How to use this calculator
- Choose the size system. Pick metric module (mm) or imperial diametral pitch (1/in) and enter its value.
- Set the pressure angle. Choose the pressure angle — 20° is standard.
- Enter the tooth counts. Enter this gear’s tooth count, and the mating gear’s count for the center distance.
- Add a profile shift if needed. Add a positive profile shift to avoid undercut on low tooth counts.
- Read and export. Read the diameters, pitch, tooth thickness, center distance and backlash, view the tooth-profile render, and export the profile as DXF.
How it works
An involute spur gear is defined by its module m (or
diametral pitch), pressure angle α and
tooth count z. The pitch diameter is
d = m · z
and the tooth flanks are involutes of the base circle d_b = d·cos α.
Standard full-depth teeth use addendum a = m, dedendum
b = 1.25 m and clearance 0.25 m, giving a tip diameter
d_a = d + 2m and root diameter d_f = d − 2.5m. The tooth
thickness at the pitch circle is s = m·(π/2 + 2x·tan α), where
x is the profile-shift coefficient.
With a mating gear, the standard center distance is a = m·(z + z₂)/2.
When a profile shift is applied the gears run on a larger working pressure
angle α_w, found by inverting the involute function
inv α = tan α − α; the calculator solves it numerically and adjusts the
center distance accordingly. It also flags undercut — at 20° a
standard tooth is undercut below about 17 teeth unless you add a positive shift.
The involute gear route is the short search path
for this calculator, geometry guide and DXF workflow. The
involute gear geometry guide
maps each input to the pitch, base, tip and root diameter formulas, and the
involute gear formula page gives the shorter
equation-first route for profile and tooth-geometry searches.
For only the generating-circle math, use the base circle diameter calculator. To export the full outline as a standalone workflow, use the gear generator. For module/DP conversion alone, use the gear module calculator or the module versus diametral pitch guide. After geometry, use the gear ratio calculator for speed and torque and the gear mesh force calculator for shaft and bearing loads.
Gear tooth profile, DXF and generator searches
Searchers use several names for this workflow: gear tooth profile calculator, gear tooth geometry calculator, spur gear geometry calculator, involute gear DXF and involute gear generator. They all point to the same core geometry: pitch, base, tip and root diameters, tooth thickness, pressure angle and the sampled involute flank. Use the calculator above when you want the numeric dimensions and a quick DXF outline from the same inputs.
Worked example
Verified against the live calculator
A module-2 mm, 20° pressure-angle pinion with z = 20 teeth meshing with
a z₂ = 40 gear, no profile shift. The pitch diameter is
d = 40 mm, base diameter 37.59 mm, tip diameter
44 mm and root diameter 35 mm. The tooth thickness at the
pitch circle is π ≈ 3.14 mm, the circular pitch is
6.28 mm, and the center distance is m·(z+z₂)/2 = 60 mm.
With 20 teeth there is no undercut (the 20° minimum is ≈ 17). The render and DXF show
this exact profile.
Reference data
Preferred metric modules (ISO 54, series 1), with the circular pitch and the approximate equivalent diametral pitch. Sticking to a preferred module makes tooling, mating gears and replacements easier to source.
| Module (mm) | Circular pitch (mm) | ≈ Diametral pitch (1/in) | Notes |
|---|---|---|---|
| 1 | 3.142 | 25.4 | Fine-pitch instruments and small mechanisms. |
| 1.25 | 3.927 | 20.3 | |
| 1.5 | 4.712 | 16.9 | |
| 2 | 6.283 | 12.7 | Common general-machinery module. |
| 2.5 | 7.854 | 10.2 | |
| 3 | 9.425 | 8.47 | |
| 4 | 12.57 | 6.35 | |
| 5 | 15.71 | 5.08 | |
| 6 | 18.85 | 4.23 | |
| 8 | 25.13 | 3.18 | |
| 10 | 31.42 | 2.54 | Heavy power transmission. |
| 12 | 37.7 | 2.12 | |
| 16 | 50.27 | 1.59 | |
| 20 | 62.83 | 1.27 |
Source: ISO 54 preferred-module series. Diametral pitch shown for reference; DP gears use their own standard series.
Frequently asked questions
How do I calculate involute gear tooth geometry?
From the module m and tooth count z: pitch diameter d = m·z, addendum = m, dedendum = 1.25 m, tip diameter = d + 2m and root diameter = d − 2.5 m. Enter the module (or diametral pitch), pressure angle and tooth count above and the calculator returns the full geometry.
What is the difference between module and diametral pitch?
Module (mm) is the pitch diameter divided by the number of teeth; diametral pitch (1/in) is the number of teeth divided by the pitch diameter in inches. They are reciprocals scaled by 25.4: m = 25.4 / DP. Use the size-system selector to enter whichever your drawing uses.
Which pressure angle should I use?
20° is the modern standard and the right default. 14.5° is legacy (older equipment); 25° gives a stronger tooth but more separating force and noise. Mating gears must share the same module and pressure angle.
How many teeth can I have before undercut?
For a standard 20° tooth, undercut begins below about 17 teeth. Use more teeth, or add a positive profile shift. The calculator warns when undercut is likely and suggests the minimum shift coefficient.
What does the DXF export give me?
It downloads the exact involute tooth profile of the gear as a closed polyline (LWPOLYLINE), ready to open in CAD/CAM for laser, waterjet or wire-EDM cutting — the part that gear-generator searches actually want.
Does this work in metric and imperial?
Yes — toggle SI/Imperial in the header to switch diameters between mm and inches. The module-versus-diametral-pitch choice is separate, set by the size system.
Method & assumptions
- Standard full-depth involute profile (addendum = m, dedendum = 1.25 m). Stub or non-standard tooth systems differ.
- The profile-shifted center distance assumes the mating gear is unshifted; for a shifted pair, use the sum x₁ + x₂.
- Recommended backlash is a module-based rule of thumb (≈ 0.03–0.05 × module); real backlash is set by tooth-thickness allowance and the actual center distance and its tolerance.
- The DXF profile is a geometric involute with a simplified root fillet — verify cutter path, backlash, strength and tolerance requirements before production.