Mechanical & Civil Engineering
Worm Gear Lead Angle, Efficiency & Sliding Velocity Calculator
Calculate the lead angle, transmission efficiency, and sliding velocity of a worm gear set.
Your inputs
Change any value to update the result instantly.
Lead angle
6.057 deg
Efficiency
66.89 %
Sliding velocity
11.52 ft/s
Worm pitch diameter
1.5 in
What this calculator does
Worm Gear Lead Angle, Efficiency & Sliding Velocity 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
λ = atan(L/(πDw)); η = cos(φ)-f·tan(λ) / (cos(φ)+f·cot(λ)); Vs = πDwn/(60cos(λ))
- 1
Collect the inputs
Lead of worm = 0.5 in; Worm pitch diameter = 1.5 in; Coefficient of friction = 0.05; Pressure angle = 14.5 deg; Worm rotational speed = 1,750 rpm
- 2
Apply the formula
λ = atan(L/(πDw)); η = cos(φ)-f·tan(λ) / (cos(φ)+f·cot(λ)); Vs = πDwn/(60cos(λ))
- 3
Result
Lead angle = 6.057 deg
Frequently asked questions
Symbols and assumptions
- L
- Lead of worm (in)
- Dw
- Worm pitch diameter (in)
- f
- Coefficient of friction
- phi
- Pressure angle (deg)
- n
- Worm rotational speed (rpm)
- • 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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