## Sensor Size, Part II

### February 7, 2010

As I noted in an earlier post, camera makers quote sensor sizes in mystifying “fractional inch” designations. They’re much less forthcoming in giving us the actual, active dimensions of the chip.

Is this because they’re embarrassed? Even a throwaway Kodak Fun Saver uses the generous dimensions of 35mm film; while today’s $300 digital compacts might use a chip with only 3% of that area.

The common 1/2.33″ or 1/2.5″ sensors used in current point & shoots measure roughly 6mm across. That’s, you know… not big:

Now, even when you don’t have any “official” specs about the chip used in a camera, it’s usually possible to work out the sensor dimensions indirectly.

All you need is the actual focal length(s) of the camera lens; plus the manufacturer’s stated “35mm equivalents.”

Here’s a camera marked with its true, optical focal lengths. (When the smaller number is under 10mm, you’re seeing true, not “equivalent” focal lengths.)

The first thing we need to know is that “equivalency” is usually based on the diagonal angle of view of the lens. The next point is that (true) focal lengths scale directly in proportion to the dimensions of the image format.

A frame of 35mm film has these dimensions:

Notice that film’s 43.3mm diagonal is a smaller number than the 70mm “equivalent” f.l. that was quoted for the long end of the zoom range. Telephoto focal lengths will always be longer than the image diagonal.

So, the digital sensor’s diagonal must also be smaller than the lens’s true focal length when zoomed in: 10.8mm.

Divide 43.3 by 70 and you get 0.62; multiply 10.8mm by that and you get 6.7mm as the diagonal of the sensor chip.

Likewise: 43.3 divided by 35 = 1.24; multiply 5.4mm by that and you also get 6.7mm for the diagonal.

But wait, that’s not so useful—didn’t we want to know the chip’s width and height?

Well, compact cameras almost always use 4:3 image proportions (the old “television” aspect ratio). And so, conveniently, the diagonal has a nice easy-to-remember relationship to the sides.

In other words, the chip is 60% as tall as the diagonal; and it’s 80% as wide.

So for the sensor we’re talking about, a 6.7mm diagonal means it’s about 5.3mm wide and 4.0mm tall. This is what the industry calls a 1/2.7″ chip size.

And that’s a lot smaller than Lincoln’s head.