🦷 Gear Strength Calculator

Gear teeth bend under load, and the gear strength calculator checks whether the bending stress stays below the material limit. The classical check is the Lewis bending equation: σ = Wₔ / (F · m · Y), where Wₔ is the transmitted tangential load, F the face width, m the module (or diametral pitch in imperial units) and Y the Lewis form factor, a dimensionless number that captures how the tooth shape concentrates stress at the root.

Gear failure in service usually starts as a fatigue crack at the tooth root, where bending stress is highest. The Lewis check is the first screen in a gear design: if the bending stress is well below the endurance limit of the gear material, the tooth is likely safe; if not, you widen the face, increase the module or switch to a stronger material. For a first estimate the Lewis equation with the appropriate form factor gives a reliable pass/fail answer before you run full AGMA rating software.

The transmitted load Wₔ comes from the torque and pitch radius: Wₔ = T / r, where r is the pitch circle radius. The calculator accepts torque and pitch diameter directly so you do not need to compute the tangential load by hand. The module m (in mm) equals pitch diameter divided by the number of teeth, and the Lewis form factor Y depends mainly on the number of teeth and the pressure angle.

The result is compared to the allowable bending stress of the gear material—cast iron runs around 60–100 MPa, hardened steel 200–350 MPa. The calculator reports the safety factor directly so you can judge at a glance: a factor above 1.5 is the typical minimum for a quietly loaded industrial gear, higher for shock loads. If your gear is part of a machine subject to impact, review the service factor guidance alongside the torque calculator.

1. Enter the transmitted torque and the pitch diameter of the gear.
2. Enter the face width of the gear teeth.
3. Enter the module (mm).
4. Choose the number of teeth to look up the Lewis form factor automatically.
5. Enter the allowable bending stress of the material to get the safety factor.

What is the Lewis form factor?

It is a dimensionless factor introduced by Wilfred Lewis in 1893 that accounts for the shape of the tooth. A tooth with more teeth has a thicker root, so Y increases with tooth count, and the stress falls as Y rises.

Why do I also need to check contact stress?

Bending stress cracks a tooth across the root, but gears also fail by pitting when the surface contact stress exceeds the material limit. The Lewis check and the AGMA contact-stress check are two different failure modes and both must pass.

What is the difference between module and diametral pitch?

Module m (mm) = pitch diameter / number of teeth, used in metric countries. Diametral pitch P = teeth / pitch diameter (in inches), used in the US. They are reciprocals in different unit systems: P = 25.4 / m.

How much safety factor should I use?

1.5 is a common minimum for steady industrial loads. Use 2–3 for shock loads, crushers or reversing drives. The right factor also depends on the consequences of failure—an elevator gear needs far more margin than a toy mechanism.

Can I strengthen a gear without changing the material?

Yes—widen the face, increase the module (fewer but larger teeth), increase the pressure angle, or add a fillet radius at the root. Shot peening and case hardening also raise the allowable stress by improving surface residual stress and hardness.

Does the calculator handle helical gears?

The Lewis equation applies to the virtual tooth count of a helical gear, which is slightly higher than the actual tooth count because of the helix angle. For a quick estimate use the virtual teeth number; for final design consult AGMA standards for helical corrections.

The Lewis form factor assumes the load is applied at the tooth tip, which is conservative—in reality the contact point moves down the flank as the gears roll. For a quick design, a 20° pressure angle and the tabulated Y values are sufficient. Face width should be roughly 8–12 times the module for spur gears; wider faces risk uneven load distribution along the tooth. Remember the Lewis check covers bending only—surface durability (pitting) is a separate AGMA contact-stress check that can fail even when bending is fine.