Chain Length & Center Distance Calculator

Chain Length & Center Distance

CE Style

Inputs

Common: 6.35, 9.525, 12.7, 15.875 mm or 1/4″, 3/8″, 1/2″, 5/8″

Key Results

Geometry & Wrap

Length formula (pitches): L = 2·(C/p) + (Z1+Z2)/2 + (Z2−Z1)² / (4π² · C/p).
Pitch diameter: d = p / sin(π/Z). Wrap angles: θₛ = π − 2α, θₗ = π + 2α, where α = asin((rₗ − rₛ)/C).

Suggested Roundings & Resulting C

How to Use the Chain Length & Center Distance Calculator

Quickly size roller-chain drives. Enter pitch and sprocket teeth, choose whether you’re solving for chain length or center distance, then review wrap angles and rounding suggestions (whole, 0.5, or even link counts).

1) Units & Solve Mode

  • Select SI (mm) or Imperial (inch).
  • Pick Solve for: Chain Length (given center C) or Center Distance (given total link count L in pitches).

2) Pitch & Teeth

  • Enter chain pitch p (e.g., 12.7 mm for 08B or 0.5" for ANSI #40).
  • Enter sprocket teeth: Z₁ (small) and Z₂ (large).
  • The tool shows speed ratio Z₂ / Z₁ in the results.

3) If Solving for Chain Length

  • Enter center distance C.
  • Calculator returns chain length L in pitches and physical length L·p.
  • Use the Rounding menu to see nearest whole / 0.5 / even link counts.
Physical chain is assembled from whole links; 0.5 link (offset link) is allowed but may reduce fatigue strength—prefer even counts where possible.

4) If Solving for Center Distance

  • Enter total chain length L as pitches (e.g., 120, 120.5).
  • Calculator returns center distance C and physical chain length L·p.
  • Compare wrap angles and adjust L if needed (see suggestions below).

5) Rounding Options

  • Nearest whole link — robust, preferred.
  • Nearest 0.5 link — uses an offset link if required.
  • Nearest even link — convenient for standard assemblies.
The calculator also shows what C would be if you adopt each rounding choice.

6) Read the Results

  • Chain length (pitches) and physical length (mm/in).
  • Speed ratio Z₂/Z₁.
  • Pitch diameters d₁, d₂ and wrap angles on each sprocket.

7) Geometry & Wrap

  • Pitch diameter: d = p / sin(π/Z)
  • Wrap: α = asin((r₂ − r₁)/C), then θₛ = π − 2α, θₗ = π + 2α
  • Aim for good wrap on the small sprocket (rule-of-thumb ≥ 120°).

8) Suggested Centers & Roundings

  • The tool lists C from exact L and from each rounding (whole / 0.5 / even).
  • Use these suggestions to pick a feasible chain length and re-position centers if needed.

Design Tips & Checks

  • Prefer Z₁ ≥ ~17 teeth for smoother action and longer life.
  • Keep centers reasonable (many designs use ~30–50 pitches as a ballpark).
  • Plan for tensioning or an idler to absorb tolerance and wear.
  • Offset links (0.5 link) are allowed but can reduce fatigue strength.
  • Check wrap on the small sprocket (≥ ~120° recommended).
  • Verify clearances and guard spacing with physical length L·p.
  • Re-check ratio after final rounding (Z₂/Z₁ unchanged, but center may shift).
  • Lubrication and alignment matter as much as the math!

Copy-Paste Mini Workflow

  1. Choose units and solve mode.
  2. Enter pitch p, teeth Z₁, Z₂, and either C or L (pitches).
  3. Read chain length/center, physical length, and wrap angles.
  4. Use rounding options and suggested centers to pick a buildable length.
  5. Validate wrap, add tensioning if needed, and finalize hardware.