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ChainSprocketCalc

Chain Center Distance Calculator

Enter the chain's link count and both tooth counts to get the exact shaft center distance, checked against the 30–50 pitch guideline and the 120° wrap rule.

Presets

Shaft Spacing Parameters

Pitch: 15.875 mm
PD: 86.395 in
T
PD: 227.577 in
T
Use an even number

Exact Center Distance (C)

23.9in

Other unit:607.07 mm

ASME 30–50P Window

Within

Recommended:18.75–31.25 in

This drive:38.2 pitches

Small Sprocket Wrap (θ)

166.6°≥120° OK

Chain:#50

Center distance is inside the 30–50 pitch guideline.

Chain makers recommend this range for an average drive: enough wrap on the small sprocket and a span that holds tension without whipping.

Breakdown for 108 links on #50

Center distance and sprocket dimensions
ParameterValue (in)Note
Exact center distance23.9Quadratic ASME B29.1 solution
Driver pitch diameter86.39517T
Driven pitch diameter227.57745T
30 pitches (minimum)18.75Lower guideline
50 pitches (maximum)31.25Upper guideline

The Center Distance Formula, Solved for C

The ASME B29.1 chain length equation gives links from center distance. When the link count is fixed instead, for a frame, a gearbox housing or an existing chain, it is rearranged into a quadratic in C. To go the other way and find the links for a known spacing, use the chain length calculator; for a derailleur bike, the bicycle chain length calculator also adds the extra links the rear derailleur needs.

Back-solved center distance

C = (P / 4) × [ A + √(A² − 8(N₂ − N₁)² / (4π²)) ]
A
= L − (N₁ + N₂) / 2, the links left over after both wraps
L
= fixed chain length in links
P
= chain pitch
N1, N2
= driver and driven tooth counts

Worked example: 15T/45T on 520 chain, 106 links

  1. A = 106 − (15 + 45) / 2 = 76
  2. Root term = 74.79
  3. C / P = (A + root) / 4 = 37.7 pitches
  4. C = 37.7 × 15.875 = 598.45 mm

That is 37.7 pitches, inside the 30–50 pitch guideline.

Reading the 30–50 Pitch Window

The window is a design guideline, not a hard limit. Compact drives such as swingarms and bicycle frames are often forced to the short end. Check the result against your sprockets by looking up their outside diameters in the sprocket diameter calculator.

Under 30 pitches

The small sprocket has less chain wrapped around it, so fewer teeth carry the load. If the wrap falls below 120°, expect faster tooth wear.

30 to 50 pitches

The recommended range for an average drive. It leaves enough wrap on the small sprocket and a slack span that stays controlled.

Over 50 pitches

The slack span can whip and the chain sags more. Add a guide, idler or tensioner, and consider an intermediate shaft.

Chain Center Distance FAQ

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