A beginner's guide to "is equal to" vs "is equivalent to".

[David Pavlich]

The funny thing is that after all of that typing, my guess is that whether a poster uses 'equal' or 'equivalent', the reader would know exactly what a poster is referencing because there is context. Most of us have enough of a thought process to figure out what the poster is attempting to convey.

It's like when someone uses 'bokeh'. 99.9% of readers know what the poster is discussing. Only those that allow their 'intellect' to get in the way worry about it.

This is the internet, not Oxford.

David

 

[Iliah Borg]

99.9% of readers know what the poster is discussing.

"70% of all statistics are made up on the spot by 64% of people that produce false statistics 54% of the time they produce them."

More seriously, https://www.thebereancall.org/node/8045

 

[BSiler]

Well said. I would add that even at Oxford, I doubt that conversations so quickly and predictably devolve into the relentless caviling that is so common here.

 

[981S]

Concise definitions of the terms "equal" and "equivalent" would be a good start rather that trying to show the difference by example. Most good technical writing starts with a clear definition of terms before diving first into examples.

Sure. In the context of my post, "equal" means the same nominal value on the lens and/or camera whereas the term "equivalent" means the same effect in the photo.

Weak definitions, if even that. That is why your writings draw so much controversy.

Agreed, very weak. "Equal settings" and "Equal effect" might be simpler and clearer.

Even "equal settings" is unclear. The question is what aspects do you want "equal"?

Consider a full frame body set to a 24° angle of view with a 25mm aperture diameter.

On a 2X crop body, which of the following would be "the same settings"?

1. 24° angle of view and 25mm aperture diameter
2. 24° angle of view 12.5mm aperture diameter
3. 12° angle of view 25mm aperture diameter

====

Another way of describing these settings are :

a full frame with a 100mm lens at f/4 compared to a 2X crop body with

1. 50mm lens at f/2
2. 50mm lens at f/4
3. 100mm lens at f/4

====

We also get into issues of whether the resulting prints should be of "equal size" or "equal magnification" (ratio of print size to sensor size).

If we assume that the goal is to view the image from the entire sensor at the same size, and it is about getting the same composition, perspective, DOF, brightness and noise.

In that case the answer would be 50mm at f2. But you need to bring ISO in the picture.

The question is one of terminology. what does it mean to say "equal settings"? (in the context of "equal settings" vs. "equal effect") Is it reasonable to say that two cameras, both at a 24° angle of view and a 25mm aperture diameter, are at "equal settings".

Or would "equal settings" require the same focal length on both cameras?

Ah ok. I think it is clear that the settings are different, but the effect is the same after both images are amplified to the same size.

 

[kiwi2]

You're wasting your effort. Mr. Llama doesn't believe in a spherical earth...eh...equivalency.

Oh please.

So anybody that doesn't swallow hook line and sinker all of the nonsense the self appointed experts spout in these forums must be a flat-earther...???

 

[PhotoFactor]

Ah, a new equivalency thread.

 

[stevo23]

You're wasting your effort. Mr. Llama doesn't believe in a spherical earth...eh...equivalency.

Oh please.

So anybody that doesn't swallow hook line and sinker all of the nonsense the self

appointed experts spout in these forums must be a flat-earther...???

What does any of that have to do with the subject at hand? This is about equivalence. You don't "believe in" equivalence?

I'm saying that not believing in equivalence, which can be tested and proven, is not very dignified. It's like being a flat earther - foolishness in the face of proof.

 

[David Pavlich]

99.9% of readers know what the poster is discussing.

"70% of all statistics are made up on the spot by 64% of people that produce false statistics 54% of the time they produce them."

More seriously, https://www.thebereancall.org/node/8045

True, but for DPR, most of the members that are participating know what a poster discussing APS-C to FF, etc, know what that poster is talking about.

But to stop any additional thread drift, I reduce my '99.9%' to 83%.

David

 

[mamallama]

You're wasting your effort. Mr. Llama doesn't believe in a spherical earth...eh...equivalency.

Oh please.

So anybody that doesn't swallow hook line and sinker all of the nonsense the self

appointed experts spout in these forums must be a flat-earther...???

What does any of that have to do with the subject at hand? This is about equivalence. You don't "believe in" equivalence?

I'm saying that not believing in equivalence, which can be tested and proven, is not very dignified. It's like being a flat earther - foolishness in the face of proof.

What is your definition of equivalence that can be tested and proved. Is your proof mathematical or intuitive?

 

[stevo23]

You're wasting your effort. Mr. Llama doesn't believe in a spherical earth...eh...equivalency.

Oh please.

So anybody that doesn't swallow hook line and sinker all of the nonsense the self

appointed experts spout in these forums must be a flat-earther...???

What does any of that have to do with the subject at hand? This is about equivalence. You don't "believe in" equivalence?

I'm saying that not believing in equivalence, which can be tested and proven, is not very dignified. It's like being a flat earther - foolishness in the face of proof.

What is your definition of equivalence that can be tested and proved. Is your proof mathematical or intuitive?

So you're saying you don't buy it, is that it? I seem to recall that you scoff at these explanations.

 

[User7502529587]

A recent thread has spawned some confusion on the use of the word "equals" with respect to focal length and relative aperture. This often causes confusion for people when using FF lenses on APS-C cameras, so I thought it would be helpful to discuss this bit of terminology.

First off we have to discuss the "crop factor". APS-C has a "crop factor" relative to FF of 1.6 for Canon and 1.5 for everyone else. The effect of the crop factor is the same as if you used the same lens and settings on a FF camera and cropped out the middle 1.5x (or 1.6x) of the photo.

However, the crop factor can also be described in terms of what lens and settings you would use on FF to get the same results. The way in which you do this is to multiply the focal length and relative aperture of the lens by the crop factor. For example, a lens at 85mm f/2.8 on Canon APS-C (crop factor = 1.6) will be *equivalent to* (as opposed to "equal to") a lens at 136mm f/4.5 on FF.

What this means is that while the lens is actually at 85mm f/2.8, the *effect* of those settings on Canon APS-C, in terms of the appearance of the resulting photo, is the same as if you had used 136mm f/4.5 on FF from the same position with the same exposure time (the equivalent ISO setting, for the same lightness in the photo, will change by the square of the crop factor, in this example, 2.5x). The lens itself has not changed, but the *effect* of the lens settings has changed, relative to the effect on FF.

So, a full equivalence statement between Canon APS-C (1.6x) and FF would be something like: 85mm f/2.8 1/400 ISO 800 is *equivalent to* 136mm f/4.5 1/400 ISO 2000 on FF. The actual lens settings remain 85mm f/2.8 1/400 ISO 800, but had you taken a photo of the same scene from the same position with FF at 136mm f/4.5 1/400 ISO 2000, the perspective, framing, DOF, motion blur, lightness, and noise* would all be the same.

This is true whether or not the lens was specifically designed for FF or APS-C. For example, if you used a 50 / 1.4 lens designed for FF or a 50 / 1.4 lens designed for APS-C, nothing changes. If you put a 50 / 1.4 designed for FF or a 50 / 1.4 designed for APS-C on an APS-C camera, the effect of both the focal length and relative aperture remain unchanged. The equivalence is only for comparing the effect of a lens used on one format to the effect of a lens on another format.

I hope this helps with regards to any confusion between "is equal to" and "is equivalent to"!

*For equivalent settings, the same total amount of light will be projected on the sensor which will result in the same noise *if* the sensors record the same proportion of that light and add in the same amount of electronic noise (the additional noise from the sensor and supporting hardware).

Hi

There is something that i can't get my mind around it

The equivalent in lens Focal lengths and apertures are clear to me!

Also the Shutter Speed is crystal clear to me

now what exactly happens to iso?

Isn't that supposed to multiple by 1.6?

800*1.6=1280

Why here"So, a full equivalence statement between Canon APS-C (1.6x) and FF would be something like: 85mm f/2.8 1/400 ISO 800 is *equivalent to* 136mm f/4.5 1/400 ISO 2000 on FF" it gets up to 2000?(i know closest ISO to 1280 is 1600(i guess and pretty sure we wont downscale)

So a little explanation on this one would be good!

thnx for good article!

--
I FIGHT FOR USERS

 

[mamallama]

You're wasting your effort. Mr. Llama doesn't believe in a spherical earth...eh...equivalency.

Oh please.

So anybody that doesn't swallow hook line and sinker all of the nonsense the self

appointed experts spout in these forums must be a flat-earther...???

What does any of that have to do with the subject at hand? This is about equivalence. You don't "believe in" equivalence?

I'm saying that not believing in equivalence, which can be tested and proven, is not very dignified. It's like being a flat earther - foolishness in the face of proof.

What is your definition of equivalence that can be tested and proved. Is your proof mathematical or intuitive?

So you're saying you don't buy it, is that it? I seem to recall that you scoff at these explanations.

I don't know what it is that you think I'm not buying.

I am asking you about your statement that equivalence can be tested and proved. What is proved and where is it proved?

 

[981S]

Nice write up.

Thanks!

There is another dimension to this equivalence thing if we are also concerned with image quality: If the lens needs to project the same image on the smaller APS-C surface it requires a better lens to produce equal image quality.

Indeed. There's also the matter of pixel count and sensor characteristics, but both are beyond the scope of what I intended for this thread.

Yes, that complicates things further. One thing to mention is cropping.

If the image needs to be cropped by more than the sensor crop factor on the FF because focal length is not long enough, then all of a sudden a 300mm f4 on APS-C is equivalent to the same 300mm f4 on a FF.

Equivalence ultimately depends on sensor area used; not the the size of the sensor. The part of the sensor left unused or cropped away is exactly as if it was never there. If you photograph someone's face, for example, the sensor area outside of that face projected on it has no use to the capture of the face; there is no voodoo between captured subjects and the pixels or sensor area that do not render it. The face is exactly the same as if the rest of the sensor outside the face was never there; a small, face-shaped sensor.

Yes, and the point I am making is that when one says that this lens on one sensor is equivalent to that lens on another sensor, the implicit assumption is that the image from the entire sensor is used.

 

[stevo23]

You're wasting your effort. Mr. Llama doesn't believe in a spherical earth...eh...equivalency.

Oh please.

So anybody that doesn't swallow hook line and sinker all of the nonsense the self

appointed experts spout in these forums must be a flat-earther...???

What does any of that have to do with the subject at hand? This is about equivalence. You don't "believe in" equivalence?

I'm saying that not believing in equivalence, which can be tested and proven, is not very dignified. It's like being a flat earther - foolishness in the face of proof.

What is your definition of equivalence that can be tested and proved. Is your proof mathematical or intuitive?

So you're saying you don't buy it, is that it? I seem to recall that you scoff at these explanations.

I don't know what it is that you think I'm not buying.

You do think equivalency works?

I am asking you about your statement that equivalence can be tested and proved. What is proved and where is it proved?

You don't know?

 

[Great Bustard]

A recent thread has spawned some confusion on the use of the word "equals" with respect to focal length and relative aperture. This often causes confusion for people when using FF lenses on APS-C cameras, so I thought it would be helpful to discuss this bit of terminology.

First off we have to discuss the "crop factor". APS-C has a "crop factor" relative to FF of 1.6 for Canon and 1.5 for everyone else. The effect of the crop factor is the same as if you used the same lens and settings on a FF camera and cropped out the middle 1.5x (or 1.6x) of the photo.

However, the crop factor can also be described in terms of what lens and settings you would use on FF to get the same results. The way in which you do this is to multiply the focal length and relative aperture of the lens by the crop factor. For example, a lens at 85mm f/2.8 on Canon APS-C (crop factor = 1.6) will be *equivalent to* (as opposed to "equal to") a lens at 136mm f/4.5 on FF.

What this means is that while the lens is actually at 85mm f/2.8, the *effect* of those settings on Canon APS-C, in terms of the appearance of the resulting photo, is the same as if you had used 136mm f/4.5 on FF from the same position with the same exposure time (the equivalent ISO setting, for the same lightness in the photo, will change by the square of the crop factor, in this example, 2.5x). The lens itself has not changed, but the *effect* of the lens settings has changed, relative to the effect on FF.

So, a full equivalence statement between Canon APS-C (1.6x) and FF would be something like: 85mm f/2.8 1/400 ISO 800 is *equivalent to* 136mm f/4.5 1/400 ISO 2000 on FF. The actual lens settings remain 85mm f/2.8 1/400 ISO 800, but had you taken a photo of the same scene from the same position with FF at 136mm f/4.5 1/400 ISO 2000, the perspective, framing, DOF, motion blur, lightness, and noise* would all be the same.

This is true whether or not the lens was specifically designed for FF or APS-C. For example, if you used a 50 / 1.4 lens designed for FF or a 50 / 1.4 lens designed for APS-C, nothing changes. If you put a 50 / 1.4 designed for FF or a 50 / 1.4 designed for APS-C on an APS-C camera, the effect of both the focal length and relative aperture remain unchanged. The equivalence is only for comparing the effect of a lens used on one format to the effect of a lens on another format.

I hope this helps with regards to any confusion between "is equal to" and "is equivalent to"!

*For equivalent settings, the same total amount of light will be projected on the sensor which will result in the same noise *if* the sensors record the same proportion of that light and add in the same amount of electronic noise (the additional noise from the sensor and supporting hardware).

Hi

There is something that i can't get my mind around it

The equivalent in lens Focal lengths and apertures are clear to me!

Also the Shutter Speed is crystal clear to me

now what exactly happens to iso?

Isn't that supposed to multiple by 1.6?

800*1.6=1280

See the text highlighted in bold above.

Why here"So, a full equivalence statement between Canon APS-C (1.6x) and FF would be something like: 85mm f/2.8 1/400 ISO 800 is *equivalent to* 136mm f/4.5 1/400 ISO 2000 on FF" it gets up to 2000?(i know closest ISO to 1280 is 1600(i guess and pretty sure we wont downscale)

Again, the equivalent ISO setting gets multiplied by the *square* of the equivalence ratio (crop factor). An easy way to get that to make sense is to realize that if you double the relative aperture (say from f/2.8 to f/5.6), then you quadruple the ISO setting (say from ISO 400 to ISO 1600) to get the same lightness for a given scene and exposure time.

So a little explanation on this one would be good!

Hope that helps!

thnx for good article!

Thanks!

 

[mamallama]

You're wasting your effort. Mr. Llama doesn't believe in a spherical earth...eh...equivalency.

Oh please.

So anybody that doesn't swallow hook line and sinker all of the nonsense the self

appointed experts spout in these forums must be a flat-earther...???

What does any of that have to do with the subject at hand? This is about equivalence. You don't "believe in" equivalence?

I'm saying that not believing in equivalence, which can be tested and proven, is not very dignified. It's like being a flat earther - foolishness in the face of proof.

What is your definition of equivalence that can be tested and proved. Is your proof mathematical or intuitive?

So you're saying you don't buy it, is that it? I seem to recall that you scoff at these explanations.

I don't know what it is that you think I'm not buying.

You do think equivalency works?

According to Richard Butler, "Equivalence, at its most simple, is a way of comparing different formats (sensor sizes) on a common basis".

Of course that works. It is just a way of comparing different formats on a common basis.

How some of these comparisons are used to draw certain conclusions is what is debatable.

I am asking you about your statement that equivalence can be tested and proved. What is proved and where is it proved?

You don't know?

I don't know what you mean that equivalence has been tested and proved.

 

[User7502529587]

A recent thread has spawned some confusion on the use of the word "equals" with respect to focal length and relative aperture. This often causes confusion for people when using FF lenses on APS-C cameras, so I thought it would be helpful to discuss this bit of terminology.

First off we have to discuss the "crop factor". APS-C has a "crop factor" relative to FF of 1.6 for Canon and 1.5 for everyone else. The effect of the crop factor is the same as if you used the same lens and settings on a FF camera and cropped out the middle 1.5x (or 1.6x) of the photo.

However, the crop factor can also be described in terms of what lens and settings you would use on FF to get the same results. The way in which you do this is to multiply the focal length and relative aperture of the lens by the crop factor. For example, a lens at 85mm f/2.8 on Canon APS-C (crop factor = 1.6) will be *equivalent to* (as opposed to "equal to") a lens at 136mm f/4.5 on FF.

What this means is that while the lens is actually at 85mm f/2.8, the *effect* of those settings on Canon APS-C, in terms of the appearance of the resulting photo, is the same as if you had used 136mm f/4.5 on FF from the same position with the same exposure time (the equivalent ISO setting, for the same lightness in the photo, will change by the square of the crop factor, in this example, 2.5x). The lens itself has not changed, but the *effect* of the lens settings has changed, relative to the effect on FF.

So, a full equivalence statement between Canon APS-C (1.6x) and FF would be something like: 85mm f/2.8 1/400 ISO 800 is *equivalent to* 136mm f/4.5 1/400 ISO 2000 on FF. The actual lens settings remain 85mm f/2.8 1/400 ISO 800, but had you taken a photo of the same scene from the same position with FF at 136mm f/4.5 1/400 ISO 2000, the perspective, framing, DOF, motion blur, lightness, and noise* would all be the same.

This is true whether or not the lens was specifically designed for FF or APS-C. For example, if you used a 50 / 1.4 lens designed for FF or a 50 / 1.4 lens designed for APS-C, nothing changes. If you put a 50 / 1.4 designed for FF or a 50 / 1.4 designed for APS-C on an APS-C camera, the effect of both the focal length and relative aperture remain unchanged. The equivalence is only for comparing the effect of a lens used on one format to the effect of a lens on another format.

I hope this helps with regards to any confusion between "is equal to" and "is equivalent to"!

*For equivalent settings, the same total amount of light will be projected on the sensor which will result in the same noise *if* the sensors record the same proportion of that light and add in the same amount of electronic noise (the additional noise from the sensor and supporting hardware).

Hi

There is something that i can't get my mind around it

The equivalent in lens Focal lengths and apertures are clear to me!

Also the Shutter Speed is crystal clear to me

now what exactly happens to iso?

Isn't that supposed to multiple by 1.6?

800*1.6=1280

See the text highlighted in bold above.

Why here"So, a full equivalence statement between Canon APS-C (1.6x) and FF would be something like: 85mm f/2.8 1/400 ISO 800 is *equivalent to* 136mm f/4.5 1/400 ISO 2000 on FF" it gets up to 2000?(i know closest ISO to 1280 is 1600(i guess and pretty sure we wont downscale)

Again, the equivalent ISO setting gets multiplied by the *square* of the equivalence ratio (crop factor). An easy way to get that to make sense is to realize that if you double the relative aperture (say from f/2.8 to f/5.6), then you quadruple the ISO setting (say from ISO 400 to ISO 1600) to get the same lightness for a given scene and exposure time.

So a little explanation on this one would be good!

Hope that helps!

thnx for good article!

Thanks!

Oh i get it now
the iso difference is about 2 step!

thnx!

--
I FIGHT FOR USERS

 

[Michael Fryd]

...

Hi

There is something that i can't get my mind around it

The equivalent in lens Focal lengths and apertures are clear to me!

Also the Shutter Speed is crystal clear to me

now what exactly happens to iso?

Isn't that supposed to multiple by 1.6?

800*1.6=1280

Why here"So, a full equivalence statement between Canon APS-C (1.6x) and FF would be something like: 85mm f/2.8 1/400 ISO 800 is *equivalent to* 136mm f/4.5 1/400 ISO 2000 on FF" it gets up to 2000?(i know closest ISO to 1280 is 1600(i guess and pretty sure we wont downscale)

So a little explanation on this one would be good!

thnx for good article!

We can look at ISO from the perspective of the result.

Consider a full frame with a 100mm lens, f/4, 1/60 ISO 400 compared to a 2X crop body with a 50mm lens, f/2,. 1/60, ISO 100.

The sensor in the 2X crop body has 1/4 the area of the full frame. The crop body is getting four times (2 stops) the light per unit area as the full frame.

However both cameras are capturing the same number of photons per unit area of the final print. Therefore from the perspective of the resulting image, the two are capturing the same amount of light. From that perspective ISO 400 on the full frame produces the same result as ISO 100 on the 2X crop body.

It turns out that the biggest factor of image noise in low light photography is typically the noise inherent in the light itself (the "shot noise"). Shot noise is dependent on the light captured per unit area of the final image. From a Shot noise perspective ISO 400 on the full frame produces the same result as ISO 100 on the 2X crop body.

====

If your concern is the resulting image, what really matters is the number of photons captured. it doesn't make much difference if they are packed densely on a smaller sensor, or spread out on a larger sensor. A 2X crop body with an ISO 100 exposure captures the same number of photons as a full frame body with an ISO 400 exposure.

 

[Lee Jay]

I don't know what you mean that equivalence has been tested and proved.

It's just similar triangles, so of course it's tested and proven. Another way of thinking of it is the same as a teleconverter. Do you accept than the new equivalent focal length and equivalent f-stop when you add a teleconverter are the old focal length and old f-stop multiplied by the teleconverter magnification ratio? Assuming you do, you accept equivalence, because it's exactly the same thing, and for the same reason.

 

[Zed Man]

I don't know what you mean that equivalence has been tested and proved.

It's just similar triangles, so of course it's tested and proven. Another way of thinking of it is the same as a teleconverter. Do you accept than the new equivalent focal length and equivalent f-stop when you add a teleconverter are the old focal length and old f-stop multiplied by the teleconverter magnification ratio? Assuming you do, you accept equivalence, because it's exactly the same thing, and for the same reason.

Doing the math, we say 16:9 image A is "equivalent" to 1:1 image B. We say they have the same AoV.

But most with eyes and a brains look at A and B and says, no freakin' way are they the same!!

What they mean is, maybe they are "equivalent", but they look very different and are not equal. And they probably prefer one over the other.

To a lesser extent, this happens when comparing 3:2 and 4:3.