There are plenty of different pinholes you can make! Assuming I am being a little bit less creative and I am making a matchbox pinhole camera lens using a drawing pin in a sheet small sheet from an aluminium can, how can I calculate the aperture and what is it likely to be?
If the diameter of the shaft of a standard pin is about 0.5 mm, then the aperture of that is based on the focal length and that should be the distance between the sensor and the lens mount (flange focal distance). So, given that, the math is: FFD/2 assuming a 0.5 mm pinhole. So, on a Canon EF mount with a 44mm flange focal distance, the aperture is f/88.
For formula purposes:
aperture = flange focal distance/diameter of pin
You can image a red laser across the room shining on your pinhole, and measure the diameter (in pixels) of your first dark ring (if your pinhole is a clean circle). Then knowing pinhole-to-detector distance and the formula for the angular diameter of that first dark ring (about 2.44 * wavelength / pinhole_diameter, in radians) figure out your pinhole diameter. You'll need to look up the pixel size for your detector to do this. The red laser is likely a HeNe laser, around 0.632 microns wavelength.
I have DIY a pinhole lens. I used an aluminum foil. I used a needle to make a very tiny hole on it. I took several pictures by it. I used the photo editing software to check the photos and adjusted the exposure time accordingly. Until I got a good picture (i.e. not too bright and not too dark), I found the aperture of the hole made by a needle is about f/95 to f/120.
See here for my work - http://daddiest.com/pinhole-photography-dirt-cheap-pinhole-lens-diy/