Unshifted Spur Gear Reference Geometry
Calculate reference circles, pitch and center distance from entered module, tooth counts and tooth-height coefficients.
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Result
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Calculation steps
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How to calculate
Use unshifted spur-gear reference geometry. Calculate pitch, base, outside/root diameters and the nominal center distance for the two entered tooth counts.
Pitch diameter=m×z; base diameter=pitch×cos(pressure angle); outside=m(z+2ha); root=m(z−2hf)
Worked example
Module 2 mm with 20 teeth gives pitch diameter 40 mm. Addendum coefficient 1 and dedendum 1.25 give outside 44 mm and root 35 mm; pairing 40 teeth gives center distance 60 mm.
Assumptions and input details
Reference geometry only; no involute tooth coordinates, profile shift, helical angle, undercut check, mesh compatibility, strength or safe operating load. Coefficients are entered choices, not a claim of a particular standard. Thickness reduction applies only to this gear’s reference tooth thickness, not an inferred allocation of pair backlash.
References: KHK: reference gear dimensions
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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