When I do rough calculations for the length of materials in a TH (and they are always rough, in my experience, since every occasion gives me slightly different results in real life), I generally resort to the Pythagoras theorem, since the line segment from two connected loops on opposite sides of the band can be regarded as the hypotenuse of a right triangle, and the width of the band is one of the sides. The other side has to be calculated as follows: the desired circumference of the knot, divided by twice the number of loops around the edge,, times the number of leads. This results in a segment of the circumference, i.e. 5/22nds of the circumference of a 5x11 is the distance around the circumference from a loop to a point opposite where it reaches the other side of the knot.

If you know how wide the knot will be, and how long the path is going to be, you can find the hypotenuse, multiply by the number of bights, then double that, to find a reasonable guess as to how much material will be required.

I've got a page or so of discussion of this on my website, where I also mention the possibility, and the undesirability, of considering the path as a messy sine curve and integrating over its length using calculus. Pythagoras is far easier, and no less useful.

In any case, the closer you figure it, the more important it is to leave yourself some room for error. It's far more frustrating to start over than it is to scrap a short section of material that isn't needed for the complete knot. 5% is good, 10% might be excessive.

Loren