Focal length conversion for APS-C designed lenses

Lenses are fitted to cameras based on need. We are talking, angle of view, magnification, and light gathering ability, to name a few.

Now the camera, under most circumstances, projects a miniature image of the outside world onto the flat surface of a digital sensor or film. Only the central portion of the projected images is servable as image acuity and brilliance falls off with distance from center. The central good area is called the circle of good definition. The camera format is formed by masking the projected image.

For the full frame camera, this is a rectangle 24mm height by 36mm length diagonal measure 43.3mm. For the APS-c (advanced photo system – classic) 16mm height by 24mm length diagonal measure 28.8mm. Note—dividing the two diagonal measures thus 43.3 ÷ 28.8 = 1.5 this is the origin of the “magnification factor / crop factor). We use this method when we wish to relate behaviors of lenses when mounted on different camera formats. However, the crop factor is mainly of value two a gray-hair who has been using one of the formats for years and then switches to a smaller or larger format.

Now lenses are fitted to cameras based on the size of the image format. If we fit a lens with a focal length approximately equal to the diagonal measure of the format. Such a lash-up delivers a horizontal and angle of view of approximately 45°, and by tradition, considered the “normal focal length for that format. Let me add, the diagonal angle of view for these formats will be approximately 53°. It is this, likely useless information that is most likely published. Similar as to how TV sets are sold by their diagonal measure.

Translated, the full frame has a focal length that delivers a “normal” angle of view, it is approximately 45mm however by custom the focal length is generally rounded up to 50mm. The “normal for the APS-C, is typically rounded up to 30mm. Note 30 x 1.5 = 45. This math tells me that a 30mm on an APS-C will approximately equate to a 45mm mounted on a full frame.

We need a variety of focal lengths to satisfy our imaging needs. A wide-angle is generally 70% of “normal” or shorter. Thus for the full frame, it will be 35mm or shorter. For this APS-C, this works out to 20mm or shorter.

Telephoto is generally considered twice longer then “normal”. For the full frame 50mm x 2 = 100mm or longer. For the APS-C 30x 2 = 60mm or longer. None of these values are engraved in stone.

Historically, the APS-C was a film format of the 1990’s. It was a failed format, a hybrid between film and digital. The film had a transparent magnet coat that could record digital data and a chemical coat that recorded via being developed. We had high hopes for this system but it came too late, the digital era had dawned. The APS-C never came to blossomed.
 
What term (instead of "field of view") would I use to communicate that by putting on a 24mm lens, I'm getting a wider area in my picture vs a 50mm? Like for instance during shooting, I would say "Hey I want a wider __________ to get these clouds and foreground in the picture, so I'm gonna put on my 24mm lens"?
Context is king. If you're swapping lenses on the same body, obviously a shorter focal length will give you a wider FOV.
Assuming I were using a full frame body and not switching cameras, by going from 50mm to 24mm I would accurately say "I want a wider field of view for this shot, so I'm going to use a 24mm"?

Thank you for reminding me about the more extreme versions of focal length relating to different sensors with examples. Definitely helped me to more accurately grasp the connection of lens/body, and not think of lenses themselves having inherent properties like distortion or compression on their own. The 100mm being super wide on larger cameras is a great example.

I feel like I have a much better handle on everything from yours and others great responses, but I still feel unsure about the APS-C designed 16mm to full frame equivalent. I'm going to re-read these posts and hope that it sinks in better with time. If I were to post a picture taken with my 16mm APS-C designed lens with my APS-C camera, and put the info underneath, would I list it as 24mm or 16mm?

For example: Sony A6000, 1/250th, f8, ____mm
You'd say "16mm", because that what the lens is. "Designed for APS-C" just means the image circle created by the lens is smaller, it doesn't change the focal length.

If the viewer wants to know the equivalence to FF, let them do the math :-)
 
You'd say "16mm", because that what the lens is. "Designed for APS-C" just means the image circle created by the lens is smaller, it doesn't change the focal length.
That's what I figured in the first place, but the description below in the specs of the lens made me think that maybe the 16mm APSC lens on my APSC camera actually gives the field of view of 24mm, not of a 16mm lens.

"Wide-angle prime is designed for APS-C-format Sony E-mount mirrorless cameras and provides a 24mm equivalent focal length"

Thank you for clarifying!
 
You'd say "16mm", because that what the lens is. "Designed for APS-C" just means the image circle created by the lens is smaller, it doesn't change the focal length.
That's what I figured in the first place, but the description below in the specs of the lens made me think that maybe the 16mm APSC lens on my APSC camera actually gives the field of view of 24mm, not of a 16mm lens.
Well, it does. It's still a 16mm lens though, but the angle of view is "equivalent" to the angle of view of a 24mm lens on a FF camera.

If you want to tell someone the focal length of the lens you used, you would still say 16mm, NOT 24mm.
"Wide-angle prime is designed for APS-C-format Sony E-mount mirrorless cameras and provides a 24mm equivalent focal length"
Thank you for clarifying!
 
You'd say "16mm", because that what the lens is. "Designed for APS-C" just means the image circle created by the lens is smaller, it doesn't change the focal length.
That's what I figured in the first place, but the description below in the specs of the lens made me think that maybe the 16mm APSC lens on my APSC camera actually gives the field of view of 24mm, not of a 16mm lens.

"Wide-angle prime is designed for APS-C-format Sony E-mount mirrorless cameras and provides a 24mm equivalent focal length"

Thank you for clarifying!
Welcome to to the frustrating world of photography, where so much that is taught to beginners, intermediates, and enthusiasts, as well as most things written by camera marketing departments, is just plain wrong. 😜

The equivalency is in the field of view, not the focal length. It's poorly worded copy.
 
You'd say "16mm", because that what the lens is. "Designed for APS-C" just means the image circle created by the lens is smaller, it doesn't change the focal length.
That's what I figured in the first place, but the description below in the specs of the lens made me think that maybe the 16mm APSC lens on my APSC camera actually gives the field of view of 24mm, not of a 16mm lens.

"Wide-angle prime is designed for APS-C-format Sony E-mount mirrorless cameras and provides a 24mm equivalent focal length"

Thank you for clarifying!
Here's another example. I have a fuji x100f. The exif data lists it as a "f2.8, 1/160, 23mm" because it's a 23mm lens. However, 23mm is an odd choice for a focal length (usually it would be 24mm). The chose 23mm because on their crop sensor (1.5x), it gives a 34.5mm (or 35mm) equivalent, which is the exact focal length they wanted for that style of camera. If I put my 16-35mm on my full frame camera and framed the exact same scene with both cameras, I would shoot the fuji at its only focal length of 23mm, and I would have to shoot my full frame camera at 35mm to cover the exact same scene. The exif info would list 23mm and 35mm respectively. If I kept my 16-35mm/full frame combo in the same spot and zoomed back to 23mm, I would see much more around the scene (it would be a wider angle of view). Then the exif info on both with read 23mm, but the scene would look different because of the sensor size difference (the crop factor).

APS-C lenses will often be at odd/uncommon full frame focal lengths because they have the intention of replacing a full frame equivalent lens. Fuji lenses are a great example of this. Their 23mm lens is a 35mm equivalent, then they have a 56mm lens (instead of 50) to give you an 84mm equivalent to replicate the look of 85mm on full frame. Your 16mm APS-C lens is designed to replicate (the look of) a 24mm lens on a full frame camera.
 
The equivalency is in the field of view, not the focal length. It's poorly worded copy.
So when I take a picture with that 16mm APSC lens on my APSC camera, the picture will have the field of view of a 24mm lens on a full frame camera?



My understanding now is: even though its a 16mm lens, because of the APSC lens design and camera, I'm *essentially* getting the field of view of 24mm when I take a picture? The picture will have the field of view of what you'd expect from a 24mm lens, not a 16?
 
The equivalency is in the field of view, not the focal length. It's poorly worded copy.
So when I take a picture with that 16mm APSC lens on my APSC camera, the picture will have the field of view of a 24mm lens on a full frame camera?

My understanding now is: even though its a 16mm lens, because of the APSC lens design and camera, I'm *essentially* getting the field of view of 24mm when I take a picture? The picture will have the field of view of what you'd expect from a 24mm lens, not a 16?
Yes.
 
The equivalency is in the field of view, not the focal length. It's poorly worded copy.
So when I take a picture with that 16mm APSC lens on my APSC camera, the picture will have the field of view of a 24mm lens on a full frame camera?

My understanding now is: even though its a 16mm lens, because of the APSC lens design and camera, I'm *essentially* getting the field of view of 24mm when I take a picture? The picture will have the field of view of what you'd expect from a 24mm lens, not a 16?
After replying to this and continuing to read, I got to thinking. What does it matter? Really - my wife and I used APS-C for 10 years before going full frame. If APS-C is all you’ve ever shot - it just looks like what it looks like. If you need wider, get a wider lens. If you need a tighter view, get a longer lens.



16mm looks like it looks through your viewfinder. If that’s how you want to frame the scene, then take the picture. There really shouldn’t be a lot of mental fatigue about whether it’s really 16mm or what it would be if I was using a different camera.



It mattered back when experienced photographers were switching from years of 35mm film shooting and all affordable digital options were APS-C. They knew a look they wanted and which lens to get it. They had to do some equivalence just to get the same framing.



I only learned about the equivalence stuff when we switched to full frame this year. Helpful to know our 24-240 is wider at the wide end then our old 18-250 on our Rebel, but doesn’t have near the reach.



But if you’re only shooting one format and aren’t already used to another, I don’t know what it changes for you. I hope the above doesn’t read as hostile. It’s meant just for discussion.
 
The equivalency is in the field of view, not the focal length. It's poorly worded copy.
So when I take a picture with that 16mm APSC lens on my APSC camera, the picture will have the field of view of a 24mm lens on a full frame camera?
Correct, but not because it's an "APS-C lens", but because it's a 16mm lens on an APS-C camera. This is an important point - it doesn't matter if the lens was designed for APS-C or FF, it's still just a 16mm lens.
My understanding now is: even though its a 16mm lens, because of the APSC lens design and camera,
No, it has nothing to do with "APCS lens design", it has to do with the size of the APS-C sensor.
I'm *essentially* getting the field of view of 24mm when I take a picture?
Correct, if you're referring to using a 24mm lens on a FF camera.
The picture will have the field of view of what you'd expect from a 24mm lens, not a 16?
Again, if referring to a FF camera. As another poster commented, if all you ever use is an APS-C camera, then the angle of view will be what you expect from a 16mm lens on your camera.
 
The equivalency is in the field of view, not the focal length. It's poorly worded copy.
So when I take a picture with that 16mm APSC lens on my APSC camera, the picture will have the field of view of a 24mm lens on a full frame camera?

My understanding now is: even though its a 16mm lens, because of the APSC lens design and camera, I'm *essentially* getting the field of view of 24mm when I take a picture? The picture will have the field of view of what you'd expect from a 24mm lens, not a 16?
16mm looks like it looks through your viewfinder. If that’s how you want to frame the scene, then take the picture. There really shouldn’t be a lot of mental fatigue about whether it’s really 16mm or what it would be if I was using a different camera.
This ^^
It mattered back when experienced photographers were switching from years of 35mm film shooting and all affordable digital options were APS-C. They knew a look they wanted and which lens to get it. They had to do some equivalence just to get the same framing.
Exactly. Since I started long ago with 35mm film, knowing this was useful when I started shooting APS-C. For many others who have chosen APS-C (or m34) and plan to stick with it, it really doesn't matter.
 
You'd say "16mm", because that what the lens is. "Designed for APS-C" just means the image circle created by the lens is smaller, it doesn't change the focal length.
That's what I figured in the first place, but the description below in the specs of the lens made me think that maybe the 16mm APSC lens on my APSC camera actually gives the field of view of 24mm, not of a 16mm lens.

"Wide-angle prime is designed for APS-C-format Sony E-mount mirrorless cameras and provides a 24mm equivalent focal length"

Thank you for clarifying!
Welcome to to the frustrating world of photography, where so much that is taught to beginners, intermediates, and enthusiasts, as well as most things written by camera marketing departments, is just plain wrong. 😜

The equivalency is in the field of view, not the focal length. It's poorly worded copy.
Completely agree.
 
What term (instead of "field of view") would I use to communicate that by putting on a 24mm lens, I'm getting a wider area in my picture vs a 50mm? Like for instance during shooting, I would say "Hey I want a wider __________ to get these clouds and foreground in the picture, so I'm gonna put on my 24mm lens"?
Context is king. If you're swapping lenses on the same body, obviously a shorter focal length will give you a wider FOV.
Assuming I were using a full frame body and not switching cameras, by going from 50mm to 24mm I would accurately say "I want a wider field of view for this shot, so I'm going to use a 24mm"?

Thank you for reminding me about the more extreme versions of focal length relating to different sensors with examples. Definitely helped me to more accurately grasp the connection of lens/body, and not think of lenses themselves having inherent properties like distortion or compression on their own. The 100mm being super wide on larger cameras is a great example.

I feel like I have a much better handle on everything from yours and others great responses, but I still feel unsure about the APS-C designed 16mm to full frame equivalent. I'm going to re-read these posts and hope that it sinks in better with time. If I were to post a picture taken with my 16mm APS-C designed lens with my APS-C camera, and put the info underneath, would I list it as 24mm or 16mm?

For example: Sony A6000, 1/250th, f8, ____mm
16mm

You really are making heavy going of this most simple concept. It's been repeated for you time and time again.
 
The equivalency is in the field of view, not the focal length. It's poorly worded copy.
So when I take a picture with that 16mm APSC lens on my APSC camera, the picture will have the field of view of a 24mm lens on a full frame camera?
the above is reasonably stated, but the lens being designed for APS-C is not relevant.
My understanding now is: even though its a 16mm lens, because of the APSC lens design and camera, I'm **essentially** getting the field of view of 24mm when I take a picture? The picture will have the field of view of what you'd expect from a 24mm lens, not a 16?
I’m sorry, it’s like you haven’t read anything anyone in this thread has written. You’re back to square one, thinking there’s a magical field of view inherent to the 24mm focal length. I give up. Sorry I couldn’t explain it better.

Edit: hopefully this helps you visualize what’s going on:
 
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I've got a question regarding focal length conversion of lens to/from APS-C sensors:

Full frame lens to APS-C: 1.5(ish) X focal length

I get that since we're taking a larger area, and cropping it down by (theoretically) making the focal length of the lens longer, to bring down to the smaller sensor size of APS-C cameras
That's not a change of focal length, per se. It is an inverted description of the angle of view, using the angle of view on a FF sensor as the point of reference. Angle of view is not a focal length; angle of view is always a combination of focal length, lens distortion, and sensor size.

All that the 1.5 really means is that the angle of view with that lens is about 0.667x with the DX sensor as with an FX sensor. There is no 1.5x magnification of any kind, and nothing gained in detail because of the "crop factor"; any increase in detail would be due to higher pixel density than a FF camera; not the "crop".
My question is: with a lens *designed for APS-C* with a 16mm focal length, why is it listed as 24mm full frame (aka 35mm) equivalent?
The only time I see "FF equivalent" focal lengths printed on a lens or camera is with fixed-lens cameras, and they usually have both the actual focal length, and a FF equivalent. Usually the real focal length is on the front of the lens, and perhaps the "equivalent" focal length is on the barrel, or in the display. I think that real focal lengths should be the main number presented, and FF equivalent focal lengths should only be there as an extra aid to show how wide or narrow the angle of view will be, using FF as a standard. It would be very confusing if an APS-C camera had two sets of lenses available; ones multiplied by 1.5, and ones not multiplied. One scale is necessary to keep things straight between lenses. If you only owned an APS-C camera, you might not even know or remember that some of your lenses were designed for FF cameras.
This seems backward to me since if it were 24mm on full frame, shouldn't it be about 36mm on APS-C? I understand the conversion when going from bigger to smaller (full frame to APS-C), but I don't get why an APS-C 16mm lens would be a 24mm equivalent on a full frame (smaller to bigger).
Did you write something backwards? I have never heard that statement before, and it doesn't make any sense, especially since you did not say if your "APS-C 16mm lens" refers to how lenses are actually marked, or how you would like to mark them.

Anyway, there is no such thing an APS-C 16mm lens; there can be a 16mm lens designed for APS-C, to optimize optical character in the smaller sensor area, or make the lens smaller or lighter, but it is still just plain 16mm, as far as focal length is concerned. If you successfully mounted it on a FF camera, it would just fail to put light into the corners of the sensor or fail to have decent optical quality going into the corners, but the magnification in the center of the frame is the same as with the APS-C camera, and the FF image could crop away the low quality outer areas and be the same as with an APS-C sensor.
I'm assuming that when a lens is designed specifically for APS-C, the listed focal length in the title is the exact length when put on an APS-C camera, without the need for any conversion multiplication?
Not at all. It is the real focal length, which is not the inverse of a specific angle of view when combined with a sensor. Why would you want some lenses marked 16mm to give an angle of view about 1.5x as wide as others that are also marked 16mm? You're looking to add confusion, I think.
 
You'd say "16mm", because that what the lens is. "Designed for APS-C" just means the image circle created by the lens is smaller, it doesn't change the focal length.
That's what I figured in the first place, but the description below in the specs of the lens made me think that maybe the 16mm APSC lens on my APSC camera actually gives the field of view of 24mm, not of a 16mm lens.

"Wide-angle prime is designed for APS-C-format Sony E-mount mirrorless cameras and provides a 24mm equivalent focal length"

Thank you for clarifying!
Welcome to to the frustrating world of photography, where so much that is taught to beginners, intermediates, and enthusiasts, as well as most things written by camera marketing departments, is just plain wrong. 😜

The equivalency is in the field of view, not the focal length. It's poorly worded copy.
More precisely, in the FOV we have equality, and in the FL, we have equivalency.
 
I've got a question regarding focal length conversion of lens to/from APS-C sensors:

Full frame lens to APS-C: 1.5(ish) X focal length

I get that since we're taking a larger area, and cropping it down by (theoretically) making the focal length of the lens longer, to bring down to the smaller sensor size of APS-C cameras

My question is: with a lens *designed for APS-C* with a 16mm focal length, why is it listed as 24mm full frame (aka 35mm) equivalent? This seems backward to me since if it were 24mm on full frame, shouldn't it be about 36mm on APS-C? I understand the conversion when going from bigger to smaller (full frame to APS-C), but I don't get why an APS-C 16mm lens would be a 24mm equivalent on a full frame (smaller to bigger).

I'm assuming that when a lens is designed specifically for APS-C, the listed focal length in the title is the exact length when put on an APS-C camera, without the need for any conversion multiplication?
Summary:

Focal length alone does not tell us the angle of view.

Focal length is a physical property of the lens. A "50 mm lens" always has a focal length of 50mm, no matter what camera it is mounted on.

Angle of view is determined by the combination of focal length and sensor size.

When mounted on the same camera, A 50 mm lens designed for an APS-C camera yields the same angle of view as a 50 mm lens designed for a full frame camera.

Angle of view is sometimes described in units of "Focal length needed on a traditional 35mm Film SLR". For instance, a 24 mm lens on a 1.5X crop body results in about a 60° angle of view. This is sometimes described as "36 mm equivalent" or "36 mm effective" because on a traditional 35mm film SLR you would need a 36mm lens for about a 60° angle of view.
 
I've got a question regarding focal length conversion of lens to/from APS-C sensors:

Full frame lens to APS-C: 1.5(ish) X focal length

I get that since we're taking a larger area, and cropping it down by (theoretically) making the focal length of the lens longer, to bring down to the smaller sensor size of APS-C cameras

My question is: with a lens *designed for APS-C* with a 16mm focal length, why is it listed as 24mm full frame (aka 35mm) equivalent? This seems backward to me since if it were 24mm on full frame, shouldn't it be about 36mm on APS-C? I understand the conversion when going from bigger to smaller (full frame to APS-C), but I don't get why an APS-C 16mm lens would be a 24mm equivalent on a full frame (smaller to bigger).

I'm assuming that when a lens is designed specifically for APS-C, the listed focal length in the title is the exact length when put on an APS-C camera, without the need for any conversion multiplication?
Summary:

Focal length alone does not tell us the angle of view.

Focal length is a physical property of the lens. A "50 mm lens" always has a focal length of 50mm, no matter what camera it is mounted on.

Angle of view is determined by the combination of focal length and sensor size.

When mounted on the same camera, A 50 mm lens designed for an APS-C camera yields the same angle of view as a 50 mm lens designed for a full frame camera.

Angle of view is sometimes described in units of "Focal length needed on a traditional 35mm Film SLR". For instance, a 24 mm lens on a 1.5X crop body results in about a 60° angle of view. This is sometimes described as "36 mm equivalent" or "36 mm effective" because on a traditional 35mm film SLR you would need a 36mm lens for about a 60° angle of view.
It might cause less confusion to just use descriptive terms, like 'normal', 'ultra-wide', 'moderate telephoto', etc.
 
Summary:

Focal length alone does not tell us the angle of view.

Focal length is a physical property of the lens. A "50 mm lens" always has a focal length of 50mm, no matter what camera it is mounted on.

Angle of view is determined by the combination of focal length and sensor size.

When mounted on the same camera, A 50 mm lens designed for an APS-C camera yields the same angle of view as a 50 mm lens designed for a full frame camera.

Angle of view is sometimes described in units of "Focal length needed on a traditional 35mm Film SLR". For instance, a 24 mm lens on a 1.5X crop body results in about a 60° angle of view. This is sometimes described as "36 mm equivalent" or "36 mm effective" because on a traditional 35mm film SLR you would need a 36mm lens for about a 60° angle of view.
It might cause less confusion to just use descriptive terms, like 'normal', 'ultra-wide', 'moderate telephoto', etc.
I'm a fan of specifying angle of view in degrees rather than the corresponding focal length needed on a traditional 35mm film SLR. But then, very few people listen to me.

I do agree that names like 'normal', 'ultra-wide', 'moderate telephoto', etc. are useful for general classification of angles of view.
 
You'd say "16mm", because that what the lens is. "Designed for APS-C" just means the image circle created by the lens is smaller, it doesn't change the focal length.
That's what I figured in the first place, but the description below in the specs of the lens made me think that maybe the 16mm APSC lens on my APSC camera actually gives the field of view of 24mm, not of a 16mm lens.

"Wide-angle prime is designed for APS-C-format Sony E-mount mirrorless cameras and provides a 24mm equivalent focal length"

Thank you for clarifying!
Welcome to to the frustrating world of photography, where so much that is taught to beginners, intermediates, and enthusiasts, as well as most things written by camera marketing departments, is just plain wrong. 😜

The equivalency is in the field of view, not the focal length. It's poorly worded copy.
More precisely, in the FOV we have equality, and in the FL, we have equivalency.
Thank you, I see the nuance there.

But as an aside, does the term FL equivalency carry any additional useful meaning beyond implying FOV equality?

If not, it seems that the term FL equivalency just causes confusion, and the slippery slope of language laziness* leads people to drop the term equivalency and begin to declare their FF lens has a genuine new focal length when mounted on an APS-C camera.

* = I'm guilty of it too; see why you responded to me in the first place. Requires constant vigilance!
 
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