We all know the "crop factor" of MFT is 2, right? Wrong!

Just kidding here. For all intents and purposes, using a 2x crop factor works fine, and nothing of what I'm going to write here actually matters.

The thing I wondered was: as the crop factor applies to the

*diagonal* angle of view, what does this mean for the

*horizontal* and

*vertical* angles of view, when you compare 3:2 sensors to 4:3 sensors? In other words, when I take a picture with a 25mm lens on MFT (4:3), how does it compare to 50mm on FF (3:2)? Let's say I'm photographing a building, and the building fills up the entire frame horizontally using 50mm on FF, will it still fit in the frame when standing in the same spot and taking the picture with 25mm on MFT?

So let's do some math. These are the physical dimensions of the imaging areas of the sensors we are discussing:

FF: width=35.6 mm, height=23.8 mm, diagonal=sqrt(35.6²+ 23.8²)=42.82 mm, area=35.6*23.8=847.28 mm²

MFT: width=17.3 mm, height=13 mm, diagonal=sqrt(17.3²+13²)=21.64 mm, area=17.3*13=224.9 mm²

The usual way to calculate the crop factor is to divide the diagonals; in this case: 42.82/21.64 =

**1.98** (indeed very close to 2).

What's also interesting to calculate is the ratio between the sensor areas. From a 2x crop factor, you'd expect that an FF sensor is 4 times larger than an MFT one. In fact, the ratio is 847.28/224.9=3.77. (So an MFT sensor is larger than you think.) When you take the square root of that, you get another option for the crop factor:

**1.94**.

But now the most interesting part: what about the horizontal and vertical angles of view?

The ratio between the horizontal dimensions is 35.6/17.3 =

**2.06**, so compared to a 50mm lens on FF you'd have a tiny bit smaller angle of view with a 25mm lens on MFT. You would need a 24mm lens to have the same horizontal angle of view. I'd say this is a negligible difference.

The ratio between the vertical dimensions is 23.8/13 =

**1.83**, so compared to a 50mm lens on FF you would capture more of the scene with a 25mm lens on MFT (similar to what a 46mm lens would capture on FF).

Another way to look at this is that if you applied a "perfect" crop factor of 2 to an FF sensor (thereby leaving just 1/4 of the sensor area, and keeping the aspect ratio to 3:2), you would end up with a sensor with a width of 35.6/2=17.8 mm and a height of 23.8/2=11.9 mm. So compared to that, you "lose" 0.5 mm in the horizontal dimension with an MFT sensor (2,8%), and "gain" 1.1 mm in the vertical dimension (9%).

So my conclusion is: using a crop factor of 2 is pretty accurate, but you will get some pixels

**for free** in the vertical dimension. The building still fits horizontally, but you will include more of it vertically. Awesome, right?

I have seen some people on the internet claim that for instance the Panasonic 15mm lens "is actually closer to a 35mm equivalent than a 30mm one, because of the 4:3 aspect ratio", but I don't believe that's true, now that I've done the calculations. Horizontally, you still get the angle of view of a 30mm on FF, but vertically it's closer to a 28mm.

Of course, different lenses with the same focal length might still produce a different angle of view (even within the same system). For example I read somewhere that the Olympus 25mm f/1.8 is a bit wider than the Panasonic 25mm f/1.4. So you might get a bit different results when you actually do the comparison (between 25mm MFT and 50mm FF) in practice. But in general I think it's safe to assume that your "equivalent" lens will be able to cover at least the same field of view as an FF one, but offers a little bit more in the vertical dimension.