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GEAR TRAIN CALCULATOR

Helical Gear Cutting Made Easier
Calculate ratios Select change gears Cut with precision
"The right ratio makes the helix."
⬇ Swipe to learn
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Function

Why Do We Need a Gear Train?

A gear train synchronizes three things at once:
1Table movement
2Workpiece rotation
3Required helix angle
The correct ratio helps produce the intended helical tooth path. A wrong ratio produces the wrong helix.
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Motion Chain

Follow the Motion

Table lead screw
⬇
Change gear train
⬇
Dividing-head worm shaft
⬇
Workpiece rotation
Correct synchronization produces the required helical path.
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Types

Know Your Gear Trains

1. Simple Gear Train
One driver and one driven gear pair
2. Compound Gear Train
Multiple gear pairs — wider range of ratios
3. Idler Gear Arrangement
Alters rotation direction; magnitude unchanged for a simple idler
Compound trains are often used when the required ratio is large or needs high precision.
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Setup

The Change-Gear Setup

1Table lead screw
2Driver gears
3Driven gears
4Intermediate shaft
5Banjo arm
6Dividing head
7Worm shaft
Correct mounting and gear meshing are essential — a loose or jammed gear trains introduces error.
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Step 1

Calculate Gear Lead

Lg = (π × D) / tan(β)
Gear lead (mm or in)
Lg Gear lead
D Pitch circle diameter
β Helix angle
Use consistent units for diameter and lead.
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Step 2

Find the Machine Constant

C = p × R
Machine constant (mm)
p
Lead screw pitch
R
Dividing-head ratio
Example
p = 6 mm  •  R = 40
C = 6 × 40 = 240 mm
Confirm the actual lead-screw pitch and dividing-head ratio on your machine.
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Step 3

Calculate the Ratio

i = C / Lg
Required gear ratio
i = Zdriven / Zdriver
Simple gear train
i = (Zd1 × Zd2) / (Zg1 × Zg2)
Compound gear train
Match the gear-train ratio to the required calculated ratio.
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Worked Example

A Real Helical Gear Example

p 6 mm
R 40
D 80 mm
β 25°
Lg = (π × 80) / tan(25°) ≈ 538.98 mm
C = 6 × 40 = 240 mm
i = 240 / 538.98 ≈ 0.4453
REQUIRED RATIO ≈ 0.4453
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Selection

Find a Suitable Combination

Simple gear train
One gear pair may provide a close match
Compound gear train
Multiple pairs can provide a wider range of ratios
The calculator compares candidate gear ratios against the required ratio. Verify the selected combination against the gears actually available on your machine.
⚠️ A tooth-count pair is only a candidate — confirm availability and check the resulting helix before cutting.
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Before Cutting

Set Up With Confidence

1 Confirm machine specifications
2 Calculate the required ratio
3 Select suitable available change gears
4 Mount gears • adjust the banjo arm
5 Check gear meshing and backlash
6 Verify the table swivel angle
7 Inspect the setup before cutting
A wrong ratio or a wrong table angle produces an incorrect helix.
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Ready to Calculate Your Gear Train?

Calculate the lead. Find the ratio. Compare gear combinations.
Lead Constant Ratio Gears
OPEN THE GEAR TRAIN CALCULATOR READ THE HELICAL GEAR GUIDE →
Helical Gear Calculator Simple Indexing Differential Indexing Spur Gear
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