Belt Length Calculator

This function calculates the belt length of a two-pulley drive, or the distance between the axes when the length of the belt is given.

To perform the calculation, use the radio button to select whether the belt length or center distance should be calculated. Then enter the required values and click the 'Calculate' button.

Diameter, distances and length have the same unit (e.g. meter or cm)

Calculate belt length   What should be calculated ? Belt length Axis distance of the pulleys  Input Delete Entries Diameter pulley 1 Diameter pulley 2 Distance of the axes Decimal places 0 1 2 3 4 6 8 10  Result Belt length

Belt length formulas

Belt length

\(\displaystyle L=(d_L+d_S) \cdot \frac{π}{2}+(d_L-d_s)\cdot asin\left(\frac{d_L-d_S}{2\cdot D}\right) \) \(\displaystyle +2\cdot \sqrt{D^2-0.25\cdot (d_L-d_S)^2} \)

The formula above is also used by this calculator. However, another formula is also common, which approximates the formula above:

\(\displaystyle \frac{π}{2}\cdot(d_L+d_S)+2\cdot D+ \frac{(d_L-d_S)^2}{4\cdot D}\)

The formula works well for two pulleys of similar size or ones that are farther apart. The estimation will fail if one pulley is much larger than the other and they are close together. Such cases are unusual, however, as they can lack the adequate drive.

Distance of the axes

The following formula also used by this calculator.

\(\displaystyle D=\frac{b+\sqrt{b^2-32\cdot(d_L-d_S)^2}}{16}\)

\(\displaystyle b= 4\cdot D - 2\cdot π\cdot(d_L+d_S)\)

\(d_L\) = the diameter of the large pulley
\(d_S\) = the diameter of the small pulley
\(D\) = the distance between the centers of the pulleys
\(L\) = the length of the belt