Predicting Thumbnail Sizes from PIL

[Roger]

I need to calculate the thumbnail sizes PILL will produce from an image. 
  In most cases I can divide and round by adding .5, but PIL seems to 
round differently on odd sized images.

For example, I want to reduce an 800x816 image to have a maximum size of 
697.  (697/816) * 800 = 683.33, so my rounding results in 683.  But PIL 
produces an image of 684x697.

Is there an easy rule that will always work -- like adding .67 instead 
of .5?

Roger