Paritian

Mechanics

Taper Calculator (Angle, Ratio, Taper per Foot, Tailstock Offset)

Half angle for the compound slide, included angle, 1 : n ratio, taper per foot and tailstock offset for a taper turned between a large and a small diameter.

Results

Half angle (set-over for the compound slide) 2.8624 °
Included angle 5.7248 °
Taper ratio, 1 : … 10.000
Taper (change in diameter per unit length) 0.10000
Taper per foot (if the sizes are in inches) 1.2000
Tailstock offset 12.500 mm
The shape, to scale
Taper Calculator (Angle, Ratio, Taper per Foot, Tailstock Offset)Taper Calculator (Angle, Ratio, Taper per Foot, Tailstock Offset): d = 20.0 mm, D = 30.0 mm, L = 100.0 mmD = 30.0 mmd = 20.0 mmL = 100.0 mm

What this tool does

A taper is described in four ways that all say the same thing: the included angle, the half angle (what you actually set on a lathe's compound slide), a ratio such as 1 : 20, and — in inch shops — inches of diameter change per foot of length. Morse tapers are all close to 1 : 20. Turning a taper by offsetting the tailstock only works between centres and over the whole length: the offset is half the diameter difference times the total length over the length of the taper, so a short taper on a long bar needs a bigger offset. Check the fit with marking blue on the mating part.

Formula

half angle = atan((D − d) ÷ (2L)) · taper = (D − d) ÷ L · 1 : n with n = L ÷ (D − d) · tailstock offset = (D − d) ÷ 2 × total length ÷ L

Variables

SymbolMeaningUnit
dlLarge diametermm
dsSmall diametermm
lLength of the tapermm
ltTotal length of the workpiece between centresmm
HAHalf angle (set-over for the compound slide)°
IAIncluded angle°
RNTaper ratio, 1 : …—
TPTaper (change in diameter per unit length)—
TFTaper per foot (if the sizes are in inches)—
TOTailstock offsetmm

Worked example

  • Large diameter30 mm
  • Small diameter20 mm
  • Length of the taper100 mm
  • Total length of the workpiece between centres250 mm
  • Half angle (set-over for the compound slide)2.8624 °
  • Included angle5.7248 °
  • Taper ratio, 1 : …10.000
  • Taper (change in diameter per unit length)0.10000
  • Taper per foot (if the sizes are in inches)1.2000
  • Tailstock offset12.500 mm

Limitations

  • Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
  • The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.