V-Belt / Timing Belt — Length & Center Distance
CE Style
Inputs
Pitch diameter
Key Results
Geometry & Wrap
Formula: L = 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)²/(4C). Wrap on small pulley: θₛ = π − 2·asin(|D₂ − D₁|/(2C)).
How to Use the V-/Timing Belt Length & Center Distance Calculator
Quick steps to size belt length or shaft center distance for two-pulley drives. Works for V/flat belts using pitch diameters and for timing belts using pitch & tooth counts, with wrap and speed ratio shown.
1) Select Mode & Units
- Units: SI (mm) or Imperial (in).
- Belt Type: V-/Flat (uses pitch diameters) or Timing (uses tooth pitch & counts).
- Solve For: choose Length L (enter C) or Center C (enter L or belt teeth).
For V-belts, always work with pitch diameter (not OD). Timing pulleys compute pitch diameter from pitch × teeth.
2) Enter Pulley Data
- V-/Flat: enter D₁ and D₂ (pitch diameters) and optionally the center C or length L depending on the solve mode.
- Timing: enter pitch p (e.g., 5 mm, 3/8 in) and teeth N₁, N₂. The tool derives pitch diameters automatically.
- Enter input speed n₁ to see output speed n₂ from the ratio.
3) Solve for Length (L)
- Select Solve For = Length and enter C plus pulley data.
- Length uses:
L = 2C + (π/2)(D₁ + D₂) + (D₂ − D₁)²/(4C). - Timing mode: the calculator also shows nearby discrete tooth counts that approximate the continuous L.
4) Solve for Center Distance (C)
- Select Solve For = Center and enter a belt length L.
- Timing mode: you may enter belt teeth Nbelt instead — L = Nbelt·p.
- The tool inverts the length equation numerically (bisection) to find C.
- If C ≤ |D₂ − D₁|/2, wrap becomes invalid — increase C or change pulley sizes.
5) Wrap & Ratio
- Small-pulley wrap:
θₛ = π − 2·asin(|D₂ − D₁|/(2C))(shown in degrees). - Rule-of-thumb: keep wrap on the small pulley ≥ 120° for V-/flat; for timing belts, aim for ≥ 6 teeth engaged.
- Speed ratio: Timing → N₂/N₁; V/flat → D₂/D₁. Output speed n₂ = n₁/ratio.
6) Timing Belts (Discrete)
- Belts come in discrete lengths (integer teeth). The tool lists the nearest lower & higher tooth counts and the C they produce.
- Pick the belt that gives acceptable C and wrap; add a tensioner or adjust center distance as needed.
Quick Checklist
- Using pitch diameters (V/flat) or correct pitch & teeth (timing)
- Chosen solve mode matches the input you provided (L or C)
- Wrap on small pulley meets guideline
- Speed ratio and n₂ are reasonable
- Timing: selected Nbelt is an available size
- C is not near |D₂ − D₁|/2 (avoid very small C)
- Provision for tensioning or belt stretch
- Units consistent across all entries
FAQ & Tips
OD vs pitch diameter?
Use pitch diameter for calculations. Many catalogs list it; for timing pulleys the tool derives it from pitch & teeth.
Length is between two catalog sizes.
Pick the nearest catalog belt and adjust C (or use a tensioner). The timing section shows both directions.
Wrap angle is low.
Increase C, reduce diameter difference, add an idler, or swap pulley sizes to improve wrap.
Speed is off target.
Adjust D₁/D₂ (or N₁/N₂) to move the ratio, then recompute L or C.
