One of the most common situations in the workshop: you have a broken or worn gear in your hand, you need to cut a new one, but the module is unknown. The solution takes two simple measurements: count the teeth and measure the tip diameter with a caliper. The tool below calculates the module from these two values, suggests the nearest standard module, checks whether the gear might be inch/DP based, and gives you a span measurement to verify the result with a caliper.
How to find the module of a gear, step by step
On a standard spur gear the tip diameter follows dₖ = m · (z + 2); inverting the formula gives m = dₖ / (z + 2). In practice: first mark one tooth with a pen and count the teeth one by one (z). Then set the caliper across two opposite tooth tips and measure the tip diameter (dₖ); avoid burred and dented areas, measure at several points and take the largest value. Example: on a 22-tooth gear you measure dₖ = 72 mm, so m = 72 / 24 = 3 mm. If the result comes out as something like 3.02, the gear is almost certainly still module 3 — the difference is measurement and wear allowance. To settle the decision, the tool above shows the deviation percentage.
The standard module series
Modules do not take arbitrary values; cutting tools are made to a standard series. The preferred series I: 0.5 – 0.6 – 0.8 – 1 – 1.25 – 1.5 – 2 – 2.5 – 3 – 4 – 5 – 6 – 8 – 10 – 12 – 16 – 20 – 25. Series II, used when unavoidable: 0.7 – 0.9 – 1.75 – 2.25 – 2.75 – 3.5 – 4.5 – 5.5 – 7 – 9 – 11 – 14 – 18 – 22. If your calculated module is not close to either series, there are three possibilities: the gear is inch (DP) based, it is profile-shifted, or the measurement is wrong.
Getting an "odd" module? It may be a DP gear
On machines of American and British origin, gear size is defined by the diametral pitch (DP), and the module equivalents of DP gears are fractional: DP 12 → m = 2.117 · DP 10 → m = 2.54 · DP 8 → m = 3.175 · DP 6 → m = 4.233. If your calculation shows a value like 2.54 or 3.18, the gear must be cut with a DP cutter, not a metric one; a DP gear cut with a metric module cutter will not mesh properly with its mate. The tool above automatically checks the DP possibility on every calculation and highlights whichever system has the smaller deviation.
Verification with the span measurement (W)
A module derived from the tip diameter is an estimate; definitive verification is done with the span measurement (measurement over teeth, W). The caliper jaws are closed over a certain number of teeth so that they sit tangent to the tooth flanks; the theoretical value of the measured distance is W = m · cosα · [π(z_w − 0.5) + z · invα] (invα = tanα − α, in radians). This measurement has two big advantages: it is unaffected by wear on the tooth tips, and it gives an exact result on gears with odd tooth counts too. The tool automatically calculates how many teeth to measure over and the W value you should read — just close the caliper and compare.
Cases to watch out for
Odd tooth count: with an odd number of teeth the caliper cannot land on two directly opposite tips, so the measured diameter is slightly smaller than the true dₖ; in that case rely on the span measurement (the tool warns you). Profile-shifted gear: the rule dₖ = m(z+2) no longer holds; this is the most common reason for results that fit no standard value. Helical gear: if the teeth are inclined this method does not apply — on a helical gear the normal module and helix angle must be determined together; we will publish a separate tool for that. Wear: on a gear with long service life even the tooth tips wear; measuring on the less-used edge zone of the gear is more reliable.
Frequently asked questions
Which cutter do I use once I know the module?
Module milling cutters come in sets of 8, and the cutter number is chosen by tooth count: for example No. 4 for 21–25 teeth, No. 5 for 26–34 teeth. A separate tool that gives the dividing-head calculation and cutter selection on one card is coming soon.
Does this method work on internal gears?
No. On an internal gear the tip diameter is measured inward and the formula differs; measurement is done with pins. If the mating pinion is available, the most practical route is to find the pinion's module — meshing gears share the same module.
What happens if I miscount the teeth?
Even one tooth of difference changes the module noticeably: on a 72 mm gear, z=22 gives m=3.00 while z=23 gives m=2.88. Always mark the tooth you start counting from; if unsure, count twice.
This tool is intended for education and preliminary identification; it applies to standard spur gears without profile shift — verify the results before any manufacturing decision. Once you know the module, you can work out all gear dimensions with the spur gear calculator and calculate machine speeds and feeds here.
Other gear calculators: helical gear calculator · rack and pinion calculator · bevel gear calculator · gear formulas for every type