Timing Belt Pitch Length Calculator

Work out timing belt pitch length instantly with clear inputs, formula shown and shareable results.

About Timing Belt Pitch Length Calculator

Belt pitch length is 2C + (pi/2)(D1 + D2) + (D2 - D1)squared/(4C). Because belts come only in whole numbers of teeth, the centre distance normally has to be adjusted to suit a standard belt rather than the other way round.

Formula

Belt length

L = 2C + (pi/2)(D1 + D2) + (D2 - D1)^2 / (4C); teeth = L / pitch

Worked example

With the default values below, Timing Belt Pitch Length Calculator returns Belt pitch length of 631.06. Change any input above and every figure here is recalculated in your browser.

Inputs used

Centre distance: 240 mm
Driver pulley teeth: 20 teeth
Driven pulley teeth: 40 teeth
Belt pitch: 5 mm

Results

Belt pitch length: 631.06 mm
Belt teeth required: 126 teeth
Reduction ratio: 2.00 :1
Small pulley wrap angle: 172.40 °

Step by step

1Values used
2Belt length
3Belt pitch length= 631.06 mm
4Belt teeth required= 126 teeth
5Reduction ratio= 2.00 :1
6Small pulley wrap angle= 172.40 °

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 2 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why does the wrap angle matter?

Fewer teeth in mesh means each tooth carries more load and the belt is more likely to ratchet. At least six teeth in mesh is the usual minimum.

Should I pick the belt or the centre distance first?

Pick the belt from the standard range, then set the centre distance to suit it, allowing a tensioner or idler for adjustment.