Taper calculator (taper ratio, included angle, compound-rest angle)
From the large diameter, small diameter and length: taper ratio (1:x), included angle, and half angle (the angle to set the lathe compound rest).
◁Taper calculator
x in taper ratio 1 : x—
Included angle (2α)—°
Half angle α (compound-rest angle)—°
Slope (one side)—
Taper = (D − d) ÷ L = 1 : x α = atan((D − d) ÷ (2 × L)) Included angle = 2α Slope = (D − d) ÷ (2 × L)
Notes
- “Taper” divides the difference in diameter by the length; “slope” divides the difference in radius (one side). Check which one the drawing specifies.
- When cutting with the compound rest on a lathe, swivel it by the half angle α.
All values are guides. Start from the tool maker’s recommended cutting data and adjust for your machine, workholding and coolant. Calculations run in your browser; nothing you enter is sent anywhere.