How to use this calculator
- Enter the belt tooth pitch. Enter the belt pitch p — GT2 = 2 mm, GT3 = 3 mm, HTD-5M / T5 = 5 mm, XL = 5.08 mm.
- Enter the pulley tooth counts. Enter the driver and driven pulley tooth counts. The pitch diameter is D = N · p / π.
- Enter the centre distance. Enter the distance between the two pulley centres.
- Pick a stock belt. Leave selected belt teeth at 0 for the nearest whole-tooth belt, or enter the catalog belt tooth count you plan to buy.
- Read the results. Read the belt pitch length, exact teeth, selected-belt centre distance, centre shift, wrap, teeth in mesh, pitch diameters and speed ratio. Add the driver RPM for belt and driven speed.
How it works
A timing (synchronous) belt has teeth that mesh with grooved pulleys, so it
transmits motion without slip. Each pulley turns its tooth count into a
pitch diameter through the belt tooth pitch p:
D = N · p / π
The pitch diameter is the effective working diameter at the belt pitch line —
not the outer rim.
With both pitch diameters the belt pitch length of an open
(non-crossed) two-pulley drive is
L = 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)²/(4C), where C is
the centre distance. The belt is specified in teeth, so the
length in teeth is L / p, rounded to the nearest whole number.
Because belts only come in fixed tooth counts, you normally pick the nearest
standard tooth count and then back-solve the centre distance to
suit that belt; an idler or spring tensioner takes up the small difference and
sets the tension. The speed ratio is the tooth-count ratio,
i = N₂ / N₁, and the driven speed is n₂ = n₁ · N₁ / N₂.
The selected-belt workflow runs that last step directly: a selected belt has
pitch length L_sel = z_sel · p, and the same belt-length equation
is solved backward for C_sel. The centre shift tells you how far
the entered centre distance must move to fit that whole-tooth belt.
| Check | Use this result | Why it matters |
|---|---|---|
| Catalog belt | Selected / nearest belt | Timing belts are sold by whole tooth count, not decimal length. |
| Mount adjustment | Centre distance shift | Shows slot, eccentric or idler travel needed after choosing the belt. |
| Tooth engagement | Small-pulley teeth in mesh | Flags very short wrap before relying on torque capacity. |
Worked example
Verified against the live calculator
A GT2 belt (p = 2 mm) runs a 20-tooth driver and a 40-tooth driven
pulley at a 100 mm centre distance. The pitch diameters are
D₁ = 20 × 2 / π ≈ 12.73 mm and
D₂ = 40 × 2 / π ≈ 25.46 mm. The belt pitch length is
L = 2(100) + (π/2)(12.73 + 25.46) + (25.46 − 12.73)² / (4 × 100) ≈ 260.40 mm,
which is 260.40 / 2 ≈ 130.2 → 130 teeth. A 130-tooth belt is
260 mm long, so the centres move to about 99.80 mm,
or 0.20 mm closer than the entered distance. The small pulley has
about 9.6 teeth in mesh. The tooth-count ratio is
2:1, so the driven pulley turns at half the driver speed.
Frequently asked questions
How do I calculate timing belt length?
First find each pulley pitch diameter from its tooth count and the belt tooth pitch p: D = N · p / π. Then the belt pitch length of an open two-pulley drive is L = 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)²/(4C), where C is the centre distance. The belt length in teeth is L ÷ p, rounded to a whole number. For example a GT2 (2 mm) belt on 20- and 40-tooth pulleys at 100 mm centres works out to about 260.4 mm, or 130 teeth.
What is the pitch diameter of a timing pulley?
The pitch diameter is where the belt pitch line sits — not the outer rim. For a synchronous pulley with N teeth and belt pitch p it is D = N · p / π. A 20-tooth GT2 (2 mm) pulley has a pitch diameter of 20 × 2 / π ≈ 12.73 mm. Use the pitch diameter, not the OD, for length and ratio.
What are the common timing belt pitches?
GT2 = 2 mm, GT3 = 3 mm, HTD-3M = 3 mm, HTD-5M = 5 mm, T5 = 5 mm, T2.5 = 2.5 mm, XL = 5.08 mm (1/5 in), L = 9.525 mm (3/8 in). GT2 and GT3 dominate 3D printers and small motion; HTD and T-series are common on larger industrial drives.
How do I pick a standard belt and set the centre distance?
Belts come in fixed tooth counts, so you do not usually hit your exact centre distance. Pick the nearest standard belt tooth count, then back-solve the centre distance to suit that belt. The small remaining slack is taken up by an idler or a spring tensioner, which also sets belt tension.
Can I calculate centre distance from a selected timing belt?
Yes. Enter the stock belt tooth count in Selected belt teeth. The calculator multiplies that count by pitch, solves the belt-length equation backward, and reports the centre distance and centre shift needed to fit that belt.
How many timing belt teeth should be in mesh?
A common quick screen is about six or more teeth engaged on the smaller pulley, but final capacity depends on belt width, tooth profile, material, pulley quality, pretension and the belt maker rating.
What is the speed ratio of a timing belt drive?
The speed ratio is the driven tooth count divided by the driver tooth count: i = N₂ / N₁. Because a toothed belt does not slip, the ratio is exact. The driven speed is n₂ = n₁ · N₁ / N₂ — so 20 driver teeth to 40 driven teeth is a 2:1 reduction and halves the speed.
Does this work in metric and imperial?
Yes — enter the tooth pitch and centre distance in mm or inches, and the belt length and pitch diameters come back in the same system. Tooth counts are pure numbers. Toggle SI/Imperial in the header.
Method & assumptions
- Open (non-crossed) two-pulley drive; the closed-form length is exact for an open belt and the standard approximation otherwise.
- Pitch diameter D = N · p / π uses the belt pitch line, not the pulley outer diameter.
- A toothed belt has effectively zero slip, so the speed ratio equals the tooth-count ratio exactly.
- Belt length is rounded to a whole number of teeth — in practice you choose the nearest standard belt or enter a catalog belt tooth count, then back-solve the centre distance.
- Teeth in mesh is a screening check only; belt width, torque, tooth form, pretension, pulley material and manufacturer ratings control capacity.