These specs from vendors are notoriously inaccurate, and there's really only one way to be sure - measure them yourself (or use someone else's actual measurements). The easiest way is to measure the width of a full-screen item and the distance to the item measured.
I have a post over at cam-it that shows how to do it with a ruler and rod and gives examples, but you can do it with a fence, a wall, or anything that's easy to measure:
http://www.cam-it.org/index.php?topic=5424.0
The problem with working this backward to give your lens size, as CamFan found, is that it doesn't give your actual lens size, only your virtual lens size. For instance, a given 4mm lens will have a particular image circle size at its focal plane, while a different 4mm lens will have a different image circle size. If you order 3 different 4mm lenses for 1/3" sensors, each will give different results and will appear to be different lens sizes. Generally, the image circle is a good bit bigger than the sensor it's designed for; an image from a 1/3" lens will often cover most or all of a 1/2" sensor, based on my tests.
Add in different sensor sizes, and the problem's worse. A 1/3" 4mm lens will give a different FOV on 1/3", 1/2.8", and 1/4" sensors, and not all 1/3" (or whatever) sensors are the same size or sample the same number of pixels from the sensor.
It's also good to know that a 1/3" sensor isn't actually 1/3" diagonally. The specs for these sensors will often list them as "1/3" class" or similar. The sizing comes from the days when imagers were in vacuum tubes, and the size was the outside diameter of the glass tube. Nobody's willing to give the actual sensor size, as it would make them look smaller than the competition, and their marketing would suffer.
You can ballpark the actual size by multiplying the marketing size by 0.7, but to get the precise size, you need the image area dimensions from the spec sheet for the sensor.