Lumen
SI derived unit · quantity: luminous flux
01 · Definition
The lumen is the luminous flux emitted by a source of one candela into a solid angle of one steradian. The quantity describes all the light a source gives out, regardless of where it goes: the whole sphere holds 4π steradians, so a lamp shining evenly at one candela emits about 12.6 lumens.
It was lumens that replaced watts on lamp packaging, once LEDs made power a meaningless measure of brightness: a sixty-watt incandescent bulb and an eight-watt LED both give the same eight hundred lumens.
A watt says how much the device eats, a lumen how much light it gives out. An eighty-watt bulb of Soviet days shone more weakly than today’s ten-watt one: the power grew while the efficacy stood still.
An incandescent bulb gives about thirteen lumens per watt, a halogen twenty, a fluorescent sixty, a modern LED between a hundred and twenty and two hundred. The theoretical ceiling is 683, and only for a single wavelength.
The top of the scale is the Sun: 3.6·10²⁸ lumens. Of these about a hundred thousand lux reach the ground at noon, and no lamp argues with that.
02 · Conversion
Enter a flux and the passport will break it down by unit
Conversion into candelas is only possible with a caveat about the solid angle, so the table computes for uniform emission in all directions. The watts in the last row are not power but the equivalent by efficacy: how much a lamp of each type would draw for this flux.
Lumens alone are not enough to choose a lamp: two sources with the same flux differ in colour temperature and in colour rendering. Two thousand seven hundred kelvin reads as warm, six thousand as daylight, and the same eight hundred lumens will feel quite different in a bedroom and in a workshop.
| Unit | Name | Value | Where it is met |
|---|---|---|---|
| lm | lumen, an SI unit | 800 | lumen, an SI unit |
| klm | kilolumen | 0.8 | kilolumen |
| Mlm | megalumen | 0 | megalumen |
| mlm | millilumen | 800000 | millilumen |
| cd·sr | candela per steradian — the very same thing | 800 | candela per steradian — the very same thing |
| lm·h | lumen-hour: quantity of light, flux over burning time | 800 | lumen-hour: quantity of light, flux over burning time |
| W(LED) | watts of an LED: what it would draw for this flux | 5.71 | watts of an LED: what it would draw for this flux |
| W(inc) | watts of an incandescent bulb — a habit from the last century | 61.5 | watts of an incandescent bulb — a habit from the last century |
| HK | Hefner candle: the German standard on amyl acetate | 88.9 | Hefner candle: the German standard on amyl acetate |
The factor of four pi works only for uniform emission in all directions.
03 · Orders of magnitude
from an indicator to a lighthousehundreds and thousands: a room lamp, a desk lamp, a car headlight
04 · Measuring instruments
What luminous flux is measured with
A hollow sphere with a white diffuse coating: light from the lamp inside is reflected thousands of times, and the illuminance on the wall becomes proportional to the total flux regardless of how the beam was shaped. The main method for lamps.
The detector slowly travels around the source over a sphere, recording the luminous intensity in every direction; the flux follows by integration. The measurement takes hours but gives the full picture of how the light is distributed.
It splits the light into a spectrum and weights every wavelength by the luminosity curve. The only way to measure flux without a systematic error on sources with narrow lines — LEDs and discharge lamps.
Hidden inside the very definition of the lumen is the luminosity curve — the averaged sensitivity of the eye, recorded in the 1920s on a few dozen observers. That is why two lamps with the same number on the box can look different: the flux is equal, the spectrum is not.
A specially selected incandescent lamp with a stabilised current, whose flux is certified at a national institute. Spheres and photometers are calibrated against it, and the lamp itself ages: its certificate has an expiry date.
05 · Writing rules
Both letters lower case, and not to be confused with the lux
The symbol of the unit is two lower-case Latin letters, lm, in upright type. The name comes from the Latin lumen — light — so there are no capitals in it. The Russian symbol is лм.
The symbol of the quantity is an italic Greek Φ. The lumen describes the source, the lux the lit surface: to give a lamp a value in lux is to leave out the distance, and the number ceases to mean anything.
At projectors one writes «ANSI lumens»: the same lumen, but measured by a standard procedure with nine points on the screen. Figures without the ANSI mark are not worth comparing — the maker is free to measure them however it pleases.
06 · Neighbouring units
The lumen stands between the candela and the lux: the candela says how brightly a source shines in one direction, the lumen how much light it gives in total, the lux how much of that reached the surface.
luminous intensity in a direction
the whole flux of the source
what reached the surface
Of the Simetrium passports neighbours of the lumen candela and steradian from the definition, lux as flux over area, foot-candle in Anglo-American practice, and watt, to which luminous flux is tied by the luminosity curve.
07 · Historical section
From a candle to the number on the box
The German standard was the Hefner lamp, burning amyl acetate with a wick of precisely fixed diameter. It gave about nine tenths of the new candela, but depended on humidity and on the carbon dioxide in the room — which is exactly why it was abandoned.
The International Electrical Congress introduced the lumen together with the lux and the phot. The name was taken from the Latin lumen — light; the same root served in optics, where lumen meant the clear opening of a tube.
Beside it lived a unit for the quantity of light — the lumen-hour, flux multiplied by burning time. That is how the consumption of gas and kerosene lamps was reckoned: not brightness, but how much light the lamp had given over an evening.
Richard Ulbricht proposed a hollow sphere with a diffuse coating in which light is reflected until it loses all direction. Measuring flux, which had previously required going round the source point by point, became a single reading.
European labelling required luminous flux to be printed larger than power: watts stopped saying anything about brightness once an LED gave six times more light per watt than a bulb.
The number 683, inherited from a candle
The figure of 683 lumens per watt that stands in the definition of the candela looks arbitrary — and arbitrary it is. It was chosen in 1979 so that the new candela would come out as close as possible to the old one, defined by the glow of molten platinum. A century of measurement is folded into that number.
Those 683 are the maximum for monochromatic light at 555 nanometres, where the eye is most sensitive. For white light the ceiling is lower, around 350 lumens per watt: part of the spectrum is needed for whiteness yet is barely seen by the eye.
Catalogue · units of measurement
A passport for every quantity
Seven SI base units, twenty-two derived ones with names of their own, and the non-SI units that neither engineering nor daily life can do without. Each gets its own sheet: definition, conversion, instruments, writing rules. In 6 languages.
SI derived units with names of their own
the lumen sheet is openSI base units
in amber — the candela the lumen is built fromLuminous flux in other notations
Passport language
6 languages. The symbol lm is international, but the habit of colour temperature is not: Northern Europe and America like warm light at 2700 K, Asia prefers cold daylight, and the recommendations in standards differ accordingly.