Calculator
Example Data Table
| Scenario | z1 | z2 | Module (mm) | φ (°) | Face (mm) | Speed (rpm) | Power (kW) | Key Output |
|---|---|---|---|---|---|---|---|---|
| Conveyor drive | 24 | 48 | 2.50 | 20 | 25 | 1200 | 3.00 | Center distance ≈ 90 mm, ratio 2.00 |
| Light duty gearbox | 18 | 54 | 2.00 | 20 | 20 | 1500 | 2.20 | Pitch diameter ≈ 36 mm, Wt depends on load |
| High speed test rig | 30 | 30 | 1.50 | 25 | 18 | 3000 | 1.50 | Higher velocity; check dynamics and lubrication |
Formula Used
- Module–DP conversion: m(mm) = 25.4 / DP, and DP = 25.4 / m.
- Pitch diameter: d = m · z.
- Circular pitch: p = πm.
- Base diameter: db = d · cos(φ).
- Outside and root diameters: do = d + 2a, and dr = d − 2b.
- Center distance: C = m(z1 + z2) / 2.
- Gear ratio: i = z2 / z1.
- Torque: T = 9550 · P(kW) · η / n(rpm).
- Pitch line velocity: v = πdn / 60.
- Tangential and radial forces: Wt = 2T / d, and Wr = Wt · tan(φ).
- Lewis factor (screening): Y ≈ 0.154 − 0.912 / z1 (clamped for stability).
- Bending stress estimate: σ ≈ (Wt · SF) / (b · m · Y).
- Contact pressure index: CPI = (Wt · SF) / (b · d).
How to Use This Calculator
- Select units and choose Module or Diametral Pitch mode.
- Enter pinion teeth (z1). Add gear teeth (z2) for ratio outputs.
- Provide pressure angle and face width for geometry and stress indices.
- Set speed, input power, efficiency, and service factor for loading.
- Click Calculate to display results above the form.
- Use CSV/PDF buttons to export the result table for records.
Technical Notes
Geometry inputs that drive accuracy
Spur gear sizing starts with teeth count and pitch definition. The calculator links module and diametral pitch, then derives pitch, outside, root, and base diameters. Pressure angle influences the base circle and the split between tangential and radial forces. Face width affects bending and contact indicators because it spreads load along the tooth. Addendum and dedendum factors change whole depth and clearance, helping you compare standard teeth against modified profiles during concept work.
Transmitted power and torque relationships
Given speed and power, torque is computed using the common rotational conversion constant. Efficiency is applied to estimate delivered power and the resulting torque at the pinion. From torque and pitch diameter, tangential tooth load is calculated, then combined with pressure angle to obtain radial load. These values support bearing selection, shaft sizing, and verifying that center distance fits the intended ratio and packaging limits.
Screening stress indicators for quick comparison
For preliminary checks, bending stress is estimated using a Lewis form factor approximation. This is not a substitute for full rating methods, yet it helps rank options when you vary module, face width, or tooth count. The contact pressure index provides a second comparison by relating load to projected area. Use both indicators to flag combinations that may be too slender, too heavily loaded, or likely to need larger pitch.
Service factor and duty interpretation
Real transmissions see starts, shocks, and fluctuating loads. The service factor scales tangential load to reflect duty severity. Light, steady drives may use a modest factor, while reversing loads, frequent starts, or impact-prone machinery typically require higher margins. If your application includes temperature extremes or contamination, add allowances for lubrication quality, alignment error, and manufacturing variation.
Using results to iterate designs faster
Start with an approximate ratio by selecting z1 and z2, then adjust module to reach target pitch diameter and center distance. Increase face width to reduce estimated stress, but watch packaging and weight. If velocity is high, consider dynamics and noise, then revisit tooth count and pressure angle. Export CSV or PDF outputs to document iterations and keep a traceable record for detailed verification in real projects.
FAQs
1) Should I enter module or diametral pitch?
Use whichever value your drawing or catalog provides. The calculator converts between them automatically, so you can stay consistent with metric or imperial procurement documents.
2) Why are results shown in millimeters in imperial mode?
Reporting geometry in millimeters keeps calculations consistent and avoids rounding drift. You can still enter face width in inches and power in horsepower.
3) What does the service factor change?
It scales the tangential load used in the stress indicators. Higher factors represent harsher duty, shocks, or frequent starts, and will increase the reported stress estimates.
4) Is the bending stress value an AGMA or ISO rating?
No. It is a screening estimate based on a Lewis factor approximation. Use it to compare options, then apply your full standard method for final design approval.
5) What if I do not know the mating gear teeth?
Set z2 to zero and the tool will compute pinion geometry and loads only. Add z2 later to obtain ratio and center distance.
6) How can I reduce the reported stresses quickly?
Increase module, increase face width, or choose a higher tooth count for the same ratio when feasible. Lower duty assumptions and improved efficiency also reduce computed loading.