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Taper Angle and Ratio Calculator — result sheet
Calculate diameter change, taper per length, one-in ratio, half-angle, included angle, and slanted edge length from two diameters and a taper length.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Diameter change ΔD = D−d; diameter taper per length = ΔD/L; one-in-N ratio N = L/ΔD; half-angle α = arctan(ΔD/(2L)); included angle = 2α; slanted edge = √(L²+(ΔD/2)²).
The page distinguishes diameter change from the half-angle of one tapered face and from the included angle between faces. That prevents the common mistake of using the full diameter difference as the opposite side of the half-angle triangle.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Large-end diameter — mm; minimum 1.0E-6; maximum 100000000
- Small-end diameter — mm; minimum 1.0E-6; maximum 100000000
- Taper length — mm; minimum 1.0E-6; maximum 100000000
Worked example
| Input | Value |
|---|---|
| Large-end diameter | 50 |
| Small-end diameter | 30 |
| Taper length | 100 |
Diameter change = 20 mm; taper = 0.2 mm/mm or 1 in 5; half-angle ≈ 5.7106°, included angle ≈ 11.4212°, and slanted edge ≈ 100.4988 mm.
Assumptions and limits
- The part is a straight, symmetric circular taper with a larger and smaller end diameter and a measured axial length.
- The one-in-N ratio uses diameter change per axial length; the half-angle uses the corresponding radius change.
- Tool nose radius, runout, tolerance, surface finish, stock allowance, standard taper families, and machining setup are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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