The True Crop Factor of Micro Four Thirds

frankmulder

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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. :)
 
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stevedo

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I started to read your post and maybe lasted 10 seconds before I started to fall asleep :). All I know is that my sensors are micro 4/3 in format and are not cropped at all.

;)
 
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mfturner

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When I sold my Canon ASP-C setup to try out mu43, I realized that they are closer than you might think in the short dimension. That meant that I didn't have such a huge adjustment, just a little cropping of the top and a decent crop of of the sides compared to what I was used to. Since I cropped a bunch anyway with my Canon images, I replaced primes with zooms and just try to have better framing now, which is a win-win for me.
 

Lumix G Experience UK

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It's interesting to dive into the maths for a while and to think about how aspect ratios have an impact on the width and height of the view we see through the viewfinder. Once we get into the figure though and start rolling around in the finer details it is easy to forget that we rarely know the real focal lengths of the lenses we are talking about without actually measuring them. Manufacturers are quite casual in their descriptions and the marked mm figure is almost always rounded up or down, sometimes by a surprising amount. This inconstant element then renders all our hard work with the calculator irrelevant.
Doesn't mean it isn't fun to do though :)
 

Erich_H

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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. :)
I got as far as a bit into the math paragraph. Lost it completely in the neighborhood of the square roots. Skipped to the end.

I agree completely with your reasoning!
Because you're worth it!
 

WT21

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It’s because the aspect ratio is different, and for me, I start there. I actually prefer 4:3 over 3:2.

FF has an overall advantage just because the sensor is so much bigger, but vs APSC choices (all of which are 3:2) the gap closes much more, and especially if you are shooting square (which i often do) or shooting people. I like the extra head room on 43 when shooting people and I toss away much less sensor when shooting square.

the reverse is true if one favors 16:9 or 16:10. That’s closer to 3:2 so requires less of a crop

4:3 format is also one way m43 lenses can be made smaller than similar 3:2. If the height of either image circle were the same, the width has to be greater for 3:2, and because lens produce round images, the overall diameter has to be greater.

tl;dr - I agree with you, and I put it mostly down to the aspect ratio, which I actually prefer over 3:2 anyway
 
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ektar

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I guess I'm a sucker for numbers and I appreciate that someone will dive into the arcane, but I read the whole OP. I'm sure this has been discussed before, but: I don't even visually remember what the 35mm aspect ratio looks like full frame on screen. I haven't shot 35 in forever, and I don't own a FF camera. But, I recently was gifted an APS-C camera, and keep looking at the images and thinking that the aspect ratio just looks strange to my Four Thirds (happy @Ross the fiddler ?) calibrated eyeballs.
 
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frankmulder

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I started to read your post and maybe lasted 10 seconds before I started to fall asleep
We've found the ultimate cure for insomnia! 🤡

All I know is that my sensors are micro 4/3 in format and are not cropped at all.
Fair enough. My post is only useful when you compare systems. If you only use MFT, and never feel the need to understand what kind of pictures a "50mm lens on FF" or a "35mm lens on APS-C" produces when compared to your "25mm lens on MFT", then you can safely ignore what I wrote. Well, you can do that anyway, as I said. :)

I personally like to understand what people say who use other systems, to understand their EXIF data, and to make predictions on what results certain setups would produce (without having to own all those systems). A practical example of this is when a friend asked me to photograph her PhD defence. I wanted to be prepared for the circumstances, so I looked at pictures of PhD defences that were held in the same room. Those pictures were taken with FF and APS-C cameras. From the EXIF data of those pictures, I found out that the room was very dimly lit, and I could predict the settings that I would have to use in order to get good pictures. I knew that I would have to combine high ISOs with fast primes (and I knew which focal lengths I would need). Because I knew I had to use primes, I could ask for permission beforehand to walk around during the defence (to "zoom with my feet"). I got the permission, and the pictures turned out great. If I hadn't done my preparation (armed with "crop factor knowledge"), I might've just brought my f/2.8 zooms, and would've got worse pictures.

I put it mostly down to the aspect ratio, which I actually prefer over 3:2 anyway
Yes, that was the whole point of my post: to understand what the consequences are of the difference in aspect ratios (between 3:2 and 4:3) on the field of view. ;)

And as a side effect of all of this, we can also reach similar conclusions to what @mfturner said:

When I sold my Canon ASP-C setup to try out mu43, I realized that they are closer than you might think in the short dimension.

I used to think that there is a 1 stop difference between MFT and APS-C, and a 1 stop difference between APS-C and FF. This turns out not to be true. APS-C is closer to MFT than it is to FF. (The difference between MFT and Canon APS-C is about 0.64 stops, and between MFT and other APS-C sensors: 0.83 stops. And there's indeed even less difference when you only consider the height of the sensor.)
 
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Erich_H

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..... I personally like to understand what people say who use other systems, to understand their EXIF data, and to make predictions on what results certain setups would produce (without having to own all those systems).....
As taking the opposite route to you, I can tell you that your way put a LOT less stress to available lebensraum!
 

Mountain_Man_79

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I'm pretty sure he is not on this site any more. His profile page shows "Oops! We ran into some problems. — This user's profile is not available."

We can all empty our ignore lists again. :D
😭But I hadn’t yet told him about my new 1-step exposure technique 😭
 

frankmulder

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...I obviously missed something...
There was this user called "BushmanOrig" whose actual name was Siegfried, and he would start or participate in threads about things like:
  • sensors, photons and ETTR
  • the "conspiracy" against Micro Four Thirds (how people are trying to kill our beloved system by spreading misinformation)
  • his "revolutionary" approaches to achieving the best IQ out of MFT gear (like his "2 step exposure technique", which entailed using wrong settings in step 1, like stopping down the aperture too much and therefore having to raise the ISO unnecessarily, and then in step 2 suddenly realising that you could open up the aperture, decrease the ISO and magically obtain better IQ).
His way of talking about these subjects caused many of these threads to derail and end up in the Back Room subforum. (You can still find those threads, but all of his messages have been removed, so they can be a bit hard to follow.) Many users also opted to put him on the "ignore list", so they wouldn't be distracted by his posts. I am not sure whether he left the site himself, or one of the admins removed him.
 

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