Continuous bias tape: a magic formula

I'm not going to start this post with an apology for not posting, because I don't have to!  Mwa ha ha!  I've been too busy with paid work and chasing a toddler around.

I have been knitting (as always) and I'm still sewing, but I can't post anything yet.

Nevertheless, I thought I'd spend a few moments in thought about continuous bias tape.  The Coletterie has a lovely tutorial on how to make continuous bias tape, which I highly recommend.  I'm not going to try and give you such a tutorial here when a good one already exists.  However, having followed their tutorial measurements to the letter a few times, I note that I do not get the whole number of 1" strips marked across the fabric as they show for their step 4.  The result is that I get less than the 100" of bias tape they propose.  This is probably because I do not edge-stitch as they suggest in step 2: instead, I use a 1/4" seam to match the one they suggest in step 6. 

I like the 1/4" seam and I do not want to do their flimsy edge-stitch.  Fortunately maths comes to the rescue and I bring you the magic formulas for cutting continuous bias tape.

For this method, follow the Colette tutorial, but substitute my measurements.  Also, use a 1/4" seam in steps 2 and 6.

I want to make a total length (T) of bias strip of width (w).

When I come to draw my lines on the fabric (see tutorial step 4), I'll need to draw enough to separate my fabric into n strips, where n = sqrt(T/(2w).  I'll have to round up to the nearest integer to make sure I get at least length T and I don't end up with half a strip.

I therefore need to start in step 1 with a fabric square of side D = n*w*sqrt(2) + 1/2".

So, to put numbers in my example, say I'd like to make 98" of bias tape of width 1".
w = 1"
T = 98"
So I need to draw lines in step 4 to separate my fabric into n = sqrt(98"/2") = sqrt(49) = 7.  I need to draw 7 strips.
n = 7
Now I need to start in step 1 with a square of D by D, where D = 7*1"*sqrt(2) + 1/2" = 10.4"
D = 10.4".

Therefore, I ought to have started the Colette tutorial with approximately a 10 3/8" square, not a 10" square.  No wonder it went wrong!

Don't stop there: use the magic to find the square size D for however much tape of whatever width you want!  THE POWER IS IN YOUR HANDS!