# Math for comparing APS-C to full frame?

Started Oct 15, 2013 | Discussions
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 Math for comparing APS-C to full frame? Oct 15, 2013

Hi all, I understand that a full frame sensor has a x1 crop factor, compared to x1.5 for APSC.

So, for example, a 24mm lens on APSC is roughly the same as a 36mm on full frame.

My question: is there a similar conversion factor for the aperture?

For example, is f2.8 on a 36mm full frame the same as f2.8 on 24mm APSC?

Thanks!

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 Re: Math for comparing APS-C to full frame? In reply to turnstyle, Oct 15, 2013

It's the same 1.5 conversion so F2.8 on APS-C is equivalent to F4.2 on full frame.

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 Re: Math for comparing APS-C to full frame? In reply to turnstyle, Oct 15, 2013

turnstyle wrote:

Hi all, I understand that a full frame sensor has a x1 crop factor, compared to x1.5 for APSC.

So, for example, a 24mm lens on APSC is roughly the same as a 36mm on full frame.

My question: is there a similar conversion factor for the aperture?

For example, is f2.8 on a 36mm full frame the same as f2.8 on 24mm APSC?

There is, but you have to be aware of when to use it.

24/2 on APS-C has the same DOF as 35/2.8 (close enough since there are no 35/3 lenses) on FF.

24/2 exposes with the same light density as 35/2.  But because the FF sensor is larger, 24/2 on APS-C captures are much light over the sensor as 35/2.8 on FF.  This affects signal:noise ratio and is basically another way of saying that you can shoot FF at a higher ISO.  (You'd have to shoot the 35/2.8 at a higher ISO than the 24/2 to get the same image brightness).

Whether you care to make those conversions, either for depth of field or for a ballpark idea of low light capability is entirely up to you.

In my opinion, it's pretty reasonable to think of the new NEX with 35/2.8 as roughly equivalent to an APS-C NEX with 24/1.8.  One sensor may outperform another this year or next; that's not worth worrying about IMO.  Practically, I don't think the APS-C combo does anything the FF combo doesn't.

- Dennis

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 Re: Math for comparing APS-C to full frame? In reply to Dennis, Oct 15, 2013

Dennis wrote:

turnstyle wrote:

Hi all, I understand that a full frame sensor has a x1 crop factor, compared to x1.5 for APSC.

So, for example, a 24mm lens on APSC is roughly the same as a 36mm on full frame.

My question: is there a similar conversion factor for the aperture?

For example, is f2.8 on a 36mm full frame the same as f2.8 on 24mm APSC?

There is, but you have to be aware of when to use it.

I always took ait t as SQRT(2) (1.4x), but ProfHankD calculated the area ratio to be 2.3x. SQRT(2.3) = 1.5x, so it matches the crop factor.

2x is one full stop. One full stop is reported as SQRT(2) = 1.4x. So 1.5x is slightly more than a full stop.

24/2 on APS-C has the same DOF as 35/2.8 (close enough since there are no 35/3 lenses) on FF.

24/2 exposes with the same light density as 35/2. But because the FF sensor is larger, 24/2 on APS-C captures are much light over the sensor as 35/2.8 on FF. This affects signal:noise ratio and is basically another way of saying that you can shoot FF at a higher ISO. (You'd have to shoot the 35/2.8 at a higher ISO than the 24/2 to get the same image brightness).

e.g. ISO 6400 versus ISO 3200.

Whether you care to make those conversions, either for depth of field or for a ballpark idea of low light capability is entirely up to you.

In my opinion, it's pretty reasonable to think of the new NEX with 35/2.8 as roughly equivalent to an APS-C NEX with 24/1.8. One sensor may outperform another this year or next; that's not worth worrying about IMO. Practically, I don't think the APS-C combo does anything the FF combo doesn't.

- Dennis

As long as you compare 'equivalent' apertures (and FOV), as in your exampe (32/2.8 vs 24/2.0), the two solutions will run neck-to-neck, assuming that each exposure for FF uses a higher ISO and smaller aperture (e.g. ISO 1600 at f/5.6 for FF versus ISO 800 at f/4.0 for APS-C).

If you start using the same apertures, e.g. ISO 800 at f/4.0 for FF as well, the DOF effect will kick in and you end up with shallower DOF in many situations. Sometimes (often) preferable, sometimes not.

But once you start using fast lenses, such as 35/1.8, or even 35/1.4 (such as legacy SLR and RF lenses), you essentially are (capable of) using the same lens on both FF and APS-C, and then the difference is that FF can be used 1.5x higher in ISO. Or, ISO 1600 on APS-C compares to ISO 4000 on FF, and so on.

If the two sensors have the same number of pixels, e.g. both 24Mp, then the pixels in the larger sensor are 2.3x larger than the pixels in the smaller sensor. This will also increase the DR and lower th e noise floor (this is why the FF tolerates higher ISO). Generally, you will get cleaner images under low light than you would get with an APS-C sensor.

Not to throw you off, but e.g. the Nex+1650 kit lens compares roughly to the RX100 (IQ/noise/ISO). If you then replace the 1650 kit lens on the Nex with e.g. the 35/1.8 lens, the Nex produces much cleaner images than the RX100.

Similar for the FF: if you use the 35/2.8 versus the 24/1.8, you can expect 'similar' results, but once you replace the 35/2.8 with a faster lens (35/2.0, 35/1.4), the FF results start improving over the APS-C results.

But as long as you are not maxed out, neither by ISO nor by aperture, the FF and APS-C results will be fairly equivalent, except for DOF effects.

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Henry

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 Re: Math for comparing APS-C to full frame? In reply to turnstyle, Oct 15, 2013

http://www.imprezzion.com/jl/blog/?p=234

turnstyle wrote:

Hi all, I understand that a full frame sensor has a x1 crop factor, compared to x1.5 for APSC.

So, for example, a 24mm lens on APSC is roughly the same as a 36mm on full frame.

My question: is there a similar conversion factor for the aperture?

For example, is f2.8 on a 36mm full frame the same as f2.8 on 24mm APSC?

Thanks!

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 Re: Math for comparing APS-C to full frame? In reply to turnstyle, Oct 15, 2013

Here's how I see it:

• Focal length: x1.5
• Aperture: x1.5
• ISO: x2.8

So, take for example the new 35mm f/2.8, shot wide open at ISO280 on a FF body.

You will be able to get the approximately same effect (capture the same image) using the 24mm f/1.8 shot wide open at ISO100 on APS-C.

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 Re: Math for comparing APS-C to full frame? In reply to Dennis, Oct 15, 2013

Let's not forget that the 35mm f/2.8 for full frame would be smaller than the 24mm f/1.8 for APS-C and likely perform better wide open along with producing more natural bokeh.

So the ff 35 f/2.8 does have an advantage over aps-c 24mm f/1.8

Dennis wrote:

turnstyle wrote:

Hi all, I understand that a full frame sensor has a x1 crop factor, compared to x1.5 for APSC.

So, for example, a 24mm lens on APSC is roughly the same as a 36mm on full frame.

My question: is there a similar conversion factor for the aperture?

For example, is f2.8 on a 36mm full frame the same as f2.8 on 24mm APSC?

There is, but you have to be aware of when to use it.

24/2 on APS-C has the same DOF as 35/2.8 (close enough since there are no 35/3 lenses) on FF.

24/2 exposes with the same light density as 35/2. But because the FF sensor is larger, 24/2 on APS-C captures are much light over the sensor as 35/2.8 on FF. This affects signal:noise ratio and is basically another way of saying that you can shoot FF at a higher ISO. (You'd have to shoot the 35/2.8 at a higher ISO than the 24/2 to get the same image brightness).

Whether you care to make those conversions, either for depth of field or for a ballpark idea of low light capability is entirely up to you.

In my opinion, it's pretty reasonable to think of the new NEX with 35/2.8 as roughly equivalent to an APS-C NEX with 24/1.8. One sensor may outperform another this year or next; that's not worth worrying about IMO. Practically, I don't think the APS-C combo does anything the FF combo doesn't.

- Dennis

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 Re: Math for comparing APS-C to full frame? In reply to love_them_all, Oct 15, 2013

love_them_all wrote:

http://www.imprezzion.com/jl/blog/?p=234

That article is a bit confused and it turns into an opinion piece about half way through.

http://www.josephjamesphotography.com/equivalence/

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 Re: Math for comparing APS-C to full frame? In reply to NexOffender, Oct 15, 2013

NexOffender wrote:

love_them_all wrote:

http://www.imprezzion.com/jl/blog/?p=234

That article is a bit confused and it turns into an opinion piece about half way through.

http://www.josephjamesphotography.com/equivalence/

Not Joseph James' article.

This article has been heavily disputed and was discarded as incorrect in past conversations (by non m43 users). Per his reasoning (extrapolated), an Iphone camera is equivalent to a FF camera.

Last time I checked this was not the case ...

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Cheers,
Henry

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 Re: Math for comparing APS-C to full frame? In reply to blue_skies, Oct 15, 2013

blue_skies wrote:

NexOffender wrote:

love_them_all wrote:

http://www.imprezzion.com/jl/blog/?p=234

That article is a bit confused and it turns into an opinion piece about half way through.

http://www.josephjamesphotography.com/equivalence/

Not Joseph James' article.

This article has been heavily disputed and was discarded as incorrect in past conversations (by non m43 users). Per his reasoning (extrapolated), an Iphone camera is equivalent to a FF camera.

Last time I checked this was not the case ...

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Cheers,
Henry

Totally agree

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 Re: Math for comparing APS-C to full frame? In reply to blue_skies, Oct 15, 2013

blue_skies wrote:

NexOffender wrote:

love_them_all wrote:

http://www.imprezzion.com/jl/blog/?p=234

That article is a bit confused and it turns into an opinion piece about half way through.

http://www.josephjamesphotography.com/equivalence/

Not Joseph James' article.

This article has been heavily disputed and was discarded as incorrect in past conversations (by non m43 users). Per his reasoning (extrapolated), an Iphone camera is equivalent to a FF camera.

Last time I checked this was not the case ...

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Cheers,
Henry

Well, if it was extrapolated then it's not his reasoning anymore is it? What you have there is a logical fallacy know as the straw man. Joseph James' article is nowhere near as bad as the confused ramblings in that other article.

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 Re: Math for comparing APS-C to full frame? In reply to blue_skies, Oct 15, 2013

blue_skies wrote:

NexOffender wrote:

love_them_all wrote:

http://www.imprezzion.com/jl/blog/?p=234

That article is a bit confused and it turns into an opinion piece about half way through.

http://www.josephjamesphotography.com/equivalence/

Not Joseph James' article.

This article has been heavily disputed and was discarded as incorrect in past conversations (by non m43 users).

Yeah, there are plenty of people that dispute and discard the facts.  Then again, there are plenty of people that dispute Evolution, too.

Per his reasoning (extrapolated), an Iphone camera is equivalent to a FF camera.

Last time I checked this was not the case ...

Could you quote from the article where it says, or implies, that "an Iphone camera is equivalent to a FF camera", or anything remotely like that? I missed where it said, or implied, that all together.

Thanks!

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 Re: Math for comparing APS-C to full frame? In reply to blue_skies, Oct 15, 2013

blue_skies wrote:

NexOffender wrote:

love_them_all wrote:

http://www.imprezzion.com/jl/blog/?p=234

That article is a bit confused and it turns into an opinion piece about half way through.

http://www.josephjamesphotography.com/equivalence/

Not Joseph James' article.

This article has been heavily disputed and was discarded as incorrect in past conversations (by non m43 users). Per his reasoning (extrapolated), an Iphone camera is equivalent to a FF camera.

Last time I checked this was not the case ...

The Joseph James article is clearly-written, correct, and a good, solid reference.

Joe

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 Re: Math for comparing APS-C to full frame? In reply to NexOffender, Oct 15, 2013

NexOffender wrote:

It's the same 1.5 conversion so F2.8 on APS-C is equivalent to F4.2 on full frame.

DOF not light if we are talking optics

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 Re: Math for comparing APS-C to full frame? In reply to Yxa, Oct 15, 2013

NexOffender wrote:

It's the same 1.5 conversion so F2.8 on APS-C is equivalent to F4.2 on full frame.

DOF not light if we are talking optics

Both if we are talking results.

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 Re: Math for comparing APS-C to full frame? In reply to Yxa, Oct 15, 2013

Yxa wrote:

NexOffender wrote:

It's the same 1.5 conversion so F2.8 on APS-C is equivalent to F4.2 on full frame.

DOF not light if we are talking optics

It's both DOF and light. That is, for the same DOF and shutter speed, the same total amount of light falls on the sensor for all systems, which will result in the same noise for equally efficient sensors.

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 Small correction. In reply to seachicken2000, Oct 15, 2013

seachicken2000 wrote:

Here's how I see it:

• Focal length: x1.5
• Aperture: x1.5
• ISO: x2.8

So, take for example the new 35mm f/2.8, shot wide open at ISO280 on a FF body.

ISO x 1.5² = x 2.25, not x 2.8.  Of course, we have to either round up or down to the nearest 1/3 stop (e.g. ISO 100 x 2.25 = ISO 225, so we'd use ISO 200 or ISO 250).

You will be able to get the approximately same effect (capture the same image) using the 24mm f/1.8 shot wide open at ISO100 on APS-C.

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 Re: Small correction. In reply to Great Bustard, Oct 15, 2013

Great Bustard wrote:

seachicken2000 wrote:

Here's how I see it:

• Focal length: x1.5
• Aperture: x1.5
• ISO: x2.8

So, take for example the new 35mm f/2.8, shot wide open at ISO280 on a FF body.

ISO x 1.5² = x 2.25, not x 2.8.

True, but using your formula if the systems were three stops apart, the ISO would be:

ISO x 3² = 9 x ISO .. something's wrong, since ISO100 and ISO800 are three stops apart.

Using the formula I used:

ISO x 2³ = 8 x ISO

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 Re: Small correction. In reply to seachicken2000, Oct 15, 2013

seachicken2000 wrote:

Great Bustard wrote:

seachicken2000 wrote:

Here's how I see it:

• Focal length: x1.5
• Aperture: x1.5
• ISO: x2.8

So, take for example the new 35mm f/2.8, shot wide open at ISO280 on a FF body.

ISO x 1.5² = x 2.25, not x 2.8.

True, but using your formula if the systems were three stops apart, the ISO would be:

ISO x 3² = 9 x ISO .. something's wrong, since ISO100 and ISO800 are three stops apart.

Using the formula I used:

ISO x 2³ = 8 x ISO

The systems are not 1.5 stops apart, however -- the crop factor is 1.5, which makes them ln 1.5 / ln sqrt 2 = 1.17 stops apart, and, 2^1.17 = 2.25.

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 Re: Small correction. In reply to Great Bustard, Oct 15, 2013

Great Bustard wrote:

The systems are not 1.5 stops apart, however -- the crop factor is 1.5, which makes them ln 1.5 / ln sqrt 2 = 1.17 stops apart, and, 2^1.17 = 2.25.

Ah yes, that's right, 2.25 x ISO it is then.

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