Calculate a 1:10 taper half-angle, included angle, end diameter, required length, or measured taper ratio in metric and imperial units.

Enter the small-end diameter and axial length.

A 1:10 diametral taper changes diameter by one unit per ten units of axial length. Its radial surface slope is 1:20. Dimensions use 0–10¹² mm; required positive dimensions must be at least 10⁻¹² mm.

Related Calculators

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)
  • D_L is the diameter at the large end (mm)
  • D_S 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 (D_L) in millimeters.
  2. Next, measure the diameter at the small end (D_S) in millimeters.
  3. Then, measure the length of the taper (L) in millimeters.
  4. Use the formula TA = atan((D_L – D_S) / (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 (D_L) = 50 mm

Diameter at Small End (D_S) = 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.