Timing belt length, explained: the stock-belt step everyone skips

Timing-belt math runs in teeth, not millimeters — the belt is a loop of whole teeth, the pulleys engage whole teeth, and the catalog only sells whole-tooth lengths. The length formula gives you a decimal; the design step that matters is what you do with the fraction.

The two relations

D = N·p/π · L = 2C + (π/2)(D₁+D₂) + (D₂−D₁)²/4C · teeth = L/p

Pitch diameter follows from tooth count and pitch alone; the open-drive length is the two straight runs, the half-wrap of each pulley and a correction for the wrap asymmetry. The timing belt calculator returns the length both ways — millimeters and teeth — plus ratio, driven RPM and belt speed.

Worked example — GT2, 20:60 at 100 mm centers

A 2 mm-pitch GT2 drive, 20-tooth driver at 1,200 RPM, 60-tooth driven, 100 mm center distance:

D₁ = 12.73 mm · D₂ = 38.20 mm · L = 281.6 mm = 140.8 teeth · ratio 3:1 → 400 RPM · v = 0.80 m/s

No catalog sells a 140.8-tooth belt. The stock answer is the 140-tooth (280 mm) loop — and the centers move to suit: 99.18 mm puts exactly 280 mm of pitch length around the pair. That 0.8 mm of adjustment is the whole reason timing-belt mounts have slots, eccentrics or idlers; design the adjustment in, don't discover it at assembly. In the calculator, enter 140 as the selected belt teeth to get that center distance, center shift, small pulley wrap and teeth-in-mesh screen directly.

Why pitch, not outside diameter

The belt's working line is its tension-cord layer, which rides above the pulley teeth — so the pitch diameter is larger than anything calipers touch. Tooth counts carry all the exact information: ratio is N₂/N₁ with zero slip (the reason these drives hold position in printers and steppers), and length in teeth is the part number. The same arithmetic with slip and wedge friction instead of teeth is the V-belt length calculator's territory, the chain version lives in the sprocket calculator, and plain diameter-ratio drives in the pulley calculator.

Common mistakes

• Measuring pulley OD for the ratio. Tooth counts are exact and printed on the pulley; the OD is pitch diameter minus the tooth engagement and tells you neither ratio nor length.
• Designing centers with no adjustment. Fixed centers demand a belt length the catalog probably doesn't sell; budget ±half a tooth of center movement minimum.
• Confusing belt pitch with pulley pitch diameter. Pitch p is tooth-to-tooth along the belt (2 mm for GT2); pitch diameter is per pulley, D = N·p/π.
• Forgetting wrap on the small pulley. Big ratios at short centers shrink the driver's wrap angle and with it the teeth in mesh — six teeth engaged is a common minimum rule from belt makers; check their data when the drive transmits real torque.

Frequently asked questions

How do you calculate timing belt length?

Pitch diameters first — D = N·p/π from each pulley's tooth count and the belt pitch — then the open-drive length L = 2C + (π/2)(D₁+D₂) + (D₂−D₁)²/4C. A GT2 drive with 20 and 60 tooth pulleys at 100 mm centers needs 281.6 mm of belt, which is 140.8 teeth.

What if the calculated belt length isn't a stock size?

It almost never is — belts come in whole tooth counts and catalog lengths. Pick the nearest stock belt and move the center distance to suit: the 140.8-tooth answer becomes a stock 140-tooth (280 mm) belt with the centers pulled in to 99.18 mm. That is why timing-belt layouts need a slotted mount or an idler.

Is timing belt pitch diameter the same as the pulley's outside diameter?

No — the pitch line runs through the belt's tension cords, slightly above the pulley teeth. A 20-tooth GT2 pulley has a 12.73 mm pitch diameter but a smaller measured OD. Length and ratio math always uses pitch diameter; calipers on the flange tell you nothing about either.

Does a timing belt change the speed ratio like gears?

Exactly like gears, minus the slip a V-belt would add: ratio = N₂/N₁ from tooth counts alone. The 20:60 example is a true 3:1 — 1,200 RPM in, 400 RPM out — and the belt itself travels at 0.80 m/s.