How to Measure a Gear and Find Its Module
You have a worn or broken gear and no drawing. With a caliper, a tooth count and one formula you can identify the module and tell a gear manufacturer exactly what you need.
- m = da / (z + 2)standard spur gear
- d = m × zpitch diameter
- DP = 25.4 / mmodule to diametral pitch
- 20°usual pressure angle
What Is the Module of a Gear?
The module is the size of the teeth. It is the pitch diameter in millimetres divided by the number of teeth, so a gear with 40 teeth and a 120 mm pitch diameter has module 3. Two gears only mesh if they share the same module and pressure angle.
Metric gears are specified by module (m). Gears designed in inches use diametral pitch (DP), the number of teeth per inch of pitch diameter. The two convert with DP = 25.4 / m, so module 2 is DP 12.7 and DP 8 is module 3.175.
Modules follow a standard series, and that is what makes identification possible: once your calculation lands close to a standard value, you have very likely found it.
Formulas at a glance
- Pitch diameterd = m × z
- Tip diameterda = m × (z + 2)
- Modulem = da / (z + 2)
- Centre distancea = m × (z1 + z2) / 2
- Diametral pitchDP = 25.4 / m
- Common modules1 · 1.5 · 2 · 2.5 · 3 · 4 · 5 · 6 · 8 · 10
- Valid forstandard spur gears
How Do You Measure the Module of a Spur Gear?
You need a caliper and five minutes. The method works for standard external spur gears.
- Count the teethMark one tooth and count all the way round. Count twice: one tooth off changes the result.
- Measure the tip diameterMeasure across the tooth tips through the centre. With an odd tooth count, measure from the bore wall to a tip, double it and add the bore diameter.
- CalculateDivide the tip diameter by the tooth count plus two. 126 mm and 40 teeth gives 126 / 42 = module 3.
- Compare with the seriesA result of 2.96 is module 3 with worn tips. A result far from any standard value points to an inch gear or a profile-shifted gear.
- Check the mating gearCount its teeth and measure the centre distance between the shafts. For standard gears it equals m × (z1 + z2) / 2.
Which Dimensions Does a Gear Manufacturer Need?
The teeth are only half of the part. These are the dimensions we ask for when there is no drawing.
| Dimension | How to get it | Why it matters |
|---|---|---|
| Number of teeth | Count, on both gears of the pair | Fixes the ratio and, with the module, the diameter |
| Tip diameter | Caliper across the tooth tips | Gives the module |
| Face width | Caliper along the tooth | Load capacity and fit in the housing |
| Bore and keyway | Caliper or bore gauge; keyway width and depth | The gear has to fit the shaft |
| Helix angle and hand | Photograph the teeth from above; note left or right hand | Helical gears only mesh with the correct angle and hand |
| Centre distance | Between the two shaft centres in the housing | Confirms the module and shows any profile shift |
| Hub, shoulders, bolt holes | Sketch with dimensions, or photos with a ruler | Everything apart from the teeth |
| Hardness, if you can test it | Portable hardness tester or file test | Points to the original heat treatment |
What About Helical, Worn or Modified Gears?
Helical gears
On a helical gear the formula uses the normal module, measured at right angles to the tooth. The tip diameter becomes da = mn × z / cos β + 2 × mn, where β is the helix angle. Measure the angle as well as you can and compare the result with the standard series; the right combination of module and angle usually stands out. More on helical gears.
Worn teeth
Wear removes material from the tips and flanks, so a worn gear measures small. Use the less worn gear of the pair, usually the larger one, and trust the centre distance more than a damaged tooth.
Span measurement
A more exact method is the span over several teeth, taken with a caliper or a disc micrometer. Measure across k teeth and across k + 1 teeth. The difference is the base pitch, and for a 20° pressure angle the module is that difference divided by 2.952.
Profile shift and special teeth
Pinions with few teeth are often cut with profile shift, and some gearboxes use non-standard pressure angles. The tip diameter then no longer fits the simple formula. In these cases we measure the part ourselves and prepare a drawing for your approval before anything is cut.
Questions About Measuring Gears
What is the formula for the module of a gear?
Module is the pitch diameter divided by the number of teeth. For a standard spur gear you can calculate it from the tip diameter: m = da / (z + 2), with the diameter in millimetres.
How do I convert module to diametral pitch?
DP = 25.4 / module, and module = 25.4 / DP. Module 4 is DP 6.35, and DP 10 is module 2.54. If your result is not a standard module, check whether it is a round DP value.
My result is not a standard module. What now?
Worn tips give a slightly low result, so look at the nearest standard value above it first. If it still does not fit, the gear may be an inch-series gear, a helical gear or a gear with profile shift. Send us the measurements and photos and we work it out.
Can you make a gear from a sample or from photos?
Yes. From a worn part, or from photos with the main dimensions, we determine the gear data, prepare a drawing for your approval and manufacture the gear. See replacement gears.
Should I replace one gear or the pair?
If the mating gear is also worn, a new gear runs on a damaged flank and wears quickly. Send photos of both gears and we tell you whether one part is enough.
Have the gear but no drawing?
Send photos and the main dimensions. We identify the gear and quote the new one.
Send your measurements. Get an answer within 24 hours.
Tooth count, tip diameter, face width, bore and a few photos are enough to start. We reply with questions or a quotation.