The concept of 'equivalence*1' is still somewhat controversial and not always clearly understood. We thought it was about time we explained - and demonstrated - what equivalence means and what it doesn't.

### What is equivalence?

Equivalence, at its most simple, is a way of comparing different formats (sensor sizes) on a common basis. This is already the way most lenses are talked about: it's quite common to say that a compact camera includes a '28-120mm lens' but the key and (often unspoken) word in that description is 'equivalent.' It's a simple way of describing the range of fields-of-view that the lens offers, cancelling out the effect of sensor size by using a common reference point.

A 100mm equivalent lens on a small-sensor camera will give the same framing and (because that means shooting from the same position) the same perspective as an actual 100mm lens does on a full frame camera, regardless of sensor size, because they are equivalent.

Camera Sensor
Format
Sensor
diagonal
Crop factor Focal length Diagonal Angle
of View *2
Canon EOS-1D X Full Frame (864mm2) 43.3mm 1 100mm 24.4deg
Olympus OM-D E-M5 Four Thirds (224mm2) 21.6mm 2 50mm 24.4deg

It's this logic that the idea of 'crop factors' is based on. The 'Four Thirds' sensor format has a diagonal very close to half that of a 'full frame' sized sensor. And, sure enough, if you calculate the angle-of-view of a 50mm lens on a system with a crop factor of 2, it's the same as for a full frame camera with a 100mm lens.

 Equivalence helps compare different lenses and cameras by using 35mm 'Full Frame' as a reference point. This doesn't mean that Full Frame is the best, or even the optimal format, it's just a reasonably well understood point of comparison.

However, it's not just focal lengths that can be thought of in equivalent terms. In our recent reviews of fixed-lens cameras, we've tended to include a chart showing 'equivalent' aperture values and how they change as you progress through the zoom range. In the rest of this article, we'll discuss and demonstrate how apertures and sensor sizes interact.

The reason we do this is because it's become quite common, for any given part of the market, to have to choose between cameras with different lenses and sensor sizes. This wasn't such a common problem in the film era since 35mm was the de facto standard. As such, most people didn't need to directly compare quality and characteristics across those different formats. 35mm was better than 110, medium format was better again and large format was still better. In the digital era, the significance of (and difference between) sensor sizes isn't always appreciated, not helped by a rather opaque naming system.

### Apertures and F-numbers

It turns out, the relationship between sensor size and aperture is very similar to that between focal length and sensor size. It's the physical size of the aperture that defines depth-of-field, not its F-number. Two lenses offering the same angle-of-view with 25mm diameter apertures will give the same depth-of-field of shot at the same shooting distance and when viewed at the same output size.

So, let's consider the effect of that 25mm aperture in the lenses we've been discussing. Both lenses give the same angle-of-view, so you're likely to shoot them with the same shooting distance - since that way you'll get the same framing in both photos.

Now think about what that means in terms of F-number (focal length/aperture diameter). The 25mm aperture in the 100mm lens would be considered to be f/4 (100mm/25mm), whereas the same-sized aperture in the Micro Four Thirds lens would be an f/2 (50mm/25mm). The table below shows the calculated depth-of-field for the two lenses, shot at the same working distance:

Camera Focal length Aperture diameter F-number Depth of field *3 Equiv.
F-number
Canon EOS-1D X 100mm 25mm f/4 Near 16.1m
Far 26.3m
Total 10.1m
f/4
Olympus OM-D E-M5 50mm 25mm f/2 Near 16.1m
Far 26.3m
Total 10.2m
f/4

As you can see, although the lenses are quite different, the 50mm f/2 lens is giving the same framing and the same depth-of-field as a 100mm f/4 lens is on Full Frame. As such, you can say that a 50mm f/2 for Micro Four Thirds is equivalent to a 100mm f/4 Full Frame lens in terms of both field-of-view and depth-of-field.

We don't expect you to take our word for this. Conveniently, it's become fashionable for manufacturers to produce 85mm equivalent, F1.2 lenses, which makes it relatively easy to show the ways in which they are, and aren't equivalent. We'll demonstrate this on the third page of this article.

*1. Not to be confused with 'Equivalents' - an influential series of abstract photographs by Alfred Stieglitz, and an approach to photography that they inspired.
*2. Calculated using TawbaWare's Angular Field of View calculator
*3. Calculated using DOF Master, with the lenses specified, focused to a distance of 20m