Pulley Belt Length & Speed Ratio Calculator

This uses the standard machine-design formula for a belt's pitch length around two pulleys a center distance C apart: for an open (uncrossed) belt, L = 2C + (π/2)(D₁+D₂) + (D₁-D₂)² ÷ (4C); for a crossed belt, the correction term uses (D₁+D₂)² instead of (D₁-D₂)². This is the widely published approximation of the exact tangent-and-arc geometry (found in Shigley's Mechanical Engineering Design and Machinery's Handbook) — it's accurate whenever the center distance is reasonably large relative to the difference in pulley size, which covers essentially every real belt drive, and it's the formula belt manufacturers' own length calculators use.

Speed ratio follows from no-slip rolling contact: both pulleys' rims move at the same linear (surface) speed, so driven RPM = driver RPM × (driver diameter ÷ driven diameter) — a smaller driven pulley always spins faster than a larger driver, and vice versa. An open belt keeps both pulleys turning the same direction; a crossed belt flips the driven pulley's rotation relative to the driver, which is the whole point of crossing it in drives where that matters (e.g. reversing a shaft without extra gearing).

Diameters and center distance share this page's metric/imperial toggle (mm or in); RPM is left un-toggled since it's already a plain rate with no unit-system counterpart to convert.