SpecCalcsReference calculators for the shop floor

Chain Drive Calculator

A 15T drive turning a 45T sprocket gives a 3:1 reduction — 1500 rpm in becomes 500 rpm out, needing a 110-pitch chain. Enter your own sprockets below.

Chain drive calculator i = N₂/N₁
Drive
Ratio & driven speed
i=N2N1,n2=n1ii = \frac{N_2}{N_1}, \qquad n_2 = \frac{n_1}{i}
N₁,N₂ drive / driven teeth · n₁,n₂ input / output rpm
Chain length (pitches)
L=N1+N22+2CP+(N2N1)24π2PCL = \frac{N_1+N_2}{2} + \frac{2C}{P} + \frac{(N_2-N_1)^2}{4\pi^2}\cdot\frac{P}{C}
Round up to an even number of pitches — chains join only at full links. C centre distance · P chain pitch
Exact centre distance for that chain
C=P8[2L(N1+N2)+(2L(N1+N2))28π2(N2N1)2]C = \frac{P}{8}\left[\,2L - (N_1+N_2) + \sqrt{(2L-(N_1+N_2))^2 - \tfrac{8}{\pi^2}(N_2-N_1)^2}\,\right]

Common chain reductions (ANSI #40, C≈500 mm, 1750 rpm in)

SprocketsRatioDriven rpmChain (pitches)
15T → 15T1:1175094
15T → 30T2:1875102
15T → 45T3:1583110
15T → 60T4:1438118
17T → 34T2:1875106
17T → 51T3:1583114
19T → 38T2:1875108
21T → 63T3:1583122
12T → 60T5:1350118
14T → 42T3:1583108

How a chain drive is calculated

Everything starts from the tooth counts. The ratio is simply driven teeth divided by drive teeth, and it scales speed inversely — a 3:1 reduction cuts output speed to a third and (ideally) triples torque. That part is easy. The geometry is where a calculator earns its keep.

Why chain length rounds to whole links

A chain can only be joined at a full link. The theoretical length that fits your exact centre distance almost never lands on a whole number of pitches, so it must be rounded — and rounded up to an even number, because a roller chain closes with an inner and outer link pair. An odd number needs an offset (cranked) link, which is weaker and best avoided. The calculator does this rounding for you and reports the chain in whole pitches.

The centre-distance catch

Once the chain is rounded to a whole even length, it no longer fits your original centre distance exactly — it's usually a few millimetres off. That's why the calculator recomputes the exact centre distance for the rounded chain. You then either set your shaft centres to that value, or keep your centres and take up the small slack with a tensioner or adjustable mount. Ignoring this is the classic reason a new chain ends up either too tight or flopping loose.

Pitch diameter and clearance

The pitch diameter PD = P / sin(180°/N) sets how big each sprocket actually is — useful for checking guard clearance and that the two sprockets don't interfere at short centres. Fewer than about 17 teeth on the drive sprocket raises chordal (polygon) vibration and wear, so for smooth high-speed drives, keep the small sprocket tooth count up.

References

  1. ASME B29.1 — Precision power transmission roller chains: pitch dimensions.
  2. Machinery’s Handbook, “Chain and Sprocket Drives” — chain length and centre-distance relations.

Last reviewed: 2026-07 · Calculation method & assumptions