V-Belt Length Calculator

V-belt pitch length and center distance for a two-sheave open drive, with wrap angle, speed ratio, driven RPM and belt speed. Metric and imperial. Free, no signup.

Inputs

View results

Solve for

Driver sheave pitch diameter (D₁)

Driven sheave pitch diameter (D₂)

Center distance (C)

Driver speed (n₁)

rpm

Results

Default result

Edit inputs

Belt pitch length(L)

1,363.8mm

Pass

calculated pitch length

Also computed

Center distance(C)400mm

known center distance

Small-sheave wrap(θₛ)158.4°

comfortable wrap for a friction belt

Speed ratio(i)2.5

reduction

Driven speed(n₂)700rpm

Belt speed(v)9.163m/s

Method notes 3 notes

Use pitch / datum sheave diameters. A V-belt rides below the outside rim, so OD usually gives a belt that is too long.
Open-drive length: L = 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)²/(4C). Center distance is solved by the positive quadratic root.
Small-sheave wrap limits grip. If it drops below about 120°, reduce the ratio, increase center distance or add an idler.

V-belt length for a two-sheave open drive is L = 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)²/(4C), using pitch or datum sheave diameters rather than outside diameters. The same equation can be solved backward for center distance from a selected standard belt length. This calculator also returns small-sheave wrap angle, speed ratio, driven RPM and belt speed.

How to use this calculator

Choose the solve direction. Solve either belt length from center distance or center distance from a known belt length.
Enter sheave pitch diameters. Use pitch or datum diameters for the driver and driven sheaves.
Enter center or belt length. Enter center distance if sizing a new belt, or a standard belt pitch length if fitting an available belt.
Check wrap and speed. Read belt length, center distance, small-sheave wrap angle, ratio, RPM and belt speed.

How it works

A two-sheave open V-belt drive is two straight spans plus the wrap arcs around each sheave: L = 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)²/(4C) where C is center distance and D₁, D₂ are pitch diameters. If you already have a standard belt length, the calculator solves the same equation backward for C using the positive quadratic root.

Worked example

Verified against the live calculator

A 100 mm driver sheave and 250 mm driven sheave on 400 mm centers need a V-belt pitch length of about 1364 mm. Small-sheave wrap is about 158°, the speed ratio is 2.5:1, and a 1750 RPM driver turns the driven shaft at about 700 RPM.

Frequently asked questions

How do you calculate V-belt length?

For a two-sheave open drive, use L = 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)²/(4C), where C is center distance and D₁, D₂ are the sheave pitch diameters.

Can I solve center distance from a standard V-belt length?

Yes. The same length equation rearranges to a quadratic in C. Enter the standard belt pitch length and the sheave pitch diameters, and the calculator returns the center distance that fits that belt.

Should I use outside diameter or pitch diameter?

Use pitch or datum diameter. A V-belt rides down in the sheave groove, so the belt line is below the outside rim. Using outside diameter usually makes the calculated belt too long.

Why does wrap angle matter?

The smaller sheave normally has the lower wrap angle, and that contact angle limits friction grip. If small-sheave wrap is much below about 120°, use an idler, larger center distance or a lower ratio.

Method & assumptions

Two parallel sheaves with an open, non-crossed belt path.
Diameters are pitch / datum diameters, not outside sheave diameters.
Center-distance solve uses the positive root of the open-belt length equation.
Does not check belt profile horsepower rating, groove angle, installation tension, centrifugal tension or belt manufacturer service factors.