Would appreciate if someone would check my math re: crop factor, f-stops, equivalents

Started Jul 30, 2012 | Discussions thread
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Amin Sabet
Amin Sabet Veteran Member • Posts: 6,763
Would appreciate if someone would check my math re: crop factor, f-stops, equivalents

Would appreciate if someone would check my math for the calculations below. I'm pretty sure they are all working correctly, but I'd like to make extra sure. Thanks in advance.

My goal was to create formulas that can be copy/pasted straight into a Google search to calculate the desired value. Google search has a pretty developed calculation function. Eg, log base 2 is abbreviated as lg.

I start off with the idea that crop factor can be calculated in two different ways which give similar but not always identical results:

1) Crop factor = the ratio of the diagonal dimensions of the respective formats

2) Crop factor = the square root of the ratio of the areas of the respective formats.

The rest of the calculations below are grouped according to which method is used for crop factor (diagonal or area).

+++++++++++++++++++++++++++++++++++++++++++++++
Calculations based on the ratio of the diagonal dimensions of the two formats:

Crop factor , where SW =sensor height (mm); SH =sensor width (mm):

  • (sqrt((36^2)+(24^2))) / (sqrt(( SW ^2)+( SH ^2)))

Difference in stops between two formats , where SW1 =sensor 1 width (mm); SH1 =sensor 1 height (mm), SW2 =sensor 2 width (mm); SH2 =sensor 2 height (mm):

  • 2 * lg((sqrt(( SW1 ^2)+( SH1 ^2))) / (sqrt(( SW2 ^2)+( SH2 ^2))))

135 format equivalent focal length , where SW =sensor height (mm); SH =sensor width (mm); FL =focal length:

  • ((sqrt((36^2)+(24^2))) / (sqrt(( SW ^2)+( SH ^2)))) * FL

135 format equivalent relative aperture (equivalent f-number) , where SW =sensor height (mm); SH =sensor width (mm); RA =relative aperture (f-number):

  • ((sqrt(2))^(2 * lg(((sqrt((36^2) + (24^2))) / (sqrt(( SW ^2) + ( SH ^2))))))) * RA

+++++++++++++++++++++++++++++++++++++++++++++++

Calculations based on the square root of the ratio of the areas of the two formats:

Crop factor , where SW =sensor height (mm); SH =sensor width (mm):

  • sqrt((36 * 24) / ( SW * SH ))

Difference in stops between two formats , where SW1 =sensor 1 width (mm); SH1 =sensor 1 height (mm), SW2 =sensor 2 width (mm); SH2 =sensor 2 height (mm):

  • 2 * lg(sqrt(( SW1 * SH1 ) / ( SW2 * SH2 )))

135 format equivalent focal length , where SW =sensor height (mm); SH =sensor width (mm); FL =focal length:

  • (sqrt((36 * 24) / ( SW * SH ))) * FL

135 format equivalent relative aperture (equivalent f-number) , where SW =sensor height (mm); SH =sensor width (mm); RA =relative aperture (f-number):

  • ((sqrt(2))^(2 * lg((sqrt((36 * 24) / ( SW * SH )))))) * RA

+++++++++++++++++++++++++++++++++++++++++++++++
A few additional Googleable calculations which may be useful:

Number of stops separating two f-numbers for a given format, where RA1 =f-number 1; RA2 =f-number 2:

  • 2 * lg( RA1 / RA2 )

F-number which is X stops slower than another given f-number ( RA ):

  • ((sqrt(2))^( X ))) * RA

F-number which is X stops faster than another given f-number ( RA ):

  • ((sqrt(2))^(- X ))) * RA

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