Taper Calculator — Taper Angle & Taper Per Foot
Enter the large-end dimension, small-end dimension and length of a tapered piece to find the included taper angle, half-angle (per side), taper ratio and taper-per-foot — useful for machining, carpentry and any fabrication work.
Мерна единица
Full angle between the two sloping sides of the taper
Difference in size (both sides contribute equally)
Half-angle: arctan(half-difference / length)
Included angle = 2 × half-angle
- 1
Half the diameter difference
(25 − 15) ÷ 2 = 5 mm - 2
Half-angle (one side)
arctan(5 ÷ 100) = 2,8624°Inverse tangent of the per-side offset divided by the axial length. - 3
Included taper angle
2 × 2,8624° = 5,7248
Как работи този калкулатор?
Taper half-angle = arctan((D₁−D₂) / (2×L)); included angle = 2 × half-angle. Taper per foot = ((D₁−D₂)/L) × 12 (for inch units). The formula applies to round shafts, flat boards, and any linear taper — just keep units consistent. Standard Morse taper has ~1.49° half-angle per size step.
Формула
How this is calculated
A taper is a gradual change in the cross-section of a workpiece along its length. For a symmetric taper (centred on the axis), each side makes an equal angle with the centreline called the half-angle. The included angle is twice this — the full wedge angle you would measure with an angle gauge from one sloping face to the other.
The half-angle is computed with the inverse tangent: arctan((D₁ − D₂) / (2 × L)), where (D₁ − D₂) / 2 is the radial difference per side and L is the axial length. Machinists and engineers also express taper as a dimensionless ratio — taper per unit length = (D₁ − D₂) / L — or in the traditional US/imperial form as taper per foot (TPF = ratio × 12) or in metric workshops as taper per 300 mm. Standard self-holding tapers (Morse, Jacobs, Brown & Sharpe) have specified TPF values that determine whether the taper self-locks or releases under load.
This calculator does not assume a round cross-section — the same formulas apply to flat tapers in woodworking or any linear taper. Enter consistent units (all mm or all inches) and the result is unit-independent.
Често задавани въпроси
The included angle is the full wedge angle measured between the two sloping sides. The half-angle is the angle each side makes with the centreline. Lathes and tapers are often specified in half-angle (the tool-setting angle), while included angle is more common in geometry and inspection.
Taper per foot expresses the change in diameter per 12 inches of length. For example, a Morse No. 2 taper has a TPF of approximately 0.5994 inches. It is the standard way to specify self-holding tool tapers in inch-based machining.
Yes. Enter the width at the large end, the width at the small end, and the length. The formula is identical whether the cross-section is circular or rectangular — only the linear dimensions along each side matter.
TG we-Calculate Editorial Team. (2026). Taper Calculator — Taper Angle & Taper Per Foot [Online calculator]. TG we-Calculate. https://we-calculate.com/bg/calculator/taper-calculator
TG we-Calculate Editorial Team. "Taper Calculator — Taper Angle & Taper Per Foot." TG we-Calculate. 2026. https://we-calculate.com/bg/calculator/taper-calculator.
TG we-Calculate Editorial Team, "Taper Calculator — Taper Angle & Taper Per Foot," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/bg/calculator/taper-calculator
@misc{wecalculate_taper_calculator, title = {Taper Calculator — Taper Angle & Taper Per Foot}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/bg/calculator/taper-calculator}}, year = {2026}, note = {TG we-Calculate} }
Помогна ли ви този калкулатор?