V-Belt / Timing Belt — Length & Center Distance Calculator

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.