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# calculating focal length when shifted and pano

#### usm

##### Active member
is there a calculator to bring down a shifted pano to a "full format" focal length?

For example: Sensor 33x44
Lens: 100mm
Ordination: portrait - 44x33
Shifted up and down 15mm - new Sensor format = 74x33
panorama: 15° left and 15° right
is a image of 9 single shots - 3 rows/3 columns

What focal length has the final image?

THanks. Mario

#### MGrayson

##### Subscriber and Workshop Member
Mario,

If the final aspect ratio is not 3:2, there is no one answer. You can go by width, height, or diagonal. Take the ratio of the respective measurements and multiply the focal length. So if the final image has dimensions, say, 120mm by 74mm, you COULD say, using diagonals, that the effective FF focal length would be 100 * Sqrt[24^2+36^2] / Sqrt[120^2+74^2] = 31mm. If you used the long edge, you'd get 100 * 36 / 120 = 30mm. By the short edge, 100 * 24 / 74 = 32mm (all answers rounded to the nearest millimeter).

For a squarer or wider image, the three answers would be more different from each other. For a 3:2 image, the three numbers would all agree.

Best,

Matt

Thanks!!

#### rga

##### Member
Apology in advance, but I'm a math luddite (amongst many other subjects). How would I calculate, as close to the 35mm equivalent, the focal length of a 50mm with a shift left and right as far as the maximum image circle of 90(mm?) will allow? I'd like to do it for both portrait and landscape orientations. Trying to keep it simple. Sensor would be a phase 100mp.
Thanks for your patience! I'm trying to put together a lightweight (not ultralight system).

#### TechTalk

##### Active member
You can find a handy field of view calculator linked below which will do the math for you and give a variety of useful information. Just enter your numbers and hit "ReCompute".

For instance, if I enter in Box 1 a native sensor size of 40 x 80 mm (height x width) then I get an image circle of 89.443 mm (close enough for me). If I then enter 50 mm for lens focal length, it tells me that I have 77.32° of horizontal coverage / 83.62° of diagonal coverage and a 35 mm equivalent focal length of 24 mm (24.19 mm). Just reverse the height and width results for vertical (portrait) orientation.

https://www.scantips.com/Field of View Calculator

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#### drevil

##### Well-known member
Staff member
At least for panos, ptgui is calculating the resulting field of view, i am not sure how effective it is when shifting but might be the same

#### rga

##### Member
You can find a handy field of view calculator linked below which will do the math for you and give a variety of useful information. Just enter your numbers and hit "ReCompute".

For instance, if I enter in Box 1 a native sensor size of 40 x 80 mm (height x width) then I get an image circle of 89.443 mm (close enough for me). If I then enter 50 mm for lens focal length, it tells me that I have 77.32° of horizontal coverage / 83.62° of diagonal coverage and a 35 mm equivalent focal length of 24 mm (24.19 mm). Just reverse the height and width entries for the sensor for vertical (portrait) orientation.

https://www.scantips.com/Field of View Calculator
Thanks so much!

#### TechTalk

##### Active member
Happy to help.

One thing to note about the calculator that I linked is that it doesn't want to calculate a sensor where the height is greater than the width. So calculate horizontally and the angles will still remain the same for the shorter and longer image dimensions regardless of camera orientation. Everything else remains the same.