Calculate the 1:10 taper angle (2.86° half-angle, 5.72° included), end diameter or length, or convert any taper ratio or taper per foot to degrees.

A 1:10 taper changes diameter by 1 unit per 10 units of axial length (radial slope 1:20).

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1:10 Taper Angle Formula

The following formula is used to calculate the 1:10 taper angle.

TA = atan[(DL – DS)/(2 · L)] · 180/π

Variables:

  • TA is the half-angle between the taper surface and its axis (degrees)
  • DL is the diameter at the large end (mm)
  • DS is the diameter at the small end (mm)
  • L is the axial length of the taper (mm; all dimensions must use the same unit)

To calculate the 1:10 taper angle, use the arctangent function to find the angle in radians and then convert it to degrees. The taper ratio of 1:10 means that for every 10 units of length, the diameter changes by 1 unit.

What is a 1:10 Taper Angle?

A 1:10 taper angle is used to describe the gradual decrease in diameter of a conical shape or the angle of the surface of a taper. It is a common specification in engineering for tapered pins, shafts, or holes, where the diameter decreases at a rate of 1 unit for every 10 units of length. The ratio describes geometry; fit and retention depend on mating tolerances, surface condition, seating or clamping force and service loads.

How to Calculate a 1:10 Taper Angle?

The following steps outline how to calculate the 1:10 Taper Angle.

  1. First, measure the diameter at the large end (DL) in millimeters.
  2. Next, measure the diameter at the small end (DS) in millimeters.
  3. Then, measure the length of the taper (L) in millimeters.
  4. Use the formula TA = atan((DL – DS) / (2 * L)) * (180 / π) to calculate the taper angle (TA) in degrees.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Diameter at Large End (DL) = 50 mm

Diameter at Small End (DS) = 40 mm

Length (L) = 100 mm. The diameter taper is (50 − 40) / 100 = 1:10. The half-angle is atan(0.05) ≈ 2.862405°, and the included angle is twice this, ≈ 5.724810°. See the taper and inclination definitions in Workshop Calculation and Science.