Mechanical & Civil Engineering
Spur Gear Bending Stress Calculator (Lewis/AGMA)
Estimate root bending stress on spur gear teeth using the Lewis equation with AGMA-style overload and dynamic factors.
Your inputs
Change any value to update the result instantly.
Bending stress
20,000 psi
Combined K factor
1.2
Face width
1 in
Lewis form factor
0.3
What this calculator does
Spur Gear Bending Stress Calculator (Lewis/AGMA): Applies the standard machine-element relationship used in design textbooks so the capacity, rating or geometry can be worked out step by step.
What your result means
The headline figure is the capacity, rating or geometric result for the element you described. Compare it with the manufacturer's rating and your required service factor.
Formula and working
σ = Wt·Ko·Kv·Ks / (F·m·Y)
- 1
Collect the inputs
Tangential load = 500 lb; Face width = 1 in; Module (diametral pitch equiv.) = 0.1 in; Lewis form factor = 0.3; Overload factor = 1; Dynamic factor = 1.2; Size factor = 1
- 2
Apply the formula
σ = Wt·Ko·Kv·Ks / (F·m·Y)
- 3
Result
Bending stress = 20,000 psi
Frequently asked questions
Symbols and assumptions
- Wt
- Tangential load (lb)
- F
- Face width (in)
- m
- Module (diametral pitch equiv.) (in)
- Y
- Lewis form factor
- Ko
- Overload factor
- Kv
- Dynamic factor
- Ks
- Size factor
- • Standard textbook geometry and steady operating conditions are assumed; shock, misalignment and wear factors are not applied automatically.
- • Material and surface-finish allowances must be chosen by the user for their actual component.
Sources and review
Reviewed 2026-09-22 · Next review 2027-09-22
- • This is an educational estimate for learning and checking, not a design deliverable.
- • Real design must follow the governing code or standard for your jurisdiction and be reviewed and signed off by a qualified engineer.
- • Safety factors, load combinations and material certification are the responsibility of the designer, not of this page.
Important limitation
This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.
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