Two parameters define gear interchangeability more than any other: module and pressure angle. Choose them correctly and your gears mesh perfectly; choose them wrong and nothing fits. This guide explains both from first principles and gives clear selection criteria for every common application.
Module (symbol m, unit mm) is the fundamental size parameter of a metric gear. It defines the ratio of the pitch circle diameter to the number of teeth:
d = m × z
where d is the pitch diameter (mm) and z is the tooth count. A module 2 gear with 20 teeth has a pitch diameter of 40 mm. Double the module and you double every linear dimension of the tooth — height, thickness, and the gear's diameter for the same tooth count.
Module is also the metric equivalent of the imperial diametral pitch (DP): m = 25.4 / DP. A 12.7 DP gear is equivalent to module 2. The two systems are incompatible — a module 2 gear will not mesh with a 12.7 DP gear even though the numbers look related.
ISO 54 defines two series of preferred modules. Always choose from Series 1 first; use Series 2 only when a Series 1 value is mechanically unsuitable.
| Series 1 (preferred) | Series 2 (secondary) |
|---|---|
| 0.5, 0.8, 1, 1.25 | 0.6, 0.7, 0.9, 1.125 |
| 1.5, 2, 2.5, 3 | 1.75, 2.25, 2.75 |
| 4, 5, 6, 8, 10 | 3.5, 4.5, 5.5, 7, 9 |
Choosing standard modules ensures that hobbing cutters, gear shaper cutters, and inspection gauges are readily available. Non-standard modules require custom tooling and significantly increase manufacturing cost.
There is no single formula that gives the optimal module — it depends on load, material, speed, and manufacturing method. However, these practical guidelines cover the vast majority of design cases:
| Application | Typical module | Notes |
|---|---|---|
| Precision instruments, watches | 0.1 – 0.5 | Requires CNC gear grinding or hobbing |
| Small RC/hobby mechanisms | 0.5 – 1 | Common in servo mechanisms and robot joints |
| 3D-printed gears (PLA/PETG) | 1.5 – 3 | Below m=1.5, FDM resolution limits accuracy |
| Laser-cut acrylic/plywood | 2 – 4 | Tooth tip needs to be ≥ 1.5× kerf width |
| Light machinery (conveyor, pump) | 2 – 5 | Steel or aluminium; designed to ISO 6336 |
| Heavy industrial / automotive | 4 – 10 | Fatigue life and surface durability govern |
A rough starting point for steel gears under moderate load: m ≈ (T / (Y × b × σ_bend × z))1/3 where T is torque (N·mm), Y is the Lewis form factor (~0.3 for 20-tooth at 20°), b is face width, and σ_bend is the allowable bending stress. For a quick estimate, choose the smallest ISO module whose tooth root can carry the applied torque with a safety factor of 1.5.
For FDM 3D printing, the minimum printable tooth tip width is roughly equal to the nozzle diameter (0.4 mm for a standard 0.4 mm nozzle). Tip width = π·m·(ha*)/(2) ≈ 1.57·m for a standard gear. This gives m_min ≈ 0.25/1.57 ≈ 0.25 mm, but in practice m ≥ 1.5 is needed for dimensional accuracy. For laser cutting, minimum tooth width should be at least 3 × kerf; with a 0.2 mm kerf, m ≥ 1.5 is safe.
The pressure angle (α) is the angle between the common normal to the tooth surfaces at the pitch point and the common tangent to the pitch circles. In simpler terms: it controls the direction of the force between meshing teeth.
| Pressure angle | z_min (no undercut) | Best for | Avoid when |
|---|---|---|---|
| 14.5° | 32 | Legacy replacement parts, instrument gears | New designs — obsolete standard |
| 20° | 17 | Almost everything — ISO 53 / DIN 867 standard | Rarely avoided |
| 25° | 11 | High-torque gears, small pinions (z < 17), maximum strength | High-speed, low-noise applications |
The global default is 20° — use it unless you have a specific reason not to. The 14.5° standard is a legacy from early 20th-century American practice (AGMA) and is now found only in replacement part applications. The 25° standard is used in aerospace and heavy machinery where bending strength is paramount and noise is a secondary concern.
The contact ratio (ε) measures how many tooth pairs are simultaneously in contact during meshing. A ratio of 1.0 means exactly one pair is in contact at all times; a ratio of 1.8 means the load alternates between one and two pairs.
Higher contact ratio = quieter, smoother operation and lower peak tooth stress.
Contact ratio is primarily controlled by:
For general applications, aim for ε ≥ 1.4. Below 1.2, vibration and noise increase significantly. At 20° with z = 20 teeth, a standard gear gives ε ≈ 1.6 — well within the comfortable range.
Module 2, pressure angle 20°, 20 teeth on the pinion, 40 teeth on the gear. This gives a 2:1 reduction, a pitch diameter of 40 mm / 80 mm, and a centre distance of 60 mm. Contact ratio ≈ 1.64. FDM-printable with a 0.4 mm nozzle at 0.2 mm layer height.
Module 0.8, pressure angle 20°, 48 teeth (escape wheel). Pitch diameter = 38.4 mm. Tooth tip width ≈ 1.26 mm — laser-cuttable in 3 mm acrylic with a 0.15 mm kerf. Use profile shift x = 0 for a standard tooth form.
Module 3, pressure angle 20°, 16 teeth. Pitch diameter = 48 mm. Since z = 16 < 17, apply profile shift x = +0.1 to eliminate undercut. Export as DXF (High Quality) from GearProfile.app for a smooth contour toolpath in Fusion 360 CAM.
Enter module, tooth count, and pressure angle — the involute profile generates instantly. Export to DXF for CNC or SVG for laser cutting.
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