Belts & Pulleys

Pulley Wrap Angle Calculator

Estimate the contact angle around each pulley from pulley diameters and shaft center distance.

Inputs

Formula

Open-belt wrap angles

alpha_small = pi - 2 asin((D-d)/(2C)); alpha_large = pi + 2 asin((D-d)/(2C))

Worked example

Using the default values shown in the calculator, the same formula gives the following result. This is a quick sanity check for the calculation, not a design recommendation.

Inputs

Large pulley diameter
250 mm
Small pulley diameter
100 mm
Center distance
500 mm

Result

Small pulley wrap angle
162.75 deg
Large pulley wrap angle
197.25 deg

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Frequently asked questions

Why is the small-pulley wrap angle important?

Less contact around the smaller pulley can reduce the available friction or tooth engagement, depending on belt type.

Does this apply to crossed belts?

No. These equations are for a two-pulley open-belt geometry.