Pinion pitch diameter
mm
Mechanics · Transmission and rotation
Gear Pitch Diameter & Center Distance Calculator
Obtain the fundamental geometry of a standard external zero-shift pair without duplicating gear ratio as an output.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
03
MetricResults
Gear pitch diameter
mm
Center distance
mm
View calculation detailsFormulas, SI conversion, numerical substitution and resultsOpen ↓
Calculation note
Full calculation details
The pair uses standard external spur gears with the same module. Profile shift is zero and center distance is nominal. Tooth counts are strictly positive integers. Internal, helical and shifted gears, backlash, tip and root geometry are excluded.
01Formulas and symbols
Formulas used
d₁
m × z₁Pinion pitch diameterd₂
m × z₂Gear pitch diametera
m × (z₁ + z₂) / 2Nominal center distance02Assumptions and limits
Scope of validity
- The pair uses standard external spur gears with the same module.
- Profile shift is zero and center distance is nominal.
- Tooth counts are strictly positive integers.
- Internal, helical and shifted gears, backlash, tip and root geometry are excluded.
03Validation example
Reference numerical case
- m = 3 mm, z₁ = 12 and z₂ = 24 give d₁ = 36 mm and d₂ = 72 mm.
- The nominal center distance is a = 54 mm.
04Frequently asked questions
Questions about the calculation
Why is d = m × z?
For standard metric gearing, module is pitch diameter divided by tooth count.
Can I enter a fractional tooth count?
No. A physical gear has an integer number of teeth.
Does this formula cover shifted gears?
No. Profile shift or a different operating pressure angle requires a fuller center-distance model.
05References
Technical references
- KHK Gears, Calculation of Gear Dimensions, table 4.1.
- SDP/SI, Elements of Metric Gear Technology, table 4-1.