Taper Calculator: Angle, Diameters & Taper Ratio
Published September 22, 2026 · MfgWorkbench editorial reference
Describe a straight circular taper using its end diameters and axial length. Results distinguish the half-angle from the full included angle.
Calculate and check
Default values are examples. Replace them with verified inputs for your job. Changing a unit or mode does not convert existing inputs.
Diameter taper is not the same as slope on one side
Let D be the larger diameter, d the smaller diameter and L the length measured along the axis. Diameter taper T = (D − d)/L. The half-angle α = atan[(D − d)/(2L)], and the included angle is 2α. A ratio written as 1:n for diameter taper has n = L/(D − d).
Use one consistent length unit. The angle is unchanged if all three dimensions are converted together. Do not use the sloping surface length in place of axial length; that gives a different result. This tool expects D greater than d.
Example: 30 mm down to 20 mm over 100 mm
Diameter taper is 10/100 = 0.1, or 1:10. The half-angle is 2.862405° and the included angle is 5.724810°. The one-sided radial change is 5 mm over the same 100 mm length. Confusing the 1:10 diameter ratio with a one-sided slope doubles the radial change.
On some lathes a compound scale is referenced differently from the part axis. Translate the geometric half-angle into the machine’s actual convention rather than entering a number without checking its zero reference.
Standard tapers and inspection
A named standard taper includes more than a ratio: gauge lines, engagement length, diameters and tolerances may all matter. Use the applicable standard or mating-part drawing for a Morse, toolholder or pipe taper.
Inspect two known axial stations to check the diameter change. A contact pattern alone does not establish every required size or fit. For an interference joint, taper seating force and friction need a separate model; the cylindrical press-fit calculator is not applicable to conical contact.
References and verification
Original explanations and worked examples by MfgWorkbench. Sources below support the stated concepts or selected reference data; they do not certify every example or a production application.
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Print a taper geometry record
Download the free taper checking sheet (PDF, 2 pages) to distinguish half-angle from included angle, rebuild the original diameter and compare two known axial stations. It provides spaces for the drawing reference and measurement uncertainty without inventing acceptance limits. Read the example and inspection boundaries. No email is needed.