angle of view to focal lenght

[Timppa]

Hi!

I have been searching for a formula to calculate the focal length with help of the angle of view.
I find this:

FOV =2arctan(half the horizontal size of the sensor/F)
with F = the focal length

a FF sensor is 36x24, so I could already change it to FOV = 2arctan(18/F)
But how do I change this formula to find F ? (F = ....)
That kind of math is a bit to rusty for me .
And an extra question, how would I formulate it in Libre office or Excel ?

Thank you in advance!

 

[Alexr25]

That FoV formula transposes to f = 18 divided by tan(1/2 of the FoV angle).
The problem to using this will be how do you measure the FoV angle, by no means impossible but at the same time not exactly straight forward.

 

[Timppa]

That FoV formula transposes to f = 18 divided by tan(1/2 of the FoV angle).
The problem to using this will be how do you measure the FoV angle, by no means impossible but at the same time not exactly straight forward.

Thank you for this!
Wel to get the FOV, I can do =2*ATAN(horizontal lenght of the object/(2*lenght to the object))

I used your formula, But the result is a negative number?

 

[Derrel]

I go here for that type of information when needed. Depth of Field, Angle & Field of View, & Equivalent Lens Calculator - Points in Focus Photography

 

[Timppa]

I go here for that type of information when needed. Depth of Field, Angle & Field of View, & Equivalent Lens Calculator - Points in Focus Photography

Thank you for this, but I would like to get the formula to put it in a excel file

 

[Alexr25]

I used your formula, But the result is a negative number?

How did you get a negative number? It sounds as if you are forgetting to divide the FoV angle by 2 before taking the tan of the angle.
If you had a spreadsheet with the FoV stored in cell C3 then formula you would enter would look like =18/TAN(C3/2)

 

[Alexr25]

That spreadsheet formula should read =18/TAN(RADIANS(C3/2)) since the spreadsheet tan function works in radians rather than degrees, this may also be why you get negative results if you are using a spreadsheet.

 

[Timppa]

Thanks for the help !
Now I came across another issue, I'm probably missing some more data.

if I calculate a FOV of 11,42 (or RAD=0,199337)
I put it in the formula, the answer is 180mm.

Then I go to: Nikon | Imaging Products | NIKKOR Lens Simulator
When I put the slider on 180mm, It says the angle of view is 13°40'. That is a different result.
Where did I go wrong? Or is there a difference between Field of View and Angle of View?

 

[Alexr25]

The lens FoV angle is generally specified across the frame diagonal rather than across the frame width so in your formula you should replace the 18 (1/2 frame width) with 21.6 (1/2 frame diagonal).

 

[Timppa]

Now it finally works!
The results are very close to what Nikon says (+-2mm)
Thank you Alexr25 !

 

[Timppa]

This is the full formula I got now:
Focal Length = (28,8444/2)/TAN((2*ATAN(B1/(2*B2)))/2)
with 28,8444 being the diagonal of a DX sensor (because thats what I will be calculating with).
B1 = The length of the object on the photo
B2 = Distance camera to object