Spur Gear Dimensions Calculator
Enter the module, tooth counts and pressure angle and this calculator returns the pitch, outside, root and base diameters, whole depth, circular pitch and center distance for a standard spur gear pair. It is what a machinist, programmer or estimator needs to size the blank and set the shaft spacing.
Your numbers
Pitch diameter divided by tooth count. Choose a standard value, see the module reference table.
The selection stores the cosine of the angle, which is what the base circle formula needs.
Your results
Geometry for standard full-depth, zero-shift involute spur gears (addendum 1 m, dedendum 1.25 m). Profile shift, undercut limits and tooth strength are not checked.
Center distance and gear outside diameter vs module
Sweeps Module from 1 to 10, holding your other inputs fixed.
Keep gear data in your ERP
Optional: a short review of how gear specifications could be stored and searched in your item master and routings.
Optional. The tool and every export work without this. No spam.
How to use it
Pick a standard module (see the related module table), then enter the number of teeth on the gear and pinion. Choose the pressure angle: 20 degrees is the modern default and 14.5 degrees appears on older equipment. Add face width and pinion speed to get pitch line velocity. The outside diameter is the blank size to turn before cutting, and the center distance is the bore spacing for the housing. The chart shows how both grow linearly with module.
Formulas and conventions
For a standard full-depth gear: pitch diameter d = m x z, outside diameter da = m x (z + 2), root diameter df = m x (z - 2.5), whole depth h = 2.25 m, circular pitch p = pi x m, and base diameter db = d x cos(pressure angle). Center distance a = m x (z1 + z2) / 2. These follow ISO 54 and ISO 53 proportions and match the usual metric handbook formulas. Diametral pitch in inch units is 25.4 divided by module.
- Addendum equals one module
- Dedendum equals 1.25 modules
- Tooth thickness at the pitch circle is pi x m / 2 with no backlash
Reading the result
With module 3, a 48-tooth gear and a 16-tooth pinion, the pitch diameters are 144 mm and 48 mm, the center distance is 96 mm and the ratio is 3:1. A pinion with 16 teeth at 20 degrees is just under the 17-tooth limit where undercut starts, so consider 17 or more teeth, or profile shift. Pitch line velocity above roughly 5 m/s usually calls for ground or at least shaved teeth and oil lubrication rather than grease.
Common mistakes
Mixing module and diametral pitch is the classic error: a 3 module gear is not a 3 DP gear. Another is ordering a blank at pitch diameter instead of outside diameter. Gear pairs must share module and pressure angle, and real drives need backlash allowance, so cut center distance tolerance and tooth thickness reduction must be specified on the drawing and on the purchase order.
Frequently Asked Questions
How do I calculate the outside diameter of a spur gear?
Multiply the module by the number of teeth plus two. For module 3 and 48 teeth the outside diameter is 3 x 50 = 150 mm. In diametral pitch units the formula is (N + 2) divided by DP, in inches.
How do I calculate center distance between two spur gears?
Add the two pitch diameters and halve the result, which equals module times the sum of both tooth counts divided by two. Add a small tolerance or backlash allowance from your tolerancing practice before finalizing bore positions.
What is the difference between module and diametral pitch?
Module is pitch diameter in millimeters per tooth, while diametral pitch is teeth per inch of pitch diameter. They are reciprocal systems: module equals 25.4 divided by DP. Gears can only mesh if they share the same module and pressure angle.
Why does the calculator ask for pressure angle?
Pressure angle sets the base circle diameter, which defines the involute profile, and affects tooth strength and bearing load direction. Meshing gears must have the same pressure angle. Twenty degrees is the common standard for new designs.
If gear dimensions live in drawings and spreadsheets while your ERP routings and item masters are retyped by hand, Netray can help connect the two.
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Guides
- How to Estimate the Cost of a Custom GearHow gear manufacturers estimate a custom gear quote: blank, hobbing, heat treat, grinding, inspection and outside processing, and where estimates go wrong.
- Gear Inspection Reports and AGMA Quality Classes: What to IncludeWhat belongs in a gear inspection report: lead, profile, pitch, runout and tooth thickness against AGMA 2015-1 or ISO 1328, and how to automate the paperwork.
- ERP for Gear Manufacturers: What to Look ForERP for gear manufacturers: routings with heat treat and grind, heat lot traceability, outside processing, gear inspection records and what job shop ERPs miss.