Power transmission calculator
Ring Gear Dimensions Calculator
Calculate internal ring gear pitch, inner tip, and root diameters, center distance, and planetary tooth counts from module or diametral pitch.
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.
Holes, bore, and plate
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.
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⌀ 160.0 mm
⌀ 43.6 mm
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Quick answer
How this ring gear dimensions calculator works
A ring gear’s pitch diameter is d2 = m·z2, its inner tip diameter is m(z2 − 2), and its root diameter is m(z2 + 2.5); a pinion meshes at a = m(z2 − z1)/2. In a planetary set, z_ring = z_sun + 2·z_planet. This covers internal gears for gear trains and planetary sets, not automotive differential ring gears.
How to use the calculator
- 1Enter module or diametral pitch and the ring tooth count.
- 2Enter the pinion (or planet) tooth count.
- 3Read the pitch, inner tip, and root diameters and the center distance.
- 4For a planetary set, choose sun and planet counts so z_ring = z_sun + 2·z_planet and check equal planet spacing.
Key formulas
Ring gear dimensions formulas
- Pitch diameter
- d2 = m·z2
- Inner tip diameter
- da2 = m·(z2 − 2)
- Root diameter
- df2 = m·(z2 + 2.5)
- Center distance
- a = m·(z2 − z1)/2
- Planetary tooth relation
- z_ring = z_sun + 2·z_planet
- Planetary ratio, ring fixed
- i = 1 + z_ring ÷ z_sun
- Sun input, carrier output.
Worked example
Module 2, 60-tooth ring
- Inputs
- m = 2 mm, z2 = 60, 20-tooth pinion.
- Result
- Pitch 120 mm, inner tip 116 mm, root 125 mm, center distance 40 mm.
As a planetary set, a 20-tooth sun and 20-tooth planets fit this ring (20 + 2 × 20 = 60) for a 4:1 reduction with the ring fixed.
Common questions
What to know before using the result
- How do you calculate ring gear dimensions?
- Pitch diameter is m·z2, the inner tip diameter is m·(z2 − 2), and the root diameter is m·(z2 + 2.5). A module 2, 60-tooth ring measures 120, 116, and 125 mm.
- How many teeth does a planetary ring gear need?
- z_ring = z_sun + 2·z_planet. A 24-tooth sun with 18-tooth planets needs a 60-tooth ring and gives 3.5:1 with the ring fixed.
- How many planets can I use?
- Equally spaced planets fit when (z_ring + z_sun) ÷ n is a whole number and neighboring planets clear each other. A 60-tooth ring with a 24-tooth sun takes 3, 4, or 6 planets.
- What is the planetary gear ratio?
- With the ring fixed, sun in and carrier out, i = 1 + z_ring ÷ z_sun. A 60-tooth ring and 20-tooth sun give 4:1.
- Is this the same as a car ring gear?
- No. An automotive ring and pinion is a bevel or hypoid gear set in the differential. This page covers internal spur gears with teeth on the inside of a ring.
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).
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.
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