How to use this calculator
- Choose pitch system. Select module, diametral pitch or circular pitch.
- Enter pitch value. Enter the pitch value shared by both gears.
- Enter tooth counts. Enter pinion and gear teeth.
- Read center distance. Read center distance, pitch diameters and gear ratio.
How it works
Pitch diameter is d = m·z. For two meshing external spur gears, the
standard center distance is half the sum of their pitch diameters:
a = (d₁ + d₂) / 2 a = m · (z₁ + z₂) / 2
In diametral pitch, the same relation is a(in) = (z₁ + z₂)/(2·DP).
Worked example
Verified against the live calculator
A 20-tooth pinion and 40-tooth gear with module 2 mm have pitch
diameters 40 mm and 80 mm. Center distance is
(40 + 80) / 2 = 60 mm, and the ratio is 40 / 20 = 2:1.
Frequently asked questions
How do you calculate gear center distance?
For standard unshifted external spur gears, center distance is half the sum of the pitch diameters: a = (d₁ + d₂)/2. With module, that becomes a = m·(z₁ + z₂)/2.
What is the center distance formula for diametral pitch?
In inches, a = (z₁ + z₂)/(2·DP), where z₁ and z₂ are the two tooth counts and DP is diametral pitch.
Do both gears need the same pitch?
Yes. Meshing spur gears must share the same module or diametral pitch and pressure angle. Tooth counts can differ, but pitch system cannot.
Is center distance the same as pitch diameter?
No. Each gear has its own pitch diameter. The center distance between two standard external gears is the sum of their pitch radii.
Can profile shift change center distance?
Yes. Profile shift and a changed working pressure angle can alter operating center distance. This page gives the standard unshifted reference distance.
Method & assumptions
- External spur gears with standard unshifted reference pitch diameters.
- Both gears share the same pitch and pressure angle.
- Backlash allowance, profile shift, helix angle and tolerance stack are not included.