Spur Gear Center Distance CalculatorGEAR CENTER DISTANCE

1. 1Enter the module m (the same for both gears).
2. 2Enter the pinion and wheel tooth counts.
3. 3Optionally enter profile shifts x1, x2 and pick the pressure angle.
4. 4Read the centre distance and diameters; check the undercut and contact-ratio notes.
5. 5Use “Generate gear” to open the spur-gear generator with these parameters and download STEP / STL.

Two standard (unshifted) spur gears mesh with their pitch circles tangent, so the centre distance is a0 = m(z1+z2)/2. With profile shifts x1 and x2, the operating pitch circles differ from the reference ones: solve inv αw = 2(x1+x2)tan α/(z1+z2) + inv α for the working pressure angle, then a = a0·cos α/cos αw. The modification coefficient y = (a − a0)/m tells you how many modules the centre distance grew.

At 20° a gear with fewer than 17 teeth is undercut; a positive shift of roughly x ≈ (17 − z)/17 fixes it (about 32 teeth at 14.5°). Tip diameters here are not shortened, so check the tip clearance (≈ 0.25m) for large shifts. For FDM printing keep the module at 1 or above; below 0.5 use resin (SLA). After generating, send the gears to Orinovate for a quote in nylon, POM or metal.

a0 = m (z1 + z2) / 2
inv αw = 2 (x1 + x2) tan α / (z1 + z2) + inv α, inv θ = tan θ − θ
a = a0 · cos α / cos αw
y = (a − a0) / m
d = m z, db = d cos α
da = d + 2m (1 + x), df = d − 2m (1.25 − x)

Results are for design reference only; confirm against supplier catalogues and the applicable standards before manufacturing.