Taper Calculator
Estimate the taper length and angle using the taper calculator.
Taper per foot1 inthe standard machine-shop way of quoting a taper
Taper per inch0.083333 in
Included angle4.77189°the full angle between the two sides
Angle from the axis2.38594°set the compound rest to this
Ratio1 : 12one unit of diameter change per 12 of length
Diameter difference0.5 in
Tailstock offset for turning between centres0.25 inhalf the diameter difference, for a taper the full length of the work
Mean diameter1.25 in
Closest standard taperJacobs taperabout 0.75 in per foot — a rough match only
Self-holding?yestapers under about 1 in per foot grip by friction; steeper ones need a drawbar
The formula
taper per foot = (D − d) × 12 ÷ length; angle = atan((D − d) ÷ 2L)
Taper per foot, and half the angle
Shops quote tapers as the change in diameter per foot of length. But when you set a compound rest or a taper attachment you need the angle from the axis — half the included angle — because the tool only cuts one side.
The self-holding threshold is around one inch per foot. Below it, a Morse or Brown & Sharpe taper wedges tightly enough to drive on friction alone. Steeper tapers like R8 and the NMTB series locate accurately but release easily, so they need a drawbar to hold them in.