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Taper Calculations

A cylindrical taper is a piece of material that decreases in diameter in a cone shape. Proportions for tapers are often expressed as Taper per Foot (TPF), or Taper per Inch (TPI). Taper calculations most often expressed in terms of the difference in diameter at the opposite ends of the taper and the length of the taper center axis.

taper  =  large end dimension - small end dimension unit of length overall length
	Term Definition d Small diameter D Large diameter L Length of taper LW Length of workpiece TPF Taper per foot TPI Taper per inch tan a Tangent of angle a TO Tailstock offset
	Find Known Values Use Formula TPI TPF TPF / 12 L, D, d (D - d) / L a tan(2 x a) TPF TPI TPF x 12 L, D, d 12 x ((D - d) / L) a 24 x tan(a) D d, L, TPF d + (L x (TPF / 12)) d, L, TPI d + (L x TPI) a, d, L d + (2 x (tan(a x L))) d D, L, TPF D - (L x (TPF / 12)) D, L, TPI D - (L x TPI) a, D, L D - (2 x (tan(a x L))) L D, d, TPF 12 x (D - d / TPF) D, d, TPI D - d / TPI a, D, d (D - d / 2) / tan a TO TPI, L (TPI / 2) x LW TPF, L (TPF / 12) x LW / 2 tan a TPF TPF / 24 TPI (TPI / 2