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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.
Diameter or width at the wide end
Diameter or width at the narrow end
Axial length of the tapered section

Unidad

Included taper angle
5,7248

Full angle between the two sloping sides of the taper

Half-angle (per side)
2,8624°
Taper per 300 mm
30 mm
Taper per unit length
0,1 mm/mm
Dimension difference (D1−D2)
10 mm
Large end = 25Small end = 15Longitud = 100
Cross-section of the tapered piece — angle exaggerated for clarity
How the angle is calculated
1

Difference in size (both sides contribute equally)

(25 − 15) / 2 = 5 mm per side
2

Half-angle: arctan(half-difference / length)

arctan(5 / 100) = 2,8624°
=

Included angle = 2 × half-angle

2 × 2,8624° = 5,7248°
Step by step
  1. 1

    Half the diameter difference

    (25 − 15) ÷ 2 = 5 mm
  2. 2

    Half-angle (one side)

    arctan(5 ÷ 100) = 2,8624°
    Inverse tangent of the per-side offset divided by the axial length.
  3. 3

    Included taper angle

    2 × 2,8624° = 5,7248
Los resultados son estimaciones con fines meramente informativos y no constituyen asesoramiento profesional — verifica siempre los resultados importantes de forma independiente antes de basarte en ellos. Leer el aviso legal completo.
Respuesta rápida

¿Cómo funciona esta calculadora?

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.

Fórmula
Half-angle = arctan((D₁ − D₂) / (2 × L)) • Included angle = 2 × half-angle • Taper per foot = ((D₁ − D₂) / L) × 12
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.

Preguntas frecuentes

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.

APA

TG we-Calculate Editorial Team. (2026). Taper Calculator — Taper Angle & Taper Per Foot [Online calculator]. TG we-Calculate. https://we-calculate.com/es/calculator/taper-calculator

Chicago

TG we-Calculate Editorial Team. "Taper Calculator — Taper Angle & Taper Per Foot." TG we-Calculate. 2026. https://we-calculate.com/es/calculator/taper-calculator.

IEEE

TG we-Calculate Editorial Team, "Taper Calculator — Taper Angle & Taper Per Foot," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/es/calculator/taper-calculator

BibTeX

@misc{wecalculate_taper_calculator, title = {Taper Calculator — Taper Angle & Taper Per Foot}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/es/calculator/taper-calculator}}, year = {2026}, note = {TG we-Calculate} }

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