Wooden Gear Pair & Ratio Calculator
Enter the ratio you want, the circular pitch of the teeth, and the largest axle spacing that fits your project. The calculator searches integer tooth pairs and reports the closest practical pair with blank sizes and speed.
Recommended tooth pair18T driver -> 54T driven
- Achieved gear ratio
- 3
- Ratio error
- 0%
- Required shaft center distance
- 145.53
- Driving gear pitch and blank diameters
- pitch 72.77 mm; blank 80.85 mm; root 62.66 mm
- Driven gear pitch and blank diameters
- pitch 218.30 mm; blank 226.38 mm; root 208.19 mm
- Driven gear speed
- 20
- Alternative tooth pairs
- 17T driver -> 51T driven: 3.0000:1, 0.00% error, 137.45 mm center; 16T driver -> 48T driven: 3.0000:1, 0.00% error, 129.36 mm center; 15T driver -> 45T driven: 3.0000:1, 0.00% error, 121.28 mm center; 14T driver -> 42T driven: 3.0000:1, 0.00% error, 113.19 mm center
Alternative tooth pairs
| Driver teeth | Driven teeth | Ratio | Error | Center distance |
|---|---|---|---|---|
| 17 | 51 | 3 | 0% | 137.45 |
| 16 | 48 | 3 | 0% | 129.36 |
| 15 | 45 | 3 | 0% | 121.28 |
| 14 | 42 | 3 | 0% | 113.19 |
Diameters are in millimeters and use standard full-depth, unshifted external spur-gear proportions.
How to use this calculator
- Enter the driven-to-driver ratio you want, such as 3 for a 3:1 reduction.
- Enter the circular pitch, which is the tooth spacing measured along the pitch circle.
- Set the maximum center distance and the tooth-count limits that fit your stock and cutter.
- Enter the driver speed if you want the driven gear speed estimate.
- Review the recommended pair and nearby alternatives before drawing or cutting templates.
How the gear pair is calculated
This calculator works backward from a desired ratio and the space available between shafts. It does not draw a tooth profile. Instead, it searches all integer tooth counts inside the limits you enter, keeps the pairs that physically fit, and ranks the survivors by ratio accuracy.
Let R be the target driven-to-driver ratio, p be circular pitch, Amax be the maximum center distance, z1 be driving teeth, and z2 be driven teeth. Circular pitch is converted to metric module with:
m = p / pi
For each possible pair, the pitch diameters are:
d1 = m x z1 and d2 = m x z2
The shaft center distance is half the sum of those pitch diameters:
a = (d1 + d2) / 2
Only pairs with a <= Amax are kept. The achieved ratio is r = z2 / z1, and the ratio error is 100 x |r - R| / R. The lowest error wins. When several exact or near-exact pairs tie, the calculator favors the pair with the largest smaller gear, then the one that uses more of the available center distance.
What moves the answer most
The center-distance limit and circular pitch usually decide how many teeth are possible. Larger tooth spacing makes both gears larger, so fewer tooth-count combinations fit in the same mechanism. A higher minimum tooth count avoids very small pinions, but it can also eliminate compact ratios. A maximum tooth count keeps the search realistic when a large driven gear would be too big to cut from the available blank.
Pitch, blank, and root diameters
The pitch diameter is the working diameter used for ratio and center-distance math. The blank diameter shown here is the standard outside diameter for a full-depth, unshifted spur gear, using da = m x (z + 2). The root diameter uses df = m x (z - 2.5). Wooden gears often need extra fitting work, so treat these as layout dimensions, not a finished tooth template.
What this tool leaves out
The calculation does not include kerf compensation, backlash, profile shift, tooth rounding, bore clearance, printer scaling, wood movement, plywood quality, grain direction, or finishing. Two gears must use the same circular pitch to mesh. After choosing a pair, generate or draw the tooth profiles with the same pitch setting and test the mesh in scrap before committing to the final part.
Worked example
Suppose you want a 3:1 wooden gear reduction, use 12.7 mm circular pitch, and have no more than 150 mm between shafts. The module is 12.7 / pi = 4.04 mm. An 18-tooth driver and 54-tooth driven gear have pitch diameters of about 72.77 mm and 218.30 mm, so their center distance is (72.77 + 218.30) / 2 = 145.53 mm.
The achieved ratio is 54 / 18 = 3.0000, so the ratio error is 0%. With a 60 rpm driver, the driven gear turns at 60 x 18 / 54 = 20 rpm. The standard outside blank diameters are about 80.85 mm for the driver and 226.38 mm for the driven gear.
Common questions
What tooth spacing should I use for wooden gears?
Use a circular pitch that your material and cutting method can reproduce cleanly. Smaller spacing makes compact gears but narrower teeth, while larger spacing gives stronger tooth forms at the cost of larger blanks and wider shaft spacing.
How do I convert circular pitch to module?
Module is circular pitch divided by pi when both values use the same length unit. For example, a 12.7 mm circular pitch is about 4.04 module because 12.7 divided by pi is 4.04.
How many teeth should a wooden pinion have?
Very small pinions are harder to cut accurately and tend to have weaker, sharper teeth. This calculator lets you raise the minimum tooth count so the search favors larger small gears when the available center distance allows it.
Why does the achieved ratio differ from my target ratio?
A gear pair can only use whole tooth counts. If no integer pair inside the tooth-count and center-distance limits equals the target ratio, the calculator returns the closest feasible ratio and shows the percentage error.
Can gears with different tooth spacing mesh?
No. Both gears in a pair need the same circular pitch, or equivalently the same module, so the teeth arrive at the mesh at the same spacing. Changing the pitch on one gear changes its tooth size and invalidates the center-distance result.
What is the difference between pitch diameter and blank diameter?
Pitch diameter is the theoretical working circle used for ratio and center-distance calculations. Blank diameter is the outside tip diameter before or after profiling, depending on the cutting method, and is larger than the pitch diameter for a standard external spur gear.