Tangential force
N
Mechanics · Transmission and rotation
Spur Gear Forces Calculator
Resolve the transmitted force magnitude at the pitch diameter without treating it as a tooth-strength rating.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
03
MetricResults
Radial force
N
Normal force
N
View calculation detailsFormulas, SI conversion, numerical substitution and resultsOpen ↓
Calculation note
Full calculation details
The model treats force magnitudes for an ideal spur gear at the pitch diameter. The pressure angle resolves the load; the ideal axial component is zero. This is not a tooth-bending, Hertz contact-stress or AGMA/ISO allowable-load check. Service, dynamic and face-load distribution factors are not included. Backlash, efficiency, friction and helical gears are excluded.
01Formulas and symbols
Formulas used
Ft
2T / dTangential force at pitch diameterFr
Ft × tan(α)Radial componentFn
Ft / cos(α)Normal force along line of action02Assumptions and limits
Scope of validity
- The model treats force magnitudes for an ideal spur gear at the pitch diameter.
- The pressure angle resolves the load; the ideal axial component is zero.
- This is not a tooth-bending, Hertz contact-stress or AGMA/ISO allowable-load check.
- Service, dynamic and face-load distribution factors are not included.
- Backlash, efficiency, friction and helical gears are excluded.
03Validation example
Reference numerical case
- T = 100 N·m, d = 200 mm and α = 20°.
- Ft = 1,000 N and Fr ≈ 363.970 N.
- Fn ≈ 1,064.178 N.
04Frequently asked questions
Questions about the calculation
Why use pitch diameter?
Torque and tangential force are related at the pitch radius, so Ft = T/(d/2).
Is axial force always zero?
It is zero in this ideal spur-gear model; that is not generally true for helical gears.
Are these forces enough to rate the teeth?
No. Tooth bending, contact, load factors and the selected standard still require separate checks.
05References
Technical references
- KHK Gears, Gear Forces, tables 12.1 and 12.2.
- SDP/SI, Elements of Metric Gear Technology, sections 2, 4 and 16.