calculations - Do I use the crop factor in calculating aperture size and area?

How do I calculate the aperture size and area, considering an 35mm equivalent focal length value and non-equivalent aperture f-number (in terms of exposure, no multiplication of the crop factor of the sensor).

For example, I have a 1.5x crop sensor. The lens is equivalent to 50mm in 35mm terms and the camera has an aperture of 2.8. What is the aperture size and area?

I know that we probably shouldn't use the crop factor in the equation because the focal length given is already in 35mm terms. The aperture is as give by the company specifications, and I don't know if it needs multiplication or not.

Answer

The aperture size is a property of the lens only and does not depend on the crop factor. It does depend, however, on the actual focal length of the lens (not the "equivalent" focal length).

So you need to obtain the actual focal length by dividing by the crop factor.

actual-focal-length = equiv-focal-length / crop-factor

You can then calculate the size (diameter) of the aperture (strictly speaking the size of the entrance pupil, which is the image of the aperture) by dividing the focal length by the f-number (which does not need to be divided by the crop factor).

aperture size = actual-focal-length / F-value
              = (equiv-focal-length / crop-factor) / F-value

So in your case the calculation is:

aperture size = (50mm / 1.5) / 2.8
              = 11.9mm