About the Belt Length Calculator
This belt length calculator finds the length of belt needed to go around two pulleys. Enter the pitch diameters of the large and small pulleys and the distance between their centres, choose an open or crossed (figure-eight) belt, and it returns the exact belt length, the wrap angle on each pulley, the speed ratio and — if you add the driver speed — the driven pulley RPM and the belt speed. Enter a stock belt length to work back to the centre distance it needs.
It is handy for replacing V-belts and timing belts on lathes, drill presses, mowers, fans, compressors and conveyors, designing a new drive, or setting up adjustable motor mounts. Belt suppliers sell by length, so knowing the exact length avoids ordering the wrong size.
Use pitch diameters (where the belt’s neutral layer runs) for V-belts and timing belts; outside diameters will slightly overstate the length. The result is a pitch length: V-belt part numbers may refer to outside or inside length depending on the belt section. Keep the wrap angle on the small pulley above about 120° to avoid slipping.
With the default inputs, the belt length (exact) is 59.05. Change any value above to recalculate instantly.
How to use the belt length calculator
- 1Choose inches or millimetres and enter both pulley pitch diameters.
- 2Measure and enter the centre-to-centre distance between the shafts.
- 3Choose an open or crossed belt.
- 4Optionally enter which pulley drives and its RPM for speeds.
- 5Read the belt length, or enter a stock belt length to find the centre distance it needs.
Formula and method
The exact length adds the two straight spans between the tangent points (each C·cos φ) to the arcs wrapped around each pulley. For an open belt the small pulley is wrapped through 180° − 2φ and the large one through 180° + 2φ; for a crossed belt both are wrapped through 180° + 2φ, which is why crossed belts are longer.
The widely quoted approximation 2C + 1.57(D + d) + (D − d)²/4C is shown for comparison and is very close when the centre distance is large. To find the centre distance for a stock belt length, the calculator solves the exact equation numerically by bisection. Speed ratio is the ratio of pitch diameters, and belt speed is π × driver diameter × RPM.
- L
- Belt pitch length
- C
- Centre distance between shafts
- D, d
- Large and small pulley pitch diameters
- φ
- Belt angle from the line of centres (radians)
Worked examples
8" and 4" pulleys, 20" apart, open belt
φ = asin(4 ÷ 40) ≈ 5.74°. The straight spans total 2 × 20 × cos φ ≈ 39.80 in, the arcs add π × 12 ÷ 2 ≈ 18.85 in plus φ × 4 ≈ 0.40 in, for about 59.05 in. The small pulley is wrapped 168.5°, and 1,750 RPM on the 4" driver turns the 8" pulley at 875 RPM.
Crossed belt on the same pulleys
With a crossed belt φ = asin(12 ÷ 40) ≈ 17.46°, so each pulley is wrapped about 214.9°. The belt must be about 60.66 in long — roughly 1.6 in longer than the open layout — and the driven pulley turns in the opposite direction.
Centre distance for a 1,000 mm belt, 150 and 75 mm pulleys
At 300 mm centres the belt would be about 958 mm. Solving the exact equation for a 1,000 mm stock belt gives a centre distance of about 321 mm, so the motor mount needs to slide out roughly 21 mm.
Frequently asked questions
How do you calculate belt length for two pulleys?+
For an open belt, a good approximation is L = 2C + 1.57(D + d) + (D − d)² ÷ 4C, where C is the centre distance and D and d are the pulley diameters. This calculator also gives the exact value using the tangent geometry.
Should I use the pulley’s outside or pitch diameter?+
Use the pitch diameter — where the belt’s load-carrying cords run. For V-belts it is slightly smaller than the outside diameter of the sheave; for timing belts it equals the pitch × number of teeth ÷ π. Using outside diameters overstates the length.
What is the minimum wrap angle for a V-belt?+
Designers generally aim for at least 120° of wrap on the small pulley. Below that the belt’s grip drops and power capacity must be derated, or the belt will slip. Increasing the centre distance or adding an idler increases wrap.
How much longer is a crossed belt?+
A crossed belt wraps more of each pulley, so it is longer than an open belt: for the same pulleys the difference is roughly D·d ÷ C. Crossed belts reverse the direction of rotation and are mainly used with flat or round belts.
How do I measure a belt I already have?+
Wrap a flexible tape around the outside of the belt to get its outside length, or run a string around the pulleys at the belt’s position. For V-belts, pitch length is typically a little less than outside length — check the manufacturer’s conversion for the belt section.