Use this simple
Mathematical Formula!

TPF" = [(LE"-SE") / L"] x 12”
SE = Small End of Taper

LE = Large End of Taper
L = Length of Taper


In the United States spindle nose tapers are commonly expressed as Taper Per Foot (TPF).

Asian and European machine tool builders often express the same spindle tapers in terms of degrees or ratios.

Regardless of the expression the calculation is still based on the above formula.

Refer to your copy of the Machinery’s Handbook for conversions.

Here are a few of the more common tapers you’ll encounter.  

Taper Per Foot Ratio Degrees Per Side
1.6” TPF 1:7.5 3° 48' 50"
2.4” TPF 1:5 5° 42' 38"
3”    TPF 1:4 7° 07' 30"