Belt Drive Ratio Calculator
Calculate driven pulley RPM, torque ratio, and belt length for a two-pulley belt drive.
Useful for HVAC, machine tools, and power transmission design.
Belt Drive Ratio
A belt drive transmits rotation between two pulleys at a speed ratio set by their relative diameters. A small drive pulley turning fast pulls a larger driven pulley slowly with proportionally more torque.
Speed Ratio
N₂ = N₁ × (D₁ / D₂)
Where:
- N₁ = drive pulley RPM
- N₂ = driven pulley RPM
- D₁ = drive pulley diameter
- D₂ = driven pulley diameter
Torque Relationship
Power is conserved between the two shafts (minus belt slip and friction losses):
T₂ = T₁ × (D₂ / D₁) × η
where T is torque and η is efficiency (typically 95–98% for V-belts, 99% for synchronous timing belts).
Belt Length (open belt, no crossing)
L ≈ 2 × C + π × (D₁ + D₂) / 2 + (D₂ − D₁)² / (4 × C)
where C is the center distance between pulley shafts. This formula is exact for slack-free belts; real belts need a small tensioning allowance.
Worked Example — 2:1 Step-Down
A 1750 RPM motor with a 75 mm drive pulley turns a 150 mm driven pulley.
- N₂ = 1750 × (75 / 150) = 875 RPM
- Torque ratio: T₂ / T₁ = 150 / 75 = 2 (with ideal efficiency)
If the motor delivers 5 N·m, the driven shaft sees ~10 N·m at 95% efficiency = 9.5 N·m.
Common Belt Types
| Belt | Use | Typical η |
|---|---|---|
| V-belt | HVAC, agricultural | 92–96% |
| Synchronous (timing) | CNC, robotics, automotive cams | 97–99% |
| Flat belt | Long-distance drives, conveyors | 95–98% |
| Round belt | Light machinery | 90–95% |
| Ribbed (Poly-V) | Auto accessory drives | 95–97% |
Belt Speed
V_belt = π × D₁ × N₁ / 60 (m/s, with D₁ in m and N₁ in RPM)
V-belts are typically rated for 5–25 m/s. Above ~30 m/s, centrifugal stretch and heat become limiting.
Wrap Angle
The angle that the belt contacts each pulley is the wrap angle. For open belts, the smaller pulley has the smaller wrap angle:
θ_wrap = π − 2 × arcsin((D₂ − D₁) / (2 × C))
Belts slip if the wrap angle drops below ~120°. That sets a practical lower bound on center distance for big speed ratios.
Caveats
The formulas assume rigid pulleys, no belt slip, and steady-state operation. Real belts stretch ~0.5–1% under load (creep), causing the actual ratio to be slightly different from the geometric ratio. For high-precision applications, use a synchronous timing belt — its teeth eliminate slip and creep entirely.