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What is the Relationship Between the Wattage of a Lightbulb and its Brightness?

What is the Relationship Between the Wattage of a Lightbulb and its Brightness?

  2013-02-25         sparksdirect         Advice » Lighting Design Advice

As incandescent bulbs are phased out of the domestic market, it's the right time to take a look at what the options are for replacements.

It's common knowledge that a modern energy-saving lamp consumes much less energy and so has a lower wattage, but still offers roughly the same amount of light.

CFL and LED light fittings are often sold as being "equal" in brightness to a traditional lightbulb: so an 11W CFL bulb emits as much light as a 60W bulb, according to the packaging. How does this work?

Well... it gets a little bit complicated. But thankfully, it also gets a little bit interesting.

Seeing Brightness

Brightness is someone's subjective judgement of the luminance of an object. Without getting too mathematical, it's based on the equation known as the luminosity function - the standardised model of brightness perception.

That's an average measurement, not a universal statement. Every person is going to judge brightness ever-so-slightly differently. What the luminosity function describes is the average human sensitivity to small differences: those aptly-named "just noticeable differences."

To illustrate the idea: one more "just noticeable difference" is that between a 'classic' chocolate bar and a smaller version introduced when the old version becomes too expensive to manufacture.

The observer will hardly be able to notice the difference unless they look very closely. How do we know it's noticeably different, then?

If test subjects notice the discrepancy in at least 50% of the tests, that's a just noticeable difference. 

(In this regard, psychophysics is an endlessly fascinating sub-discipline of marketing.)

The Lux and the Lumen

The Lumen is the measure of the perceived power of light: the "luminous flux." It's affected by the spectral sensitivity of the eye. A lumen is equivalent to one candela per steradian (1 lm = 1 cd┬Ěsr). (And a steradian, by the way, is the SI-derived unit of "solid angle" - a radiated cone of light. It's best thought of as a 2D area in a 3D space, like a patch on the surface of a sphere.)

The lumen isn't used to measure brightness, as such - that's a subjective measurement that changes with distance.

The further away you get from something, the dimmer it gets. But it is useful for comparing the power of energy-saving lamps and light fittings to their halogen and incandescent counterparts.

Some manufacturers list this information right on the box. And it gets still more complicated: lamps are rated in initial and mean lumens.

The initial lumen rating refers to the light given when the lamp is new, and as the light source sheds the chemicals inside it, or as its bulb walls darken over time, lumen deprecation takes place.

So the average rating is the lumens emitted over the useful lifespan of the device. The Lux is related to the lumen but is measures a completely different thing: it's the SI-derived measure of illuminance.

Illuminance is what we think of when we think of "visible light." It is the total amount of visible light illuminating (reflecting off) a point on a surface of a thing from all directions above that surface.

Visible light, then, is measured in lux: the luminous flux per unit area. Lux measures the intensity of light that reflects off or passes through a surface. One lux is equal to one lumen per square metre (1 lx = 1 lm/m^2).

Home lighting is about 50 lx, while TV studio lighting is usually about 1,000 lx. Daylight tends to hover around the 10 to 25,000 lx mark.

So a measurement of lux will tell you how many lumens you need to illuminate an area. 1000 lm concentrated over a square metre will illuminate that spot for an illuminance of 1000 lx, and spreading that same lm value over 10 metres will illuminate that area for 100 lx.

The Relationship Between Wattage and Luminance

The watt (W) is the measure of power, defined as 1 Joule (unit of energy) per second (1 W = 1 J/s), and the power a bulb consumes has a lot to do with its electrical resistance.

The resistance of a traditional incandescent bulb is affected by its filament, depending on its length, thickness, material, and so on.

That metallic filament needs to be heated to a high temperature until it glows, and a filament with higher resistance glows brighter - but needs more power. So if a bulb has a brighter-burning filament, it is constructed at a higher wattage.

A filament fitted within a 100W bulb has a higher resistance than a 60W bulb and so emits a brighter light. Sadly, a lot of that electrical energy is converted into heat when a lightbulb's sole purpose is to provide light.

This is considered to be wasted energy.

The rate at which a light source converts electrical power into light is known as luminous efficacy and is expressed as lumens per watt (LPW).

The higher the LPW, the more efficient the light source. So while an incandescent light source has a low LPW, an energy-saving bulb has a much higher LPW: more of the electrical input is converted to luminous output.

Wattage Equivalence

When a manufacturer claims that a CFL or LED lightbulb is "equivalent" to a 40, 60 or 100-watt lamp, what they mean is that the light output is roughly the same, as measured in lumens.

That said, it's rarely (if ever) a straight relationship; most of the time wattage equivalency is a rough figure, somewhere in the same "ball park." But in everyday use, that difference is barely noticeable - particularly with the current range of energy-saving lamps. If you'd like to take some of your own measurements and correct us on our science, you are more than welcome to do so in the comments. We stock both incandescent and energy-saving lightbulbs and lamps to aid the research.