| Morse No. | Taper/ft (in) | Included angle |
|---|
Why Taper Matters in Machining
Tapers are used everywhere in machining: tool shanks, dead centers, reamers, and locating pins all rely on a precise taper to seat and hold securely. The taper rate is usually expressed as taper per foot or as an included angle, and small errors in either compound quickly over a long workpiece. This calculator converts between large diameter, small diameter, and length to get the taper per foot, taper per inch, and both the included and half angle you would dial into a compound slide or verify with a taper gauge.
Taper Per Foot vs Included Angle
Taper per foot describes how much the diameter changes over twelve inches of length, while the included angle describes the total angle between the two tapered surfaces as seen in cross-section. Lathe operators usually work from taper per foot when setting a taper attachment, while toolmakers checking a fit against a gauge or drawing often need the included angle instead. Both describe the same physical taper, just in different units.
Standard Morse Tapers
Morse tapers are a standardized self-holding taper series used on drill shanks, lathe spindles, and tailstock sockets. Each size has a slightly different taper per foot, which is why a No. 2 Morse taper tool will not seat correctly in a No. 3 socket even though the diameters might look close. Use the reference table above to confirm which Morse number matches a taper you have measured.