Taper Calculator

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Construction

Calculate taper per foot, taper angle, and half angle for machined or fabricated tapers.

Formula

TPF = (D − d) / length × 12; Half angle = atan(TPF / 24)
  • Taper Per Foot (TPF) is the standard shop drawing notation.
  • Self-holding tapers (Morse, Jacobs, Brown & Sharpe) have included angle < 7°.
  • Steep-angle tapers (CAT, BT, ISO) require clamping force.

D=2.0 in, d=1.5 in, length=6 in

Inputs
  • Large Diameter (D): 2 in
  • Small Diameter (d): 1.5 in
  • Taper Length: 6 in

TPI = 0.5/6 = 0.0833. TPF = 0.0833×12 = 1.0 in/ft. Half angle = atan(0.0833/2) = 2.386°. Self-holding ✓.

Frequently asked questions

What is a Morse taper?
A Morse taper is a standard self-holding taper used in drill chucks and lathe centers. MT0–MT6 have TPF ranging from ~0.624 to 0.638 in/ft (about 1.5° half angle).