Quoted: Lumens, and Candlepower are both measures of how the human eye perceives light.
More scientific measurements would compare actual watts. Color temperatures also impacts the brightness. Lights that are high in output towards the middle of the spectrum tend to look brighter to the eye than equally powerful lights that favor higher or lower frequency light.
Reflectors also have a great impact on the brightness. A 10W bare bulb may not be as useful illumination as a 3W bulb with a decent reflector.
Lumens and Candlepower I believe simply measure light as it falls on a measured area. Better reflectors will boost this figure. Watts on the other hand will tell you how much light is being output.
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Watts will tell you how much power is going in. If you know Watts and the lamp's spectral efficiency, then your getting somewhere. Allot of those watts are being coverted to heat.
With area, you are referring to foot-candles.
1)1 Lumen - the amount of visible light emitted by a standard candle through a solid angle of 1 steradian. Since a sphere has 4pi = 12.57 steradians, the standard candle emits a total of 12.57 lumens. (Of course, 1 Steradian is just that solid angle over which the subtended area is exactly equal to the radius of a sphere, so, 1 sq-ft of surface area on a 1 ft sphere covers exactly 1 steradian.) Foot candle = 1 lumen/sq-ft, which is the illumination from 1 standard candle at 1 foot range.
Thats where I got the 12.5Lumen reference.