BIZOMAT MAKEOS · Gears
Crossed Helical Gears (Shafts at Right Angles)
What diameters and centre distance does this crossed helical gear pair at 90° have?
Pitch and outside diameters, centre distance, leads and ratio of a pair of helical gears on shafts at right angles, from normal diametral pitch, tooth counts and the gear helix angle.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Normal diametral pitch | 1/in | Normal diametral pitch (the pitch of the cutter). |
| Pinion teeth | teeth | Teeth on the pinion. |
| Gear teeth | teeth | Teeth on the gear. |
| Gear helix angle (pinion = 90° − this) | ° | Helix angle of the gear; the two helix angles add to 90° for shafts at right angles. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Normal diametral pitch
- What it is
- The normal diametral pitch, teeth per inch of pitch diameter measured square to the teeth; it matches the pitch of the hob or cutter, and both gears share it.
- Units and format
- Enter a number in 1/in: threads per inch. The form accepts 0.000001 1/in to 100 1/in. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 8 1/in as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- All diameters and the centre distance are inversely proportional to the normal pitch.
- Get it right
- Use the normal pitch, not the transverse pitch measured across the gear face.
What this means: Pinion teeth
- What it is
- The number of teeth on the pinion, the gear whose helix angle is 90° minus the gear’s helix angle.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 1000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- The ratio is gear teeth ÷ pinion teeth, regardless of the helix angles.
What this means: Gear teeth
- What it is
- The number of teeth on the gear, whose helix angle is entered below.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 5 teeth to 5000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Make sure this is the gear whose helix angle you enter; swapping them changes the diameters.
What this means: Gear helix angle (pinion = 90° − this)
- What it is
- The helix angle of the gear, measured from its axis. With the shafts at right angles the pinion’s helix angle is 90° minus this, and both have the same hand.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 5° to 85°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 45° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measured from the gear axis. 45° gives both gears the same helix angle.
Method and formulas
- Gear D = N ÷ (Pn cos ψ); pinion d = n ÷ (Pn cos(90° − ψ)).
- Centre distance C = (D + d)/2; outside diameters add 2/Pn.
- Lead = π × pitch diameter ÷ tan(helix angle); ratio = N ÷ n.
- Example: 20/40 teeth at 8 normal DP and 45° give a centre distance of 5.3033 in.
Limitations
- Point contact: crossed helical gears carry light loads and wear faster than parallel-axis gears.
- Both gears must have the same hand of helix for shafts at right angles.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Design or replace spiral gears on right-angle drives
- Find the centre distance for given tooth counts
- Choose helix angles to fit a centre distance
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Pitch and outside diameters
- Centre distance
- Leads
- Ratio
Interpreting the result
- Equal 45° helix angles give the same diameter ratio as the tooth ratio.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2195–2203. Topic reference; no source tables or recommended settings are reproduced.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Crossed Helical Gears (Shafts at Right Angles) calculator