Spur gear calculator with a strength check and a 3D model to print
Set the module, the tooth count and the pressure angle and get the gear's sizes, checks for undercut, bending and contact, and a 3D gear with a true involute (the tooth profile). Download it as STL or 3MF; in 2D, gears mesh and turn a whole system.
Opens without an account 3 times a day. A free account removes the limit.
- 6 gear typesfrom spur to worm
- 15 standard modulesfrom 0.5 to 12 mm per ISO 54
- 4 checksundercut, bending, contact, ratio
- 50 mechanismsready in the 2D system
What a spur gear calculator does, and what gear module is
The spur gear calculator from EduFacturing is a free online tool that builds a 3D model of a gear from its formulas and checks it for undercut, bending and contact. The profile is an involute, and the model downloads as STL or 3MF.
In “3D gear” mode you set the type, module, teeth, pressure angle, profile shift, width, material and load, and add a hub, a keyway and lightening. In “2D gear systems” mode you drag gears that mesh by themselves and are turned by a motor.
Gear module calculator: sizes, undercut and strength
Builds a gear from its formulas
The involute is drawn point by point from the module, the teeth, the pressure angle and the profile shift, for 6 gear types.
Adds a hub, a keyway and lightening
A hub, a DIN 6885 keyway, a set screw from M3 to M6, mounting holes, lightening with holes or spokes and your own holes.
Checks the gear and works out a gear train
Four checks: undercut, bending safety (Lewis), contact safety (Hertz) and ratio per stage. The train gives output speed and torque with an efficiency of 0.97 per stage.
Arranges gears in a 2D system
Gears are dragged and mesh by themselves, a motor turns them, and the tool works out the ratio to the selected one. There are 50 ready mechanisms, and the system downloads as one STL.
3D print gear calculator: reducers, mock-ups, lessons
A gear makes sense when you change the module and the teeth and see what happens.
Machine elements lesson
A student changes the module and the teeth and sees when the undercut check gives an error.
Reducer for a printer or a robot
A 24:48 stage at 600 rpm and 2 Nm gives 300 rpm and 3.88 Nm.
Plastic gear for a mock-up
POM, PLA, PETG, ABS or nylon: the safety at your own torque.
Planetary drive or rack
In 2D: a ready planetary drive with 3 to 6 planets, or a pinion with a rack.
How to calculate a gear: sizes, bending and contact stress
The sizes are calculated from the module m, the teeth z, the pressure angle α and the profile shift x. The stresses add the width F, the torque T and the material.
Sizes and profile
The addendum is m and the dedendum is 1.25·m (the ISO 53 basic profile). The tooth is an involute from the base circle, inv α = tan α − α, extruded into a closed solid.
Check
Safety is SF = allowable / σ. Bending passes at SF of 1.5, contact at SF of 1.2; between 1 and the limit is a warning, below 1 is an error.
| Applies to | Formula | Meaning |
|---|---|---|
| Sizes | d = m·z; da = d + 2·m·(1 + x); df = d − 2·m·(1.25 − x); db = d·cos α | x is the profile shift, α the pressure angle |
| Bending (Lewis) | Wₜ = 2000·T / d; σ = Wₜ / (F·m·Y) | Y is the Lewis form factor from Shigley table 14-2 (for 20°), interpolated between 12 and 400 teeth |
| Contact (Hertz) | σH = √(Wₜ·(1/R₁ + 1/R₂) / (π·b·((1 − ν₁²)/E₁ + (1 − ν₂²)/E₂))) | R is the pitch circle radius, b the width |
Reference
ISO gear standard: modules and profile
| Parameter | Value | Unit |
|---|---|---|
| ISO standard modules (minimum) | 0.5 | mm |
| ISO standard modules (maximum) | 12 | mm |
| Pressure angle | 20 | ° |
| Addendum | 1 | module |
| Dedendum | 1.25 | module |
ISO 53 and ISO 54; involute profile with a 20 degree pressure angle
A gear design calculator that names its rules
Every check names its rule
Under it is the identifier of the rule in the EDi Brain rules core, for example mech.gear.min_teeth_20deg.
From the formula to a printable body
The gear is a closed solid for STL or 3MF. The “Order printed” button sends the model to a print order.
Mounting is in the same model
A keyway, a set screw, mounting holes and spokes are part of the body of the round gears.
Lewis and Hertz are worked out for two identical gears of one material, with no dynamic factor, wear, temperature or lubrication. Y is taken from the table for 20° for all angles and types, and the allowable stresses are built into the tool.
The helical, bevel and worm gears are an involute profile twisted or tapered by the angle, not the full geometry of those drives; their calculations are those of a spur gear. The hub, keyway, lightening and holes apply to the four round types, not to the rack and the internal gear. A printed gear is for a mock-up. The formats are STL and 3MF; there is no STEP.
Gear calculator questions: module, undercut, strength
How do I calculate a spur gear?
Set the module m and the teeth z. The pitch diameter is d = m·z, the tip diameter d + 2·m·(1 + x) and the root diameter d − 2·m·(1.25 − x); x is the profile shift.
What is gear module?
The module m is the size of the tooth: the pitch diameter is d = m·z. In the tool it is one of 15 standard values from 0.5 to 12 mm.
How many teeth are needed to avoid undercut?
At a 20° pressure angle it is 17: z_min = 2 / sin² α, rounded. At 14.5° it is 32 and at 25° it is 11. Below the limit the check gives an error and suggests more teeth or a profile shift.
How is gear strength checked?
Bending by Lewis, contact by Hertz. At the defaults (m = 2, z = 24, F = 10 mm, POM, 2 Nm) the force is 83.3 N, bending 12.4 MPa against an allowable 55, contact 18.8 MPa against 95 (E = 2800 MPa, ν = 0.35). Safety is 4.45 and 5.06 against minimums of 1.5 and 1.2.
What types of gear can be generated?
Six: spur, helical (β from 5° to 45°), bevel (from 5° to 75°), internal, rack and worm (screw angle from 45° to 88°). In 2D the module runs from 1 to 8 mm.
Is the spur gear calculator free?
Yes. Without an account it opens 3 times a day. A free account removes the limit.
The gear calculator is free. Pro opens the rest
Pro costs 15 EUR a month and opens 45 Pro tools.
In the Design group:
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Make your own gear
Opens without an account 3 times a day. A free account removes the limit.