Calculation
i = z₂/z₁ = n₁/n₂
For the worm, z₁ is the number of starts, not a circumferential tooth count.
Roloff/Matek Gl. (23.14)
Worm Gear Ratio Calculator
For the worm, z₁ is the number of starts, not a circumferential tooth count.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Ratio i — The worm-drive ratio: worm speed divided by wheel speed. Because the worm's start count z₁ is small, this design achieves very high ratios in a single stage.
- Worm starts z₁ — The number of starts on the worm – how many helical threads it has (usually 1, 2 or 4), not a circumferential tooth count like an ordinary gear. Source: the worm drive's nameplate or drawing.
- Worm-wheel teeth z₂ — The tooth count of the worm wheel meshing with the worm. Source: drawing, or count them on the wheel.
Example
A single-start worm with a 40-tooth wheel gives i=40.
Assumptions and limits
Kinematic ratio without losses; consider direction and shaft arrangement separately.
Understand Worm Gear Ratio Calculator
Worm-drive ratio is a focused preliminary calculation based on Roloff/Matek. The calculator rearranges the closed-form relationship for every included quantity and deliberately separates this result from a complete component verification.
What does this quantity describe?
For worm and wheel, i=n1/n2=z2/z1. For the worm, z1 is its number of starts.
Formula and variables
i = z₂/z₁ = n₁/n₂
i = z2 / z1 = n1 / n2
| Symbol / input | Meaning |
|---|---|
| Ratio i | The worm-drive ratio: worm speed divided by wheel speed. Because the worm's start count z₁ is small, this design achieves very high ratios in a single stage. |
| Worm starts z₁ | The number of starts on the worm – how many helical threads it has (usually 1, 2 or 4), not a circumferential tooth count like an ordinary gear. Source: the worm drive's nameplate or drawing. |
| Worm-wheel teeth z₂ | The tooth count of the worm wheel meshing with the worm. Source: drawing, or count them on the wheel. |
Choose the inputs correctly
z1 is the number of worm starts, z2 the wheel tooth count and i the kinematic speed ratio.
How to use the calculator
Select the target, enter all remaining quantities for the actual component, and verify the units. Then compare the result with the stated model limits and with the required strength, safety and operating checks.
Worked example
A single-start worm and 40 wheel teeth give i=40.
Understand the result and units
More starts increase output speed for a given wheel. Efficiency and torque do not follow from ratio alone.
The calculator converts internally to coherent SI units. Length, force, torque, stress and angle may therefore use the offered units; dimensionless factors are entered as decimals.
What is taken from Roloff/Matek
Only the closed-form relationship from Kapitel 23.2.2, Gleichung (23.14) is used. Tabulated data, material limits and detailed design checks are not silently added; they remain explicit inputs or are expressly outside the model.
Typical applications
Worm-drive ratio supports option comparison, plausibility checks and early sizing within its machine-element cluster. Releasing a design requires the additional checks described in the cited chapter.
Assumptions, limits and common mistakes
Pure kinematics without losses, strength, geometry or self-locking; assess these separately in the worm-drive cluster.
Common mistake: Typical errors are misreading the effective length or force, entering percentages instead of decimals, and treating a preliminary result as a complete verification. In particular: Pure kinematics without losses, strength, geometry or self-locking; assess these separately in the worm-drive cluster.
Frequently asked questions
Is Worm-drive ratio a complete strength verification?
No. Pure kinematics without losses, strength, geometry or self-locking; assess these separately in the worm-drive cluster.
Where do the equation and validity limits come from?
Roloff/Matek, Machine Elements, Kapitel 23.2.2, Gleichung (23.14); the local 21st edition was cross-checked against the available 24th edition.
Can I order the calculated value directly as a nominal size?
Only after matching it to available standard or manufacturer series and completing the additional safety, material and operating checks.