multiply foot-candles by 10 for lux, or divide lux by 10 for foot-candles. It always comes out about 7% low going to lux, close enough for most rooms.
| fc | Exact lx | × 10 | Off by |
|---|---|---|---|
| 1 | 10.76 | 10 | 0.76 |
| 10 | 107.6 | 100 | 7.6 |
| 30 | 322.9 | 300 | 22.9 |
| 50 | 538.2 | 500 | 38.2 |
| 100 | 1,076 | 1,000 | 76 |
| 1,000 | 10,764 | 10,000 | 764 |
Distance pegs. Twice as far is a quarter of the light, three times as far is a ninth, and moving a light about 1.4 times farther away halves it. Photographers call that halving one stop.
Common mistakes
Shopping by watts. A 15 W LED is far brighter than a 15 W incandescent. Watts only hinted at brightness when every bulb worked the same way. Compare lumens.
Treating lumens and lux as the same thing. A 1,000-lumen flashlight doesn't put 1,000 lx anywhere in particular. It depends on how tightly the beam is focused and how far away the target is. Lumens need an area before they become lux.
Using the inverse-square law on a big source up close. Standing 30 cm from a 2 m LED panel, stepping back to 60 cm won't cut the light to a quarter. The law is for sources that are small compared with the distance.
A bit of history
Light was measured against flames long before anyone had a light meter, which is why "candle" survives in two unit names.
- 1860Britain's Metropolitan Gas Act sets a standard candle, made of spermaceti wax and burning at a fixed rate, for testing the brightness of town gas.
- 1948The General Conference on Weights and Measures adopts a new unit of luminous intensity, based on the glow of a blackbody at the freezing point of platinum, and names it the candela.
- 1954The candela becomes one of the base units of the system that would soon be called the SI.
- 1960The International System of Units (SI) is named, with the lumen and the lux among its derived units.
- 1979The candela is redefined from a fixed frequency of green light and a fixed power, so it no longer depends on any physical lamp or furnace.
The foot-candle never joined the SI, but American building and lighting work still uses it.
Reference table
| Lux | Foot-candles | Roughly like |
|---|---|---|
| under 1 | under 0.1 | Full moon |
| 50 | 4.6 | |
| 100 | 9.3 | |
| 300 | 27.9 | Low end for office work |
| 500 | 46.5 | Brighter office or desk |
| 1,000 | 92.9 | Dark overcast day |
| 10,000 | 929 | Bright overcast day |
| 100,000 | 9,290 | Full summer sun |
Questions people ask
How many lumens do I need for a room?
Multiply the lux you want by the floor area in square meters. A 3 × 4 m living room (12 m²) at about 150 lx needs around 1,800 lm, more if the walls are dark or the shades are thick. In feet, multiply foot-candles by square feet.
How many lux is one foot-candle?
About 10.764. A square foot is exactly 0.09290304 m², and 1 ÷ 0.09290304 is 10.7639. For quick math, call it 10.
Is a higher kelvin bulb brighter?
No. Kelvins describe the color of the light: lower numbers are warmer and more yellow, higher numbers bluer and closer to daylight. Brightness comes from the lumens.
How many lumens is a 100 W bulb?
An old 100 W incandescent gave about 1,600 lm, and LED replacements labeled "100 W equivalent" aim for about the same. Check the lumens on the box.