What is a Taper?
A taper is a gradual decrease in diameter or width along the length of an object. In construction and machining, tapers are found in tool shanks, pipe fittings, dowel pins, structural columns, and architectural elements. Precise taper calculations are essential for ensuring proper fit between mating parts and for manufacturing tapered components on lathes and milling machines.
Taper is expressed in several ways: taper per foot (TPF), taper per inch (TPI), or as an angle (half angle or included angle). Understanding the relationships between these measurements allows you to set up machine tools correctly and verify taper specifications.
Taper Formulas
Standard Tapers
| Taper Name | TPF | Included Angle | Common Use |
|---|---|---|---|
| Morse Taper #1 | 0.5986" | 2.86° | Drill press, lathe |
| Morse Taper #2 | 0.5994" | 2.86° | Drill press, lathe |
| Morse Taper #3 | 0.6024" | 2.87° | Milling machines |
| Brown & Sharpe #7 | 0.5000" | 2.39° | Milling machines |
| Jacobs Taper #2 | 0.9495" | 4.53° | Drill chucks |
Worked Example
A taper from 3" to 2" diameter over 12 inches:
TPF = 0.0833 × 12 = 1.000 in/ft
Half angle = arctan(0.0833/2) = 2.386°
Included angle = 4.773°
Frequently Asked Questions
What is taper per foot?
Taper per foot (TPF) is the difference in diameter over a 12-inch length. For example, a TPF of 0.600 means the diameter decreases by 0.600 inches for every foot of length. It is the most common way to specify taper in machine shop practice.
How do I set a lathe to cut a taper?
There are several methods: offset the tailstock by half the taper per foot times the workpiece length; use a taper attachment; or use compound rest set to the half angle. The compound rest method is most common for short tapers.
What is the difference between taper and draft?
Taper generally refers to a precise, measured change in diameter for mechanical purposes. Draft (or draft angle) typically refers to the slight taper added to mold cavities, concrete forms, or castings to allow easy removal.