# Why does this article say that a 1.5× crop factor sensor is 43% smaller than a 35mm film cell?

In the case of full-frame sensors, the pixels are spread out over a relatively large sensor: roughly 36mm by 24mm. This just happens to be the size of a 35mm film cell (remember film cameras?), and has come to be known as full-frame (despite the fact that there are even larger sensors, known as medium format sensors).

As of this writing, most consumer-grade digital cameras are not full-frame: they are cropped, meaning that they are smaller than a full-frame sensor.

For cameras with a 1.5x crop factor, the sensor is 43% smaller in both width and height than a 35mm film cell, resulting in a sensor with 66% less area than a full-frame sensor—a rather substantial loss in sensor size. This is because the crop factor is applied to both the width and the height separately.

In the example for a camera with a 1.5x crop factor, is its width (or height) 1/1.5=0.67 of the width (or height) of a full frame sensor? Why "the sensor is 43% smaller in both width and height than a 35mm film cell"?

Is its area (1/1.5)^2 = 0.44 of the area of a full frame sensor? Why "resulting in a sensor with 66% less area than a full-frame sensor—a rather substantial loss in sensor size"?

• roughly 36mm by 24mm. This just happens to be the size of a 35mm film cell (remember film cameras?), and has come to be known as full-frame Ha! Just happens to be? No. It's no coincidence. 135 film format was actually the smallest and most convenient for film for it's time. I seriously wouldn't bother about "crop sensors" unless you are used to a particular focal length of a particular format. Commented Jun 1, 2015 at 6:57
• Because whoever wrote the article can't do math correctly. Commented Jun 1, 2015 at 22:19
• @Michael: The author said he is a PhD, so it is hard for me to doubt.
– Tim
Commented Jun 2, 2015 at 18:11
• A PhD nor any other advanced degree guarantees one will never make a mistake. A PhD is, by its very nature, a very specialized degree in a narrow area of a specific field. In this case it does not appear to have been in general mathematics. Commented Jun 2, 2015 at 23:53

The article you've quoted and linked to just seems to have some bad maths.

When they're subtracting the percentages from 100, they seem to have forgotten to 'carry the one', so to speak. They've subtracted 66.66% from 100% and got 43%, and then 44% from 100% and come up with 66%.

It should say the sensor's edges are 33% shorter (not 43%), with a total area 55% less than the full-frame sensor (not 66% less).

• That depends. Canon APS-C sensors are 39% the size of a FF sensor in terms of area. Nikon and most others' APS-C camera sensors are 44% the size of a FF sensor in terms of area. Canon sensors are 62.5% the linear dimensions of a FF sensor. Most of the rest are 66.67%. Commented Jun 1, 2015 at 22:18

There are many various film and digital sensor sizes and formats.

135 film (also known as "full-frame") became the most used film in the 60s and the most common format was 3/2, meaning 36mm x 24mm frame size. The camera determined the format/ratio but was always 24mm high. There were even half frame cameras that used this film but would result in 18mm x 24mm frame sizes and would fit almost twice as many photos in one roll.

EDITED PHOTO FROM WIKI AND ABOVE LINK

APS was also a film size and the classic, 3/2 ratio/format, had a size of 24mm x 16mm (roughly).

For APS film, the height (red side) of the film was/is 16mm. This is where the "crop factor" comes in.

16mm x 1.5 = 24mm

And also relates to the field of view. If you have a 50mm lens on a full frame camera but placed it on an APS-C camera, you would get a different (cropped) field of view. So a 34mm lens, x 1.5 = 50mm (actually 52.5, but I'm rounding it down. REALLY rounding it down...).

In summary, if you had 2 cameras. 1 with ASP-C with a 35mm lens and a full frame with a 50mm lens, they would almost be seeing exactly the same thing.

Regarding surface area, yes, there is even more reduction.

So:

36mm x 24mm = 864mm² (full frame)

24mm x 16mm = 384mm² (APS-C)

As a percentage of area, the APS-C only covers 44% of the full frame. This is not the "crop factor".

EDIT: I'd like to add that digital cameras are capable of all sorts of different aspect ratios now which "crop" the sensor being used, anyway. It, in turn, changes the surface area yet will still be referred to as a FF or ASP crop camera.

• (@A K) Regarding the suggested edit, the surface area actually does have nothing to do with the crop factor. The crop factor is mainly to do with focal length. So, say you were used to a 75mm lens on FF, you would divide that by 1.5 and come to 50mm. Or vise versa, if you had 50mm on APS-C, you would multiply it by 1.5 and get 75mm for "FF equivalence". I stand by my statement that it has nothing to do with surface area. As proven, 384mm² x 1.5 ≠ 864mm². Commented Jun 1, 2015 at 23:58