Mechanical & Civil Engineering
Bevel Gear Pitch Cone Angle & Thrust Force Calculator
Determine the pitch cone angle of a bevel gear pair and the resulting axial thrust force.
Your inputs
Change any value to update the result instantly.
Pitch cone angle
26.565 deg
Axial thrust force
81.4 lb
Gear ratio
2
Complement cone angle
63.435 deg
What this calculator does
Bevel Gear Pitch Cone Angle & Thrust Force Calculator: 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
γ = atan(Np/Ng); Fa = Wt·tan(α)·sin(γ)
- 1
Collect the inputs
Pinion teeth = 20; Gear teeth = 40; Tangential force = 500 lb; Pressure angle = 20 deg
- 2
Apply the formula
γ = atan(Np/Ng); Fa = Wt·tan(α)·sin(γ)
- 3
Result
Pitch cone angle = 26.565 deg
Frequently asked questions
Symbols and assumptions
- Np
- Pinion teeth
- Ng
- Gear teeth
- Wt
- Tangential force (lb)
- alpha
- Pressure angle (deg)
- • 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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