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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
  Taper Calculations
  Taper Calculations
  Tailstock Offset
dSmall diameter
DLarge diameter
LLength of taper
LWLength of workpiece
TPFTaper per foot
TPITaper per inch
tan aTangent of angle a
TOTailstock offset
FindKnown ValuesUse Formula
L, D, d(D - d) / L
atan(2 x a)
L, D, d12 x ((D - d) / L)
atan(24 x a)
Dd, L, TPFd + (L x (TPF / 12))
d, L, TPId + (L x TPI)
a, d, Ld + (2 x (tan(a x L)))
dD, L, TPFD - (L x (TPF / 12))
D, L, TPID - (L x TPI)
a, D, LD - (2 x (tan(a x L)))
LD, d, TPF12 x (D - d / TPF)
D, d, TPID - d / TPI
a, D, d(D - d / 2) / tan a
TOTPI, L(TPI / 2) x LW
TPF, L(TPF / 12) x LW / 2
tan aTPFTPF / 24


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