Capstan wrap angle and limiting tension calculator

What this model answers

A flexible line wrapped around a cylinder can sustain different tensions on its two sides because contact friction accumulates around the wrap.

The capstan equation gives the limiting ratio at impending slip, not a unique tension for every stationary rope.

The Belt pitch length and pulley centres calculator finds geometric belt length. Only the actual contact wrap belongs in this limiting friction equation.

Keep the input conventions consistent

Enter the actual contact angle rather than an unrelated pulley rotation.

The form accepts degrees and converts them to radians in the exponential. Radius affects net transmitted torque but does not affect the ideal limiting tension ratio.

Read the result carefully

Tension ratio grows exponentially with the product of friction coefficient and wrap angle.

That explains why an extra half turn can matter more than a small increase in radius. The assumed constant friction coefficient remains an entered scenario, not a measured material property.

Wrap angle must describe actual rope contact, not merely the visible change in direction of free rope segments. The exponential tension ratio is sensitive to both that contact angle and assumed friction. It describes the stated limiting friction relation and does not certify rope strength or an anchorage capacity.

Work through the numbers

With 100 N slack-side tension, coefficient 0.3 and 180 degrees of contact, the limiting tight-side tension is about 256.633 N.

At 100 mm radius, the tension difference corresponds to 15.6633 N m of limiting transmitted torque.

Where the calculation stops

The line is idealized as flexible and the cylinder contact follows Coulomb friction.

Rope bending stiffness, V grooves, centrifugal effects and material strength are absent. The answer is not a rope working-load limit or a lifting instruction.