Fuzzy Camera Math

I have been attempting to understand the way that zoom factors are determined for cameras. Have you ever noticed that compact cameras never share their lens focal in a prominent way and on an SLR you won’t find an zoom factor? That is because of two things, first, the size of the sensor on a compact camera, and second, because zoom factors are meaningless on SLRs.

Compact cameras use a zoom ratio to specify their lens range because with their sensor size, their actual lens size is irrelevant. Take for example, Chris’s new P90 has a zoom ratio of 24x, but his physical focal length is 110.4mm. Because of his sensor size, he has an angle of view that is more like a 624mm lens when compared to a “full size” (35mm) sensor. It is much easier to just say that his lens is 24x, since his high end is 110.4mm and low end is 4.7mm, but yet he can get a closer image than my 200mm lens.

SLRs are where the fuzzy camera math gets really fun. Everything is relative on the lens, not on the sensor (since most DSLRs use a crop factor of either 1.5 or 1.6). I am considering buying a 70-300mm Nikon lens for my camera, which has an advertised zoom factor of 4.2, but yet my full kit has a crop factor of 11x, even though my longest focal length is only 200mm. Being confused by how we arrived at this particular set of numbers I decided to dive into how the numbers are calculated. Lenses are apparently measured for zoom factor based on dividing the maximum length by the minimum length. The zoom factor of a system is done by using the maximum of all the lenses and dividing by the minimum focal length of all the lenses.

For my system we get this:

Lens Range Zoom Factor System Factor
18-55mm 3x 3x
55-200mm 3.6x 11x
70-300mm 4.2x 16x


Thinking about this, zoom factor is a really sucky way to measure how far a camera can see, since the wide factors are included with this ratio as well (wide… anything below the 35mm standard “normal”, which is 50mm). Some cameras start somewhat longer than “normal”, which means they have a less impressive zoom number, even though they could have a farther reach than a camera that may have a more impressive number, that could fall short on actual distance. The problem here is “zoom” ration/number. It doesn’t measure zoom, it is simply the focal length ratio, but I guess only a Radio Shack geek could make a large focal length ratio seem impressive.

Just for fun, here is a cool link: http://www.digified.net/focallength/. This site will calculate the equivalent ranges to standard for almost any camera. To get an idea of how far the reach of a camera is, figure out its standardized maximum focal length, and then divide that by 50mm, which will be a ratio against “normal”, there you will have your true zoom ratio, and not just the focal length ratio.

On my system, this looks like this:

Lens Standard Maximum Amount of Zoom
18-55mm 82.5mm 1.65
55-200mm 300mm 6
70-300mm 450mm 9


I can even apply this formula to Chris’s bridge camera:

Lens Standard Maximum Amount of Zoom
4.7-110.4mm 624mm 12.48


And as is clear from this chart, I am still underpowered when it comes to comparing my camera to Chris’s, but I am told that SLRs have advantages over compact/bridge cameras. I won’t be the first Nikon photographer to wish that the lens for the P90 was available in f-mount (the mount type on all Nikon SLRs).