Diameter change is not radius change
Enter ΔØ = large diameter − small diameter. The geometric triangle uses half that change: tan α = ΔØ/(2L). Entering radius change as ΔØ would calculate a different cone.
Taper calculator
Calculate cone taper, half-angle and included angle from diameter change and axial length. Find diameter change from the angle, with examples.
Taper
1What data does the drawing give you?
or a standard taper:
2Enter the measurements
3Result
Click a dimension to copy it
How to use this calculation
A cone may be specified by two diameters and their axial separation, a taper ratio or an angle. This calculator relates diameter change ΔØ, length L and half-angle. It distinguishes the angle of one cone side to the axis from the full angle between both sides.
Worked example
Known measurements
Axial length L = 50 mm · diameter change ΔØ = 4 mm
Result
Half-angle α ≈ 2.291° · included angle ≈ 4.581° · taper = 1:12.5
Radius change is 2 mm. The 4/50 ratio uses diameter change and axial length.
Understanding a 1:n ratio
Diametral taper is ΔØ/L. A 1:20 ratio means a 1 mm diameter change over 20 mm of axial length; it does not mean a 1/20-degree half-angle. The cone's full included angle is 2α.
Catalogue cones and CNC programming
Standard taper examples help compare geometry but supply no acceptance tolerances or gauges. On a lathe, confirm radius or diameter X programming and which angle the cycle expects. Do not enter a half-angle into a field requesting included angle.
Frequently asked questions
How do half-angle and included angle differ?
Half-angle is between the cone axis and one side. The full included angle is twice that value.
Which length do I enter?
The axial distance between the sections where diameters are measured, not the inclined surface length.
How do I calculate diameter change from angle?
Use ΔØ = 2L · tan α with half-angle α. If you know the full included angle, halve it first.
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