Roller Chain Length in Pitches (ANSI B29.1)
The even-link round-up and corrected center distance people skip.
Example
You enter
- Small sprocket teeth N1 17
- Large sprocket teeth N2 51
- Nominal center distance C (in) 30
- Chain pitch p (in, #40 = 0.5) 0.5
You get
- Exact chain length 154.49 pitches
- Even count to order 156 pitches (even)
- Corrected center distance 30.38 in
Details, formula, and sources
L = 2(C/p) + (N1+N2)/2 + ((N2-N1)/(2 pi))^2/(C/p) pitches. The count must come out EVEN -- an odd count forces a weaker offset (half) link -- so it is rounded UP, and then the center distance is recomputed so the chain fits with proper sag. A 17-to-51-tooth #40 drive (0.5 in pitch) at a 30 in center is 154.49 pitches -> 156 to order, with a corrected 30.38 in center (0.38 in of take-up the skipped step misses); pull the center to 20 in and it is 114.73 -> 116 pitches, 20.32 in corrected. Keep the center at least ~30 pitches for wrap. A design aid; the sprocket selection and take-up govern.
Cp = C/p; L = 2 Cp + (N1 + N2)/2 + ((N2 - N1)/(2 pi))^2 / Cp; round L up to an even L_even; A = L_even - (N1 + N2)/2; C_corr = (p/4)[A + sqrt(A^2 - 8((N2 - N1)/(2 pi))^2)].
The ANSI B29.1 roller-chain and sprocket chain-length relation, with the even-pitch round-up and corrected center distance, by name; the sprocket selection and take-up govern.
The chain-length relation is a published ANSI B29.1 / machine-design result; the tooth counts, center distance, and pitch come from the drive layout.
Estimate. AHJ and licensed professional govern.
Field names used by the API: small_teeth_n1, large_teeth_n2, center_distance_in, pitch_in, length_pitches, length_even, center_corrected_in
- Even count the pitch count is rounded up to an even number to avoid a weaker offset (half) linkANSI B29.1
- Corrected center the center distance is recomputed after the round-up so the chain fits with proper sagANSI B29.1
- Wrap the center distance should be at least about 30 pitches for good wrapchain-drive practice