Formula for converting between f-number and numerical aperture

Artists use f-number (f#). Scientists use numerical aperture (NA). I use both.

f# = sqrt(1/NA^2 – 1)/2
NA = 1/sqrt(4f#^2  + 1)

Yeah!!!

For quick mental approximations, the following can also be used and is easier to remember:

f# ≈ 1/(2NA)
NA ≈ 1/(2f#)

It took me 3 years to reach this 10th post.