Sprocket Pitch Diameter (ANSI B29.1)
The pitch diameter a sprocket blank is laid out from, straight from the chain pitch and tooth count.
Example
You enter
- Chain pitch p (in, #40 = 0.5) 0.5
- Sprocket teeth N 17
You get
- Pitch diameter 2.7211 in
- Max outside (tip) diameter 2.9748 in
Details, formula, and sources
PD = p / sin(180 deg / N). It is the circle through the chain-pin centers when the chain wraps, and it -- not the tip diameter -- sets the drive's speed ratio and center distance. A 17-tooth #40 sprocket (0.5 in pitch) is 2.7211 in pitch diameter, with a maximum outside (tip) diameter OD = p(0.6 + cot(180 deg / N)) = 2.9748 in to turn the blank. A design aid; the manufacturer's tooth form and hub govern the sprocket you cut.
PD = p / sin(180 deg / N); OD = p (0.6 + cot(180 deg / N)).
The ANSI B29.1 roller-chain sprocket pitch-diameter and maximum-outside-diameter relations, by name; the manufacturer's tooth form and hub govern.
The sprocket pitch-diameter and outside-diameter relations are published ANSI B29.1 / machine-design results; the chain pitch and tooth count come from the drive selection.
Estimate. AHJ and licensed professional govern.
Field names used by the API: chain_pitch_in, tooth_count_n, pitch_diameter_in, outside_diameter_in
- Pitch diameter the pitch diameter runs through the chain-pin centers and sets the speed ratio and center distanceANSI B29.1
- Outside diameter the maximum tip diameter to turn the blank is OD = p(0.6 + cot(180 deg / N))ANSI B29.1
- Design aid the manufacturer's tooth form, tolerance, and hub dimensions govern the finished sprocketscope of this tile