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Taper half and included angle calculator
Enter the axial length, not sloping surface length. Diameters are full diameters; the factor of two converts their difference into radial change. A compound slide setting often refers to the half-angle, but confirm your machine and drawing convention.
Angle & taper calculator
Find angles, missing sides and taper geometry. All angles are measured in degrees.
Formulas and angle conventions
Right triangle: θ = atan(rise / run); travel = √(run² + rise²). With angle and run: rise = run × tan(θ); travel = run / cos(θ). The other acute angle is 90° − θ.
Find Z: Z = (major X − minor X) / (2 × tan θ). θ is the angle to the spindle axis. For a full included angle A, use θ = A / 2. Example: X2 to X1 at 30° to the axis gives Z = 0.866025 in. At a 30° included angle, Z = 1.866025 in.
Taper: radial change = (D − d) / 2; half-angle θ = atan((D − d) / (2L)); included angle = 2θ; diameter taper per unit length = (D − d) / L. Enter the axial length, not the sloping surface length. Values use one common length unit.
The diagram illustrates the angle convention and is not to scale. Confirm whether your drawing or machine setup specifies the half-angle or included angle.
Formula and inputs
Half-angle = atan((D − d) / (2L)); included angle = 2 × half-angle.
Worked example
A change from 30 mm to 20 mm over 50 mm gives 5.710593° half-angle and 11.421186° included angle.
Use the result in your setup
Confirm the input dimensions and unit system against your drawing before calculating. Keep full precision during a calculation and round only the final value to suit the measurement or programming requirement. A numerical result does not account for a machine’s complete setup, workholding or control configuration.