BIZOMAT MAKEOS · Engineering
Taper Angle and Ratio
What half-angle and taper ratio match these dimensions?
Calculate a straight conical taper from its two diameters and axial length.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Large diameter | mm | Larger end diameter on the same nominal conical surface. |
| Small diameter | mm | Smaller end diameter. |
| Axial taper length | mm | Distance between the diameter measurement planes, along the axis. |
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: Large diameter
- What it is
- The diameter of the cone at its bigger end, measured at one end of the axial taper length.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 30 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger difference between the diameters gives a steeper taper and larger angle.
- Get it right
- Measure both diameters on the same conical surface at known axial positions.
What this means: Small diameter
- What it is
- The diameter of the cone at its smaller end, measured at the other end of the axial taper length.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A smaller small diameter steepens the taper.
- Get it right
- It must not be larger than the large diameter; 0 describes a cone that comes to a point.
What this means: Axial taper length
- What it is
- The distance along the axis between the two planes where the large and small diameters were measured.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A longer length for the same diameters gives a shallower taper.
- Get it right
- Measure along the axis, not along the sloping conical surface.
Method and formulas
- Diametral taper = (large diameter − small diameter) ÷ length.
- Half-angle = atan((large diameter − small diameter) ÷ (2 × length)).
- Included angle = 2 × half-angle. Example: 30 to 20 mm over 100 mm is 1:10 diametral taper and a 2.862405° half-angle.
Limitations
- No standard taper designation or interchangeability is inferred.
- Angle is the half-angle to the axis; do not confuse it with the included angle.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- cone angle
- taper per length
- compound slide
Who it is for
- Toolmakers
- Designers
What you get
- Half-angle to axis
- Included angle
- Diametral taper
- Diametral ratio
Interpreting the result
- Use the machine’s angle convention and verify the finished taper by measurement.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 681–685. Topic reference; no source tables or recommended settings are reproduced.
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