How this is calculated. Timing belt pitch diameter comes from the tooth pitch
measured along the belt,
d = N·p/π, not from any nominal size. Belt length is the
two straight runs plus the wrap on each pulley, which the standard approximation writes as
L = 2C + π(d₁+d₂)/2 + (d₂−d₁)²/4C. That final term is small unless the pulleys
differ a lot.
Belts come in whole teeth, so the calculated length is almost never the length
you can buy — the row above solves the same relation backwards to give the centre distance
that a stocked belt actually needs, which is the number you want when placing the idler. Wrap
angle matters as much as length: torque capacity depends on how many teeth are engaged on the
small pulley, and below about six engaged teeth a timing belt will skip under load long
before it breaks.
Fewer than about six teeth are engaged on the small pulley. The belt will jump teeth under load — increase the centre distance, use a larger small pulley, or add an idler to increase wrap.