Full-frame vs Crop-sensor comparison : Depth-of-field & Perspective

When the differences between full-frame and crop-sensor cameras are discussed, there is an inevitable question about whether the crop sensor multiplies the focal length. Whether a 50mm lens on a crop-sensor acts like a 75mm lens (on a 1.5x crop sensor) or 80mm lens (on a 1.6x crop sensor).

The answers given on the photography forums are confusing – yes, the focal length effectively increases. No, it doesn’t. Two polar opposite answers. The discussion (which tend to devolve into arguments) are convincingly made for both sides. The reason is because the topic is a complex one … and therefore the answer is (kinda) complex too.

One argument goes along the lines that the crop sensor is just that, a crop. An enlargement. That nothing changes – you just get less of the scene. And that there is no “equivalent focal length” when you go to a crop sensor camera. But what really happens is more complex than that.

With this article, I want to help analyze what happens when you change lenses between a full-frame camera and a crop-sensor camera. And we’ll analyze whether there is actually an equivalency between certain focal lengths, when using a crop-sensor camera. In other words, whether your 50mm lens becomes “equivalent to” a 75mm or 80mm lens when used on a crop-sensor camera.

Since this article ended up being a long meandering discussion, I thought it best that we start with the final summary. Just to save the impatient people some work.

Summary:

Yes, a 50mm lens does indeed behave like an equivalent focal length of a 75mm lens (on a 1.5x crop sensor), or an 80mm lens (on a 1.6x crop sensor) for the same composition … however, the depth-of-field increases by about a stop.

Yes, a 100mm lens on a crop-sensor camera will give you the same perspective as a 150mm / 160mm lens (on a full-frame camera), if you don’t change position … however, the DoF increases.

But let’s discuss this with some images:

Notes on depth-of-field / DoF

Before we can go much further, we need to recap on Depth-of-Field

shallow depth of field is NOT the same as bokeh.

The image above certainly has nice, smooth bokeh. But it also has shallow-depth-of-field. Two things which seemingly are the same, but aren’t. So on that note, if you are one of those who say things like “give it some bokeh”, then you need to stop. It is meaningless.

You can not “zoom with your feet”, because if you change your position, your perspective changes.

With a zoom, the perspective does not change – you are merely enlarging the image. This distinction becomes an important point. If you put a 100mm lens on a full-frame body, and a 100mm lens on a crop body, and you want the same size for your subject in the frame, then you are going to have to move much further back to get the same image size with the crop sensor camera. And then your perspective has changed. And yes, then it will give you the same perspective as a 150mm / 160mm lens on a full-frame body when shooting at that new further distance.

A tutorial on Depth-of-Field

Our friends at Cambridge In Color have written one of the clearest explanations on DoF that I’ve ever read. Spend some time there. The concept of “circles of confusion” is an important one. It is on this that everything that you need to know about DoF, hinges upon. An important note there – DoF is defined via circles of confusion, which is specified for a certain print size, at specific distance.

The way that DoF is defined (via circles of confusion), means that viewing distance, and the size of the final image, affects how DoF is perceived. This then implies if you are comparing a 12 megapixel image and a 36 megapixel image, then you can’t judge the DoF of the image at 100% resolution. You are better off going to “full screen” on both those images, and comparing at an equal size. You have to “equalize” this for comparison, because if you view a 36 megapixel image at 100%, the DoF will seemingly be shallower than a sensor with lesser resolution.

DoF changes incrementally. In other words, the only point at which something is most definitely *in* focus, is the actual plane of focus. From there it is an incremental change in sharpness to the foreground and background. By the time you are using a small aperture then, the depth-of-field extends deeper into the background and foreground. Even then, at the extremities of that small-aperture DoF, there is no exact point at which we can immediately say the image flips from sharp to un-sharp.

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Figuring out a reasonable comparison method:

To take this tutorial away from the armchair to an actual shoot with comparison examples, the ideal would’ve been to have a full-frame camera that has exactly the same resolution as the crop-sensor camera. Just to keep things simple. And I’d have to have two lenses which are exact 1.5x versions of each other. For example 50mm and 75mm. Or 100mm and 150mm. Just to keep things even.

This doesn’t exist (that I know of), I tried a few ways of reasonably comparing the full-frame sensor and crop-sensor effect.

Then I had this brainwave – I could use these two Nikon lenses:

– Nikon 85mm f/1.4 lens (affiliate) on a full-frame camera,

– Nikon 58mm f/1.4 lens (affiliate) on a 1.5x crop sensor.

The 58mm focal length effectively acts like an 87mm lens on a 1.5x crop sensor camera. Close enough!

One obstacle here is that the two lenses display different optical qualities. For example, a harsh bokeh might make the background look sharper or crisper than a lens with smooth bokeh. And this might affect our perception of the DoF!

Then, if I use the 85mm lens on the Nikon D4 (affiliate) which has 16,16 megapixels,

and the 58mm lens on the Nikon D810 (affiliate) in crop mode (15,36 megapixels),

then I have two cameras which give me very similar resolution.

Two things which are affected when switching a lens between a full-frame camera body and a crop-sensor body, are:

– angle of view, and

– depth-of-field.

And if you move your position, your perspective changes too. That makes a direct comparison difficult too.

I used these lenses and cameras in two different ways to visually try and explain:

1. D810 at full-frame (FX) and then set to 1.5x crop (DX crop), which effectively enlarges the image, but at a huge reduction in resolution.

2. Using a D4 (at 16 megapxiels), against a D810 (36 megapixels) at 1.5x crop, i.e., 15,36 megapixels, with “equivalent” lenses.

And then, finally, we’ll have a look at what a Depth-of-Field Calculator says, and whether this corroborates what we see.

1. Full-frame vs 1.5x crop, using a single camera and “equivalent” lenses

Both these images were shot with the Nikon D810 (affiliate), but with the two different lenses. I had the camera on a tripod, and didn’t move it at all. I just changed lenses, and the crop in the camera.

Click on the image to bring up larger versions.

On the left, the full-frame (36 megapixel) image with the Nikon 85mm f/1.4 lens.

On the right, the 1.5x crop image (15,4 megapixels) with the Nikon 58mm f/1.4 lens.

Both lenses were used at f/2.8

Notice how the FF image on the left has shallower depth-of-field in the background. The city appears more blurred than the image on the right.

Keep in mind that the 58mm lens’ bokeh might have had a slight effect here, if the lens’ bokeh itself is less smooth. However, the background does look sharper.

I did have to really reduce the 36 megapixel image on the left to bring it to the same size as the lower resolution image on the right.

Just to give you an idea, here is how the actual sizes would’ve compared, if I made this composite’s size the same as the height of the full-resolution image:

The different sizes here are largely not relevant. Remember, the circles of confusion is defined for a specific print size when viewed at a certain distance. So if we bring the two images to the same size, then we see the way the DoF actually appears in the photo.

Now, if this does not seem all that convincing since we had to play with the image size, let’s look at how the DoF appears when used with two cameras with similar resolution:

2. Full-frame camera vs 1.5x crop camera, using “equivalent” lenses

This is where I used two cameras with nearly the same resolution, and two lenses who were very nearly “equivalent” to each other for the sensor size.

Top image: the Nikon 85mm f/1.4 lens on the Nikon D4. The D4 has 16,2 megapixels.

Second image: the Nikon 58mm f/1.4 lens which gives an equivalent of 87mm on the Nikon D810 when it is set to 1.5x crop in the camera. The D810 then has 15,4 megapixels.

I wanted to use the cameras on a tripod, but the cameras are at different height, so this made the tripod very clumsy when I tried to match the exact framing and composition. In the end, I hand-held the cameras, and tried for compositions as close as I could. I tried to keep our model, Olive, the same size in the frame. So there is some difference to the images in that sense – the perspective is slightly different – yet, the DoF is noticeably shallower in the full-frame image.

Now, after all this, you may still not be entirely convinced that there is an “equivalency” in the focal lengths if you simply multiply the focal lengths by the crop factor. There were uncertainties perhaps in both the ways I set these comparisons. You might still wonder what happened to the argument that a crop sensor just gives you an “enlargement” of the full-frame image.

So let’s go back to the “armchair method”, and look at what a Depth-of-Field calculator says.

3. Depth-of-field calculator

For these, I used the Simple DoF Calculator app on my iPhone. I like it. But there are others available too. In any case, you should have a DoF calculator on your phone. It just makes sense.

For the same focused distance, 12 ft, the crop-sensor (left) has more DoF than the FF camera (right), with an equivalent focal length.

Different focal length, same behavior. Shooting from the same spot, the full-frame camera gives us less DoF than the crop sensor, for an “equivalent” focal length.

Going slightly wider than a stop, we get about the same DoF now, for the same subject distance.

This is an exercise that you can play with on your own, using DoF tables, or a DoF calculator.

It works this way every time – the full-frame camera gives us shallower DoF, for the same field of view, than the crop-sensor camera does.

Summary

We bring it right back to where we started:

Yes, a 50mm lens does indeed behaves like an equivalent focal length of a 75mm lens (on a 1.5x crop sensor), or an 80mm lens (on a 1.6x crop sensor) … but, the depth-of-field increases by about a stop.

Yes, a 100mm lens will give you the same perspective as a 150mm / 160mm lens, if you don’t change position … but, the DoF increases.

So, yes, a 50mm does (kinda) act like a 75mm / 80mm when used on a crop-sensor camera. The focal length is effectively increased on a crop-sensor camera. But at the loss of the shallow DoF that a larger sensor gives you.

How important that change in depth-of-field is to you, is something you need to decide for yourself. For me, I like that extra control that shallow DoF gives me in creating a specific look to photographs. While the change in DoF might seem incremental when compared in a final image, it is an element that I do want to be available to me – the shallower depth-of-field which full-frame cameras allow.

Related links

A little bit of homework #1 – The armchair version

Let’s change it around now. What would the effect be on:

– the field of view

– the composition of your image

– the depth-of-field

if you used the same lens on a FF camera and a crop-sensor camera, but you moved your position to keep your subject the same size in your viewfinder?

A little bit of homework # 2 – Practical exercise

Better yet, do it as a practical exercise:

Shoot the same portrait of someone (who doesn’t move),

using a FF sensor camera, and then a crop-sensor camera,

while keeping to the same framing of your subject.

and also keeping the same perspective. (i.e., You can’t move.)

Now compare the DoF between the two images, for the same resolution.

Let us know what you find.

Addendum & clarifiction – as a reply to many of the comments

I do agree about the focal length remaining the same. As mentioned several times here, a 100mm lens remains a 100mm lens. It’s physics.

Anyone who follows this website will know I’m also a big supporter of using correct terminology. It helps with clarity if the same things are named the same things, and not obscured by everyone making up their own phrases.

The counter-point to this – and the main reason I wrote this article – is that it is easier to understand what happens with the FF / crop switcheroo, if you think in terms of the effective focal length changing. It really is, even if this makes you grind your teeth.

So while we could remain sticklers for the mathematics of it all – e.g., a 100mm lens remaining a 100mm lens – it is easier to understand what happens if we think in terms of the field of view changing = effective focal length being different.

If we remain in one spot, then using the same focal length lens (say a 50mm lens), on the FF camera and on a crop-sensor camera, makes little sense to a portrait photographer. You just get a crop version. This of course makes sport photographers and wildlife photographers very happy.

Now if we think of the difference in using a FF camera and a crop-sensor camera, and that this effectively brings in that 50mm / 75mm “change”, and we frame our subjects the same way on the FF camera, and with a crop-sensor camera … then there is this effect as described in the article. Call it a change in field of view … call it a change in effective focal length … there is something happening here that is more than just a crop of the image.

I honestly think that thinking of this as the focal length effectively changing on you, is more meaningful in a practical shooting sense, than thinking purely in terms of the mathematics of the optics.

I hope this makes my intent with this article more clear.