Timing Belt Calculator

Inputs

Belt tooth pitch (p)

GT2 = 2 mm, GT3 = 3 mm, HTD-5M = 5 mm, T5 = 5 mm, XL = 5.08 mm.

Driver pulley teeth (N₁)

Teeth on the driving pulley (on the motor / input shaft).

teeth

Driven pulley teeth (N₂)

Teeth on the driven pulley (on the output shaft).

teeth

Center distance (C)

Distance between the two pulley centres.

Driver speed (n₁)

Optional — for belt speed and driven RPM. 0 to ignore.

rpm

Default result

Belt pitch length(L)

260.4mm

2C + (π/2)(D₁+D₂) + (D₂−D₁)²/(4C).

Also computed

Belt length in teeth(z_b)130

Nearest standard size is 130 teeth (theoretical 130.20); set the centre distance from that belt.

Nearest whole tooth count — pick the closest standard belt.

Pitch diameter (driver)(D₁)12.73mm

D₁ = N₁·p/π.

Pitch diameter (driven)(D₂)25.46mm

D₂ = N₂·p/π.

Speed ratio(i)2

reduction (driven slower)

N₂ / N₁ (driven ÷ driver).

Driven speed(n₂)0rpm

Belt speed(v)0m/s

Surface (linear) speed of the belt.

Method notes 4 notes

Pitch diameter D = N·p/π, where N is the pulley tooth count and p the belt tooth pitch (GT2 = 2 mm, GT3 = 3 mm, HTD-5M / T5 = 5 mm, XL = 5.08 mm).
Belt pitch length L = 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)²/(4C) for an open (non-crossed) belt; length in teeth = L / p.
In practice you pick the nearest standard belt tooth count, then back-solve the centre distance to suit it — an idler or spring tensioner takes up the small difference.
Speed ratio i = N₂ / N₁ and driven speed n₂ = n₁ · N₁ / N₂. A toothed belt does not slip, so the ratio is exact.