Is a ring gear the same as an internal gear?

In gear trains and planetary sets, yes: a ring gear is an internal gear with teeth on the inside. In cars, “ring gear” also names the large bevel gear in a differential, which this tool does not make.

How do you calculate internal gear center distance?

Subtract the pitch radii: a = m·(z2 − z1)/2. A module 2, 60-tooth ring with a 20-tooth pinion has a = 40 mm.

What is the inside diameter of an internal gear?

The tooth tips sit on m·(z2 − 2), which is the bore you would see looking through the ring. For module 2 and 60 teeth that is 116 mm, while the root is 125 mm.

How many fewer teeth must the pinion have?

Keep the tooth difference z2 − z1 at about 10 or more at 20° to avoid tip and trochoid interference. The tool warns below 10 and stops below 4, and its virtual shaping trims small interference automatically.

How do I size a planetary gear set?

Use z_ring = z_sun + 2·z_planet and the same module everywhere. A 20-tooth sun, 20-tooth planets, and a 60-tooth ring give 4:1 with the ring fixed, and four or five equally spaced planets fit because (60 + 20) ÷ n is whole.

Do the ring and pinion turn the same direction?

Yes. An internal mesh keeps both gears turning the same way, unlike an external pair; the speed ratio is still z2 ÷ z1, so 60 and 20 teeth give 3:1.

Can I order the ring and pinion together?

Yes. The part list includes the ring and the pinion, and Order uploads both STEP files into one Fabworks quote. You can also download STEP, DXF, or SVG.

Is a laser-cut ring gear suitable for my drive?

Yes, for low to moderate speed and load. Laser-cut plate parts suit prototypes, robots, fixtures, and light machinery; critical, high-speed, or high-load drives need engineering review of material, thickness, hub attachment, alignment, lubrication, and wear.

Power transmission calculator

Internal Ring Gear Generator

Generate an internal ring gear and its mating pinion from module or diametral pitch, tooth counts, and pressure angle, then download STEP, DXF, or SVG or order both parts.

Design a laser-cut ring gear

Set the pitch and tooth counts for a ring gear and the pinion that runs inside it, then size the rim, bolt holes, bore, and plate.

Units

Presets

Pitch system

Module

Pressure angle

Ring teeth

Pinion teeth

Backlash allowanceTooth thinning

Rim outside diameter

Holes, bore, and plate

Rim bolt holes

Holes

Hole circle diameter

Hole diameter

Rotation

Fabworks plate material

Plate thicknessMin. feature 0.050 in · 1.27 mm

Gear dimensions

Ring pitch diameter: 120 mm
Ring inner diameter At the tooth tips: 116 mm
Ring root diameter: 125 mm
Rim outside diameter: 160 mm
Pinion pitch diameter: 40 mm
Pinion outside diameter: 44 mm
Center distance: 40 mm
Gear ratio Ring ÷ pinion · same direction: 3 : 1
Contact ratio: 1.95
Planetary sun gear With the pinion as a planet · 4 : 1 with the ring held: 20 teeth

Mesh preview

The ring's tooth spaces are generated by rolling the pinion through them, the way a gear shaper cuts an internal gear, so the pinion clears the ring through the whole mesh. Dashed circles are pitch circles.

True generated tooth form

Download the manufacturing files

100% in-browser

STEP solids are built and checked in your browser. DXF and SVG drawings use lines and true arcs at full scale. Nothing is uploaded until you order.

Ring gear
⌀ 160.0 mm
Pinion
⌀ 43.6 mm

Laser cut it at Fabworks

We generate the STEP files, add them to a new quote, and open it in a new tab where you can review material, finish, and quantity.

Quick answer

How this internal gear calculator works

An internal gear’s pitch diameter is d2 = m·z2, its tooth tips sit on an inner circle of m(z2 − 2), its roots on m(z2 + 2.5), and it meshes with a pinion at a = m(z2 − z1)/2. This generator makes internal (ring) gears for gear trains and planetary sets, not automotive ring-and-pinion differential gears. Files are generated in the browser and download as STEP, DXF, or SVG, or go straight into a Fabworks quote.

How to use the calculator

1Choose module or diametral pitch and the pressure angle shared by the ring and pinion.
2Enter the ring teeth z2 and the mating pinion teeth z1, keeping z2 − z1 at 10 or more at 20°.
3Set backlash, the rim outside diameter, and a bolt circle for mounting the ring.
4Review center distance, ratio, and the generated tooth spaces, which are cut by simulating the pinion’s motion.
5Choose a Fabworks material and thickness and clear any minimum-feature warnings.
6Download the ring and pinion, or send both to a Fabworks quote.

Key formulas

Internal gear formulas

Ring pitch diameter: d2 = m·z2; m is the module and z2 the ring tooth count.
Inner tip diameter: da2 = m·(z2 − 2); Internal teeth point inward, so the tip circle is smaller than the pitch circle.
Root diameter: df2 = m·(z2 + 2.5); The root is outside the pitch circle for an internal gear.
Center distance: a = m·(z2 − z1)/2; z1 is the pinion tooth count. The pinion sits inside the ring.
Ratio and direction: i = z2 ÷ z1, same rotation direction; Unlike an external pair, the ring and pinion turn the same way.
Planetary tooth relation: z_ring = z_sun + 2·z_planet; All three gears share one module so the planets fit between sun and ring.
Planetary ratio, ring fixed: i = 1 + z_ring ÷ z_sun; Sun is the input and the planet carrier is the output.
Equal planet spacing: (z_ring + z_sun) ÷ n = whole number; n is the number of planets.

Step by step

How to draw an internal gear profile

1Calculate d2 = m·z2, the inner tip diameter m(z2 − 2), the root diameter m(z2 + 2.5), and the base diameter d2·cos α.
2Draw the four circles; the tip circle must stay outside the base circle so the flank remains an involute.
3Draw an involute from the base circle as for an external gear. The internal gear’s tooth space has the shape of an external tooth of the same count.
4Make each tooth space π·m/2 wide on the pitch circle, plus the backlash allowance.
5Trim the space at the root circle with a fillet and the tooth tips at the inner tip circle.
6Roll the mating pinion through the mesh and remove any ring material it would hit; this generator does that automatically by virtual shaping.
7Pattern the space z2 times, then add the rim outside diameter and bolt circle.

Worked example

Module 2, 60-tooth ring with a 20-tooth pinion

Inputs: m = 2 mm, z2 = 60, z1 = 20, 20° pressure angle.
Result: Ring pitch diameter 120 mm, inner tip diameter 116 mm, root diameter 125 mm, center distance 40 mm, ratio 3:1 with both gears turning the same way.

Inner tip = 2 × (60 − 2) = 116 mm, root = 2 × (60 + 2.5) = 125 mm, and a = 2 × (60 − 20) ÷ 2 = 40 mm. The pinion turns three times per ring revolution.

Common questions

What to know before using the result

Is a ring gear the same as an internal gear?: In gear trains and planetary sets, yes: a ring gear is an internal gear with teeth on the inside. In cars, “ring gear” also names the large bevel gear in a differential, which this tool does not make.
How do you calculate internal gear center distance?: Subtract the pitch radii: a = m·(z2 − z1)/2. A module 2, 60-tooth ring with a 20-tooth pinion has a = 40 mm.
What is the inside diameter of an internal gear?: The tooth tips sit on m·(z2 − 2), which is the bore you would see looking through the ring. For module 2 and 60 teeth that is 116 mm, while the root is 125 mm.
How many fewer teeth must the pinion have?: Keep the tooth difference z2 − z1 at about 10 or more at 20° to avoid tip and trochoid interference. The tool warns below 10 and stops below 4, and its virtual shaping trims small interference automatically.
How do I size a planetary gear set?: Use z_ring = z_sun + 2·z_planet and the same module everywhere. A 20-tooth sun, 20-tooth planets, and a 60-tooth ring give 4:1 with the ring fixed, and four or five equally spaced planets fit because (60 + 20) ÷ n is whole.
Do the ring and pinion turn the same direction?: Yes. An internal mesh keeps both gears turning the same way, unlike an external pair; the speed ratio is still z2 ÷ z1, so 60 and 20 teeth give 3:1.
Can I order the ring and pinion together?: Yes. The part list includes the ring and the pinion, and Order uploads both STEP files into one Fabworks quote. You can also download STEP, DXF, or SVG.
Is a laser-cut ring gear suitable for my drive?: Yes, for low to moderate speed and load. Laser-cut plate parts suit prototypes, robots, fixtures, and light machinery; critical, high-speed, or high-load drives need engineering review of material, thickness, hub attachment, alignment, lubrication, and wear.

Reference

Module 2 internal gear dimensions, 20° pressure angle

Millimeters, standard proportions without profile shift. Center distance is for a 20-tooth pinion.

Ring teeth z2	Pitch dia	Inner tip dia	Root dia	Base dia	a with 20T pinion
40	80	76	85	75.175	20
48	96	92	101	90.210	28
60	120	116	125	112.763	40
72	144	140	149	135.316	52
80	160	156	165	150.351	60
100	200	196	205	187.939	80

Planetary gear sets that assemble with equally spaced planets

Ring = sun + 2 × planet. Ratio is sun input, carrier output, ring fixed: 1 + z_ring ÷ z_sun. Planet counts listed satisfy (z_ring + z_sun) ÷ n = whole number and leave room between neighboring planets.

Sun	Planet	Ring	Ratio	Planet counts
12	24	60	6.000:1	3
15	15	45	4.000:1	3, 4, 5
18	21	60	4.333:1	3
20	20	60	4.000:1	4, 5
24	18	60	3.500:1	3, 4, 6
30	15	60	3.000:1	3, 5, 6
18	27	72	5.000:1	3
20	30	80	5.000:1	4

Formula

a = m·(z₂ − z₁) ÷ 2 · dₐ₂ = m(z₂ − 2) · d_f₂ = m(z₂ + 2.5)

Center distance a is half the module times the difference between ring teeth z₂ and pinion teeth z₁, and both gears turn the same direction. The ring’s tooth tips sit on m(z₂ − 2) and its roots on m(z₂ + 2.5).

Engineering references

Assumptions and limits

Ring tooth spaces are generated by simulating the mating pinion’s motion, so tip interference is trimmed automatically.
A tooth difference below 10 at 20° is flagged; below 4 is not generated.
Standard proportions are used with no profile shift.
The rim outside diameter and bolt circle are user-defined and checked against minimum web size.
Laser-cut gears suit low to moderate speed and load; critical drives need engineering review.

Educational estimate

Use this result for learning and early design exploration. Verify safety-critical or production decisions with the governing standard, material data, real tooling, and a qualified engineer.

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