# Math of FF sensor size vs crop can someone help explain

Started Nov 25, 2012 | Discussions thread
Re: Math of FF sensor size vs crop can someone help explain

Frugaltraveler wrote:

Ok, been pondering about this for a while and question how is the crop factor of FF calculated?

FF is 24mm x 36mm = 864mm2

...

How do you get a crop factor for the lenses of 2 if the sensor is a fourth of the size for the 4/3 system?

It is the diagonal you want to measure, not the area, because the diagonal is the diameter of the image circle required to encompass the sensor rectangle.

It is the angle of view we wish to compare. How “wide” is the sensor, what is the equivalent focal length lens compared to the full frame sensor?

Specifically addressing your question about how one concludes that the 4/3 sensors have a crop factor of 2x: Using the Pythagorean theorem we compute the full frame (FF) diagonal to be 43.2666; the 4/3 sensor diagonal = 21.6400.

The FF diagonal is 1.999 times “wider,” or 2x. So, a 50 mm lens, say, on a FF camera would act as a 100 mm (50x2) on the 4/3 camera. A crop factor of 2x.

It is the convention to round off the crop factors of the different sensor sizes; e.g. the Canon 1D Mark IV is called a 1.3x crop, but in fact is 1.2905x. (To Canon’s credit, they note in the User’s Manual that the 1.3x is an approximation.)

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