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How to quickly calculate equivalencies between focal lengths used on different systems


Manolo Laguillo

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This is a question that arises often in this forum:

 

"how will an xyz mm Hasselblad lens behave on my Leica S?"

 

The best way of comparing different focal lengths on different formats is taking into consideration the 3 dimensions each format has:

 

a = short side

b = long side

c = diagonal

 

Begin by writing them left to right, from the shortest to the longest:

 

        a      b      c

 

Now write on the extreme left which format you will use to begin with, for instance full frame

 

                  a               b               c

 

35mm        24mm       36mm       42mm

 

This is our departing point: effectively, a 24mm is a wide wide angle, a 36mm is a moderate wide angle, and a 42mm is a 'normal' focal length. We are used to this focal lengths.

 

If we write on the next line the 4x5'' film dimensions, we'll know which focal lengths on the 4x5'' film are equivalent to the ones in FF:

 

                   a               b               c

 

35mm        24mm       36mm       42mm

4x5''         102mm      127mm     150mm

 

We can do the same with the Leica S format:

 

                   a               b               c

 

35mm        24mm       36mm       42mm

4x5''         102mm      127mm     150mm

Leica S      30mm        45mm       55mm

 

Now we can complicate it a little bit more, by halving and doubling a, b and c:

 

 

                   a/2           b/2           c/2             a             b             c             2a          2b          2c

 

35mm         12mm      18mm      21mm        24mm     36mm     42mm     48mm    72mm    84mm

4x5''            50mm      60mm     75mm       102mm   127mm   150mm   205mm  250mm  300mm

Leica S        15mm      23mm     27mm         30mm     45mm     55mm     60mm    90mm  110mm

 

a/2, b/2 and c/2 are really wide wide angles.

2a, 2b and 2c are short 'teles'.

 

Therefore, the 50mm on FF is not really a 'normal' lens on that format, neither it is the 70mm on the Leica S.

 

 

In any case, a 80mm lens is always a 80mm lens. But we must ask ourselves: how big is the image circle it draws?

We can use the 4x5'' lenses on any format which is smaller than 4x5'' as well.

We can use the Leica S lenses on the FF and smaller.

The same happens with 6x6 and 6x7 formats lenses, which can be used on the Leica S.

But the FF lenses can't be used on the Leica S, obviously.

 

I hope this is this clear enough

Edited by Manolo Laguillo
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Nah, just go here:

 

https://www.pointsinfocus.com/tools/depth-of-field-and-equivalent-lens-calculator/#fmt=13&ap=8&fl=50&dst=10&u=us

 

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Edited by Paul J
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Sorry I am not sure what you try to show but I think your values at c are wrong.... Using Leica S and 35mm, 30 * 0.8 = 24, 45*0.8=36 but 55*0.8 equals 44 and not 42.

 

I'm writing down on that chart the real values of 'a' (short side), 'b' (long side) and 'c' (diagonal).

 

Unless we use a zoom, 36mm and 42mm lenses for FF doesn't exist. We have 35mm and 40mm lenses.

 

And in 4x5'', where a = 10.2, b = 12.7 and c = 150, there are 90mm, 120mm and 150mm lenses.

 

What I am saying is this:

 

24mm on FF has the same angle a 30mm has on the Leica S. Those values equal the frame's short side a.

35mm on FF = 45mm on Leica S. That's the long side b

40mm on FF = 55mm on Leica S. That's the diagonal c.

 

A Leica S 55mm doesn't exist, but there is a Contax 55mm.

 

......

 

 

I did not mention the 6x9 format.

With it as an example perhaps it will be clearer what I want to explain.

On it, a = 60mm, b = 90mm, c = 105mm. (actually these values are smaller: a = 56mm, etc).

But the Fuji 6x9, a lovely camera which I used two decades ago, has a fixed 90mm lens on it, i.e. a moderate wide angle.

We don't need to know the conversion factor to quickly realize: the 90mm on 6x9 is like a 35mm on FF.

 

 

This is only a rough guide, where values should be rounded up.

Edited by Manolo Laguillo
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I'm writing down on that chart the real values of 'a' (short side), 'b' (long side) and 'c' (diagonal).

 

Unless we use a zoom, 36mm and 42mm lenses for FF doesn't exist. We have 35mm and 40mm lenses.

 

And in 4x5'', where a = 10.2, b = 12.7 and c = 150, there are 90mm, 120mm and 150mm lenses.

 

What I am saying is this:

 

24mm on FF has the same angle a 30mm has on the Leica S. Those values equal the frame's short side a.

35mm on FF = 45mm on Leica S. That's the long side b

40mm on FF = 55mm on Leica S. That's the diagonal c.

 

A Leica S 55mm doesn't exist, but there is a Contax 55mm.

 

......

 

 

I did not mention the 6x9 format.

With it as an example perhaps it will be clearer what I want to explain.

On it, a = 60mm, b = 90mm, c = 105mm. (actually these values are smaller: a = 56mm, etc).

But the Fuji 6x9, a lovely camera which I used two decades ago, has a fixed 90mm lens on it, i.e. a moderate wide angle.

We don't need to know the conversion factor to quickly realize: the 90mm on 6x9 is like a 35mm on FF.

 

 

This is only a rough guide, where values should be rounded up.

 

Ok I got your approach now, thanks.

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The Equivalent Lens formulas are very simple - the only problem is deciding the relative sizes of sensors that don't have the same aspect ratio. Manolo's approach is excellent!

 

Once you decide that sensor 1 is 'c' times as big as sensor 2, then to get the "same" picture from the two systems (i.e., almost indistinguishable same size prints):

 

1. focal length 1 must be 'c' times focal length 2  -- (this accounts for the FoV)

2. f-number 1 must be 'c' times f-number 2 -- (this accounts for the DoF)

3. exposure time 1 must be the SAME as exposure time 2 -- (this accounts for subject motion)

4. ISO 1 must be 'c' times ISO 2 -- (this corrects for the change in brightness from the f-number change and fixed shutter speed)

 

ALL relationships of how THIS lens will behave on THAT camera follow more or less immediately from those rules. If things like DoF or shutter speed don't matter for a particular photo, then those relationships can be changed, but those changes have exactly the same effect that they would when applied to any single camera. Or if you have a high MP camera, and hand holdability or IS enter the equations, but subject motion doesn't, then you may choose to alter exposure time and ISO.

 

Small sensor fans praise their increased DoF, but they might as well be praising their increased effective ISO for the same DoF. Compare a 50mm lens on FF to a 25mm lens on µ43. Set both lenses at f/4 and the 25mm lens has deeper DoF. Set the 25 at f/2 and they will have the same DoF, but now the µ43 camera can either use a shorter exposure or lower ISO.

 

And yes, it cannot be repeated too often. An 80mm lens is an 80mm lens no matter what camera it is in front of. What the image looks like will depend on sensor size and adjustments made relative to the equivalency relations above.

 

I'm not disagreeing with any of the answers above, I just find it helpful to have the underlying relationships clearly in mind.

 

--Matt

Edited by mgrayson3
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