Calculator Inputs
Use the grid below. Large screens show three columns. Smaller screens collapse to two, then one.
Example data table
| Case | Driver Teeth | Driven Teeth | Module | Driver RPM | Driver Torque | Driver Rotations | Gear Ratio | Center Distance |
|---|---|---|---|---|---|---|---|---|
| Reduction pair | 20 | 40 | 2 mm | 1200 | 15 Nm | 25 | 2.000 | 60 mm |
| Equal pair | 30 | 30 | 2.5 mm | 900 | 10 Nm | 18 | 1.000 | 75 mm |
| Overdrive pair | 48 | 24 | 1.5 mm | 600 | 8 Nm | 30 | 0.500 | 54 mm |
| Compact pair | 16 | 28 | 1.25 mm | 1500 | 6 Nm | 12 | 1.750 | 27.5 mm |
Formula used
1. Gear ratio
Gear Ratio = Driven Teeth ÷ Driver Teeth
2. Speed ratio
Driven RPM = Driver RPM × (Driver Teeth ÷ Driven Teeth)
3. Pitch diameter using module
Pitch Diameter = Module × Teeth
4. Pitch diameter using diametral pitch
Pitch Diameter = Teeth ÷ Diametral Pitch
5. Center distance
Center Distance = (Driver Pitch Diameter + Driven Pitch Diameter) ÷ 2
6. Pitch line travel
Pitch Line Travel = π × Driver Pitch Diameter × Driver Rotations
7. Torque estimate
Output Torque = Input Torque × Gear Ratio × Efficiency
These formulas assume an ideal external spur gear pair. Real systems may vary with backlash, friction, tooth form, and load limits.
How to use this calculator
- Select either module or diametral pitch.
- Enter driver and driven gear teeth counts.
- Provide the gear sizing value for the selected method.
- Enter driver RPM, torque, rotations, and efficiency.
- Press Calculate to show results above the form.
- Review ratio, speed, torque, travel, and center distance.
- Use the CSV or PDF buttons to export results.
- Check the Plotly graph to compare motion behavior.
FAQs
1. What does gear ratio mean?
Gear ratio compares driven gear teeth to driver gear teeth. A larger value usually reduces speed and increases torque at the output, assuming good efficiency.
2. What is center distance?
Center distance is the spacing between both gear centers. It equals half the sum of both pitch diameters for a standard external gear pair.
3. Why are module and diametral pitch both offered?
Both describe tooth size. Module is common in metric work. Diametral pitch is common in inch-based systems. The calculator supports both methods for convenience.
4. Does pitch line travel equal actual surface sliding?
No. Pitch line travel represents ideal rolling distance at the pitch circle. Real tooth contact includes sliding except at the pitch point.
5. Why does output torque use efficiency?
Efficiency accounts for losses from friction, lubrication, load, and alignment. Lower efficiency reduces the torque delivered by the driven gear.
6. Can I use this for helical or bevel gears?
This page is best for a simple external spur gear pair. Other gear types need extra geometry, angle corrections, and loading factors.
7. What happens when the ratio is less than one?
A ratio below one means the driven gear has fewer teeth than the driver. Output speed increases while output torque usually drops.
8. Is the mesh frequency useful?
Yes. Mesh frequency helps vibration and noise checks. It estimates how often teeth engage each second during operation.