Formulas
Driven RPM = driver RPM × driver dia ÷ driven dia
Belt speed = π × driver dia × driver RPM ÷ 12 (ft/min)
Belt length ≈ 2C + π(D + d) ÷ 2 + (D − d)² ÷ 4C
Wrap angle = 180° − 2 × asin((D − d) ÷ 2C)
Use pitch diameters, where the belt actually rides, not outside diameters. For classical A and B section sheaves, pitch diameter is roughly 0.25–0.35 in less than the OD.
Worked example
A 1,750 rpm motor with a 4 in sheave driving an 8 in sheave turns the shaft at 875 rpm, a 2:1 reduction. Belt speed is π × 4 × 1,750 ÷ 12 = 1,833 ft/min. At 18 in centers the belt is 55.1 in long.
Design guidelines
- Classical V-belts work best around 4,000–5,000 ft/min and shouldn't exceed 6,500 ft/min on standard cast-iron sheaves.
- Keep at least 120° of wrap on the small sheave to avoid slipping.
- Center distance is usually at least the larger sheave diameter and no more than about three times the sum of both diameters.
Frequently asked questions
- How do I slow down a motor-driven fan with pulleys?
- Use a smaller motor sheave or a larger fan sheave. Fan airflow changes in proportion to speed, but power changes with the cube, so a 10% speed cut saves about 27% power.
- Why doesn't my measured speed match exactly?
- V-belts slip 1–3% under load, and motors run slightly below their synchronous speed. 1,750 rpm on a nameplate is already the loaded speed.
Results are estimates for planning and education. Verify against the current code edition your jurisdiction has adopted, manufacturer data and a licensed professional before you build or install.