⚙️ Belt Length Calculator

Enter the center distance (C) between two pulleys and their diameters (large pulley D, small pulley d) to automatically calculate the open (non-crossed) belt length.

Belt Length (L)

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Arc Term (π(D+d)/2)

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Center-Distance Term (2C + (D−d)²/4C)

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GUIDE

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Belt Length Formula

The length of an open belt (non-crossed) connecting two pulleys can be approximated with:

L = 2C + π(D+d)/2 + (D−d)²/4C

where C is the center distance between the two pulley axes, D is the large pulley diameter, and d is the small pulley diameter. The first term (2C) is the sum of the two straight belt spans, the second term is the sum of the arc contact lengths, and the third term corrects for the difference in pulley diameters.

When Is This Used?

Used when designing or repairing machinery that connects two pulleys (or sprockets) with a belt — conveyors, belt-driven motors, sewing machines, industrial conveyor belts — to pre-calculate the required belt length before selecting a standard belt or ordering a custom one.

Accuracy and Limitations

This formula assumes a taut, thin belt (belt thickness ignored) and parallel pulley axes. In practice, belt thickness, tension-induced stretch, and V-belt groove geometry can cause slight deviations from the measured value — verify with a physical measurement or manufacturer spec sheet before final ordering.

Frequently asked questions

Can this formula be used for crossed belts?

No. This formula is for an open (non-crossed) belt. A crossed belt, where the pulleys rotate in opposite directions and the belt crosses itself, uses a different formula.

What happens if both pulleys have the same diameter?

If D=d, the correction term (D−d)²/4C becomes 0, simplifying to L = 2C + πD.

What unit should I use?

Any consistent unit works (mm, cm, in, etc.) — just use the same unit for the center distance (C) and both diameters (D, d). The result will be in that same unit.