V-Belt and Flat Belt Drive Calculator: Length, Wrap Angle and Tensions

Belt length, wrap angle, driven speed, belt speed, tension ratio and tensions for an open belt drive.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the two pulley diameters, the centre distance and the speed of the small pulley. The calculator gives the open-belt length, the angle of wrap on the small pulley, the driven speed (with any slip), the belt speed and the speed ratio.

It also gives the tension ratio on the point of slipping, e to the power of mu times the wrap angle (with the friction coefficient divided by the sine of half the groove angle for a V-belt). Enter the power and it gives the tight and slack side tensions.

Check the wrap angle is at least 120 degrees, and use the belt maker rating tables for the final belt selection, especially above 10 m/s belt speed.

Formulas used

  • L = 2C + \frac{\pi(D_1 + D_2)}{2} + \frac{(D_2 - D_1)^2}{4C}
  • \frac{T_1}{T_2} = e^{\mu\theta}
  • v = \frac{\pi D N}{60}

Worked example

With the default numbers in the calculator above:

  1. Belt length (open belt): 1718.11 mm
  2. Angle of wrap on the small pulley: 162.75 °
  3. Speed ratio: 2.00
  4. Speed of the large pulley: 725.00 rev/min
  5. Belt speed: 11.39 m/s
  6. Tension ratio (tight side over slack side, on the point of slipping): 2.34

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

What wrap angle is needed?

At least 120 degrees on the small pulley. Less gives poor grip.

Why does a V-belt grip better?

It wedges into the groove, so the normal force on the sides is bigger than the tension alone gives, like a higher friction coefficient.

Is this for a crossed belt?

No, only an open belt.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Shigley, Mechanical Engineering Design (flat and V-belt drives); AS 2784 (V-belts).

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