BIZOMAT MAKEOS · Gears
Spur Gear Measurement over Pins
What should the measurement over two pins read for this external spur gear?
Measurement over two pins (or balls) for an external spur gear with even or odd teeth, from the tooth thickness and pin size, by the involute function.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Module | mm | Module. |
| Number of teeth | teeth | Number of teeth. |
| Pressure angle | ° | Pressure angle. |
| Profile shift coefficient | Profile shift coefficient (0 if not shifted). | |
| Tooth thinning for backlash (arc, at pitch circle) | mm | Reduction of arc tooth thickness for backlash, from the gear drawing. |
| Pin diameter (0 = 1.728 × module) | mm | Actual pin or ball diameter; 0 uses 1.728 × module, a common size that contacts near the pitch circle. |
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: Module
- What it is
- The module of the spur gear: pitch diameter divided by the number of teeth.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Do not enter diametral pitch; convert it to a module first.
What this means: Number of teeth
- What it is
- The number of teeth on the gear. Even counts put the pins exactly opposite; odd counts put them nearly opposite.
- Units and format
- Enter a number in teeth: a whole number of teeth. The form accepts 6 teeth to 5000 teeth. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 25 teeth as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Count every tooth; the formula changes between even and odd counts.
What this means: Pressure angle
- What it is
- The pressure angle of the tooth profile at the pitch circle, from the gear drawing.
- Units and format
- Enter a number in °: degrees of angle. The form accepts 10° to 30°. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20° as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Use the angle of the cutter on the drawing.
What this means: Profile shift coefficient
- What it is
- The profile shift coefficient from the gear drawing, as a multiple of the module; it thickens or thins the teeth.
- Units and format
- Enter a plain number with no unit. The form accepts -1 to 1.5. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A positive shift thickens the teeth and increases the measurement over pins.
- Get it right
- 0 means an unshifted gear. Enter the coefficient, not the shift in millimetres.
What this means: Tooth thinning for backlash (arc, at pitch circ…
- What it is
- The amount the arc tooth thickness at the pitch circle is reduced to give backlash, from the gear drawing.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- More thinning reduces the measurement over pins.
- Get it right
- Enter the reduction of arc thickness, not of the measurement over pins.
What this means: Pin diameter (0 = 1.728 × module)
- What it is
- The actual diameter of the pins or balls placed in opposite tooth spaces. 0 lets the tool use a size that touches near the pitch circle.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 200 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- Measure the pins you will use; any difference from the entered value changes the reading.
Method and formulas
- Tooth thickness s = m(π/2 + 2x tan α) − thinning; d = m z; d_b = d cos α.
- inv φ = s ÷ d + inv α + d_p ÷ d_b − π ÷ z (solved for φ by Newton’s method).
- Even teeth: M = d_b ÷ cos φ + d_p. Odd teeth: M = (d_b ÷ cos φ) cos(90° ÷ z) + d_p.
- Example: module 2, 25 teeth with 3.456 mm pins measures 54.702 mm over the pins.
Limitations
- External spur gears; helical and internal gears need modified formulas.
- Pins must contact the flanks on the involute; check the contact diameter for small tooth counts.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Inspect spur gear tooth thickness accurately
- Write an inspection dimension on a gear drawing
- Check a gear without a span micrometer
Who it is for
- Gear designers
- Machinists
- Maintenance engineers
What you get
- Pin diameter used
- Pressure angle at the pin centre
- Measurement over pins
Interpreting the result
- A larger reading means thicker teeth (less backlash).
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2236–2248. 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.