Originally Posted by John Bartley
This following is not exact I know, but it may help to think of it as a ratio. If the hole is 1" and it takes 1 second to expose properly, then a hole 1/100'th as big might take 100 times as long or, 100seconds (1-1/2 minutes). .... This is just an example and not the correct math. The link Nige gave will have lots of the correct info.
The math is actually correct, ... BUT ...

The "size" of the "hole" (aperture) must be considered in terms of hole area, not diameter. A hole with a diameter of 0.010 (we are talking ratios here, so I won't bother with metric conversions) will have an area 1/10,000 as "large" as one with a diameter of 1.0" (0.000 078 54 / 0.7854). It will admit 1/10 000 as much light - so (praying that I have all my decimal points in the right places) ten thousand times more time is necessary for the same amount of light to reach the light sensitive surface. That would be 10 000 seconds (~ 14.5 "stops") or about 2 hours, 46 minutes, 12 seconds.

Reciprocity - additional time necessary due to the extended exposure - comes into play . I have not addressed that here.

I'm going to check all this with the "Pinhole Calculator" program. I may return - very quickly - with massive editing ... all this is "back of an envelope" calculating.