No matter what we are going to discuss below - the focal length and aperture of a lens isn't going so change. e.g. a 50mm f/1.8 lens is a 50mm f/1.8 is a 50mm f/1.8 lens. Whatever we mention in our review, these physical characteristics are NEVER disputed.

Now the problem is ... you don't take images with a lens. A naked lens is nothing more than an expensive paperweight. A lens makes only sense in the context of a camera and THIS is where things are getting complicated when comparing different SYSTEMS. Equivalence is a SYSTEM discussion, not only a lens discussion.

For the sake of simplicity let's pick a concrete example that we'll use throughout this article:

Some of you may already shout in agony but let's swallow this for now ... :-)

Equivalent Focal Length

(*) It is actually slightly less than that in real systems (e.g. 23.5x15.6mm on Nikon, 22.5x15.0mm on Canon)
(**) It is more like 1.55x to 1.6x in real systems

Simplistically the crop factor is just the ratio between the sensor width (or height) of a system relative to the full format (e.g. 36mm / 24mm = 1.5x for APS-C). Now you may notice that this is actually not so easy for Micro-Four-Thirds because the image ratio is different (4:3 vs 3:2). Most observers have settled for the 2x crop factor here (you can argue between 1.84x to 2.08x depending on how you look at it).

In order to compare the different focal lengths, we have to take crop factor and multiply it with the focal length:

Or we can phrase it differently - when using a smaller format, we have to use the same FOCUS DISTANCE using a SHORTER focal length in order to achieve the SAME FIELD OF VIEW in the final image (camera output) because only a crop of the full format image field is used. Which leads us to the next topic ...

Equivalent Aperture (Depth-of-Field)

CLICK HERE to open a depth-of-field calculator.

Enter the specs that we have discusses so far and a focus distance of 10m (could be any):

Then observe the depth-of-field result - it is the SAME. Again, the FIELD-OF-VIEW is IDENTICAL here. Below is a summary:

(*) This value varies a bit because APS-C format sensors are not sized to the ideal 24x16mm. The calculator is also rounding a bit. Also APS-C f/4 * 1.5x = f/6 and not f/5.6. These are still tiny error margins in the grand picture really.

So despite having used a bigger physical aperture, the DEPTH-OF-FIELD is the same. Why? Because you have to use a shorter focal length to achieve the same result. So a 150mm f/2.8 (on MFT) is equivalent to a 200mm f/4 (on APS-C) is equivalent to a 300mm f/5.6 (on FF). Thus the equivalent full format aperture in our example is therefore ... f/5.6.

Note: This calculator simplifies things a bit - the so-called "circle-of-confusion" is kept constant across all systems here.

Equivalent Speed

Let's assume that we have 3 different system cameras with 20 megapixels at ISO 200. I think we can agree on the fact that the image noise is best on the full format camera, followed by APS-C followed by Micro-Four-Thirds, right? Now ... what amount of increased image noise are we talking about here? There are, of course, variations due to different sensor technologies but let's assume for a moment that they all rely on the same ingredients. So ? Well, ISO 800 on full format will give you roughly the same image noise as ISO 400 (more like ISO 340 actually) on APS-C and ISO 200 on Micro-Four-Thirds. Or in other words - based on the same output quality - and this is the only thing that counts - full format has a 2 f-stops advantage over Micro-Four-Thirds and roughly 1 f-stop over APS-C.

Thus ... assuming the SAME OUTPUT QUALITY (same megapixels, same sensor noise) the SYSTEM SPEED is identical for a 300mm f/5.6 on a full format camera, a 200mm f/4 on an APS-C camera and a 150mm f/2.8 on Micro-Four-Thirds. You may argue that image stabilization plays a role but then just take e.g. the Sony A7 II as an example - thus a full format camera which can take advantage of in-body IS plus in-lens IS. Whatever you can do in a smaller format is technically achievable in a bigger format. Current advantages are just a snapshot in time - eventually all systems will pick up new technologies and catch up (or they disappear as Darwin told us).

Wonna have a visual here? Try the comparometer over at dpreview. If you click the link it'll give you a new window showing a comparison between the Nikon D750 (full format, 24 megapixel Sony sensor) and the Nikon D7200 (APS-C, 24 megapixel Sony sensor). Select RAW & ISO 3200 for the D750 and RAW & ISO 1600 for the D7200 (or ISO 6400 vs ISO 3200). Observe the image noise. Result: pretty much identical thus a 1 f-stop advantage for the full format camera here.

Size ...

The Pentax lens doesn't really fit there but I couldn't find a more appropriate APS-C example. The Pentax lens is longer but then the equivalent aperture is f/6.2 if we are precise there (f/4 * 1.55 = f/6.2).

Well? Ok, the Sony lens is a little heavier but the Olympus lens is actually a bit longer. We have to take off the tripod mount in case of Pentax - thus 100g or so. However, you may notice that the difference is not huge - it's certainly not a factor of 2 (MFT vs FF).

Another one maybe?

One more?

Surprising, isn't it? Not really. Why? Well, because in order to achieve the same output characteristic in the final image, you have to increase the physical aperture correlated to the smaller sensor. Bigger aperture = bigger glass = higher weight.

Let's do a quick calculation just for fun - a bit more precise this time (for equivalent lenses):