Roller Chain Length Calculator (Number of Links)
Number of links for a roller chain between two sprockets from the teeth, the centre distance and the pitch, rounded up to an even number, with the centre distance you really get.
Results
The dashed line marks the value you entered.
What this tool does
The chain length in pitches is twice the centre distance in pitches, plus the mean of the two tooth counts, plus a small correction for the difference in sprocket size. It is rounded up to an even number of links, because an odd count needs a weaker offset (cranked) link; the rounding means the real centre distance is slightly longer than the one asked for, which is what the last result gives. A common guideline puts the centre distance at 30 to 50 pitches. Chain pitch is printed on the chain: ANSI #40 is 12.7 mm (½ inch), #50 is 15.875 mm.
Formula
L (pitches) = 2C ÷ p + (N₁ + N₂) ÷ 2 + p (N₂ − N₁)² ÷ (4π² C) · rounded up to an even number of links
Variables
| Symbol | Meaning | Unit |
|---|---|---|
n1 | Teeth on the small sprocket | — |
n2 | Teeth on the large sprocket | — |
c | Centre distance wanted | mm |
p | Chain pitch | mm |
LE | Links to use (rounded up to an even number) | — |
LX | Links before rounding | — |
LM | Length of the chain | mm |
CA | Real centre distance with that chain | mm |
Worked example
- Teeth on the small sprocket17
- Teeth on the large sprocket45
- Centre distance wanted500 mm
- Chain pitch12.7 mm
- Links to use (rounded up to an even number)112
- Links before rounding110.24
- Length of the chain1422 mm
- Real centre distance with that chain511.2 mm
Limitations
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.