# Formula for distance focus per degree rotation focus ring

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### #1 vvanwillegen

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Posted 22 August 2012 - 02:47 PM

Dear users,

I'm wondering: is there a formula for calculating the distance of the focus after rotating the focus ring x degrees?

Greetings,
Vincent
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### #2 Leo Anthony Vale

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Posted 22 August 2012 - 11:53 PM

I'm wondering: is there a formula for calculating the distance of the focus after rotating the focus ring x degrees?

There is no formula. Rotating the focus ring is a mechanical function, not an optical function.
The amount of rotation varies from one lens design to another. There is no standard.
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### #3 Dom Jaeger

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Posted 23 August 2012 - 02:15 AM

Yes, it depends on the lens, they all have different focus barrel throws.

Even within a highly standardised series like say Zeiss Ultra Primes, manufactured to extremely tight tolerances, there may be slight variations in the total length of the focus scale throw (ie from infinity to minimum) between lenses of the same focal length. So each Zeiss focus ring is engraved with a focal length and a code - GG or HH etc - that identifies the length of throw and has been matched to the lens. Other high-end manufacturers hand-engrave each focus scale individually. One of the problems with cheap cine lenses is that they use generic focus scales that sometimes don't match up.

In terms of the spacing between distance marks within a focus scale, it's a type of logarithmic progression. To be perfectly accurate you'd need to include nodal points and back-focus distance in the formula, but an approximate version is

x = f² ÷ D

where f is the focal length, D is the distance to the object, and x is the distance the lens needs to be racked out from its infinity position to focus on the object. Depending on how much rotation of the focus ring causes how much focus travel (which is a function of the mechanics, be it helical thread or cam), you could work out some sort of relationship between degrees of rotation and focus distance, but it won't be linear.
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### #4 vvanwillegen

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Posted 29 August 2012 - 08:22 AM

Today I will compare the formula against some prime lenses.
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### #5 Tom Jensen

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Posted 29 August 2012 - 08:47 AM

Curious as to what you will do with this data
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### #6 Chris Millar

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Posted 29 August 2012 - 08:56 PM

Another way about it would be to tabulate it yourself with actual readings. Put those into a simple look up table into your 3D package/motion control whatever you're making - interpolate points inbetween (linear/cubic whatever complexity you choose) or maybe do a nice curve fit in excel/matlab etc... to get a function and avoid the look up table altogether
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