Figuring out Canvas Size + Composition

  I laugh when people say that artists can't do math, because there's a lot of math required for a good painting.  I've been working on the composition for this new narrative painting and I've finally got the composition down.  In my previous post, I had a really rough composition, but it's now refined and the shapes are all worked out.
   A really good tool for composition and proportion is tracing paper.  I traced the pose from a detailed study I did and then was able to move it around in the composition until I found a pleasing pose.  Then I taped down the tracing paper and drew a proportional rectangle around the composition.  All of this is done in pencil because a lot of erasing is involved.
  I also always have a sense of life-sized scale in my mind.  I keep this in mind because I want my canvas to be roughly 2/3 life size.  I measured my dog, Maea, and found out she's about 20" long when in the pose I need.  So I want her to be about 13" in scale for the canvas.  I usually measure in centimeters and then convert to inches because centimeters are more accurate with my small drawing.  

The formula I use for figuring out the final size is:   A/B = C/D

In this case: A is the width of my sketch (2.95")
                   B is the height of my sketch (3.54")

                   C is the width of my final canvas
                   D is the height of my final canvas

  This is where I keep the models size in my mind to figure out a pleasing canvas.  Since she's a small dog, I don't want a huge canvas.  Because C and D are my unknowns, I used large rulers and laid out a width that would give me enough room for the dog and surrounding.  I decided on a 24" width.  Because I know my variable, C, then I can use the formula to find out D

                 2.95(A)             24(C)                   3.54 (B) X 24 (C) = 84.96
                 ---------      =     ----------                  84.96 / 2.95 (C) = 28.8 (D)
                 3.54(B)               D

 
  The equation of (B X C) will give you a number that, when divided by C will give you D.  It's a really simple equation that I use all the time.
  After I have the final canvas size, I always lay it out on the floor to see if I think it looks good.  I always end up making small changes, even after all that math.  I ended up rounding my canvas height to 30" because it's a more pleasing rectangle.  

It's more work and it's always worth it.