Free Lathe Taper Turning Calculator
Calculate compound rest swivel angle, tailstock setover offset, taper per foot (TPF), and metric taper ratios for manual and CNC lathe machining.
⚙️ Workpiece & Taper Dimensions
Total Included Angle: 9.53° (Twice centerline angle)
• Compound Rest: Best for steep, short tapers (under 3" to 4" long due to slide travel limits). Feeds manually.
• Tailstock Setover: Best for shallow tapers on long shafts. Enables automatic power longitudinal feed.
• Taper Attachment: Preferred shop method for any taper under 10° that requires smooth power feed and threading.
Compound Protractor Alignment Tip: Lathe compound protractors can be off by 0.5° from the factory. For precision tapers, clamp a dial test indicator in the toolpost and sweep a sine bar or Morse taper gauge mounted between centers to zero in your angle.
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Geometry of Lathe Tapers
A taper is a uniform change in workpiece diameter along its longitudinal axis. In machining, tapers are specified either by the angle from the centerline ($alpha$), the Taper Per Foot (TPF), or the metric taper ratio ($1:K$):
Included Full Angle: 2 × α
Taper Per Foot (TPF): TPF = [ (D - d) / L ] × 12
Metric Ratio (1:K): K = L / (D - d)
Tailstock Setover: S = [ L_total × (D - d) ] / (2 × L)
Why the Entire Workpiece Length Dictates Tailstock Setover
When cutting a taper by offsetting the tailstock dead center, the entire workpiece pivots about its headstock center. Even if the actual tapered section is only 2 inches long at the end of a 10-inch shaft, you must calculate the setover using the full 10-inch center-to-center distance ($L_{total}$). Using only the taper length ($L$) will produce a drastically steeper, ruined taper!
Frequently Asked Questions
Why does my lathe compound scale read 90 degrees when aligned straight?
Different lathe manufacturers index their compound protractors differently. Some read 0° when perpendicular to the spindle axis (cross-slide parallel), while others read 0° when parallel to the bed. Always verify which axis your protractor zeroes against before locking the swivel.
Can I cut threads on a taper using the compound rest?
No, because the lathe leadscrew feeds parallel to the bedways. To cut tapered pipe threads (such as NPT), you must either use a dedicated taper turning attachment or offset the tailstock.
What is the standard angle of a Morse Taper?
Morse Tapers have a very shallow self-holding taper of approximately 5/8" per foot (~0.600 to 0.625 TPF), corresponding to a centerline half-angle of roughly 1.43° to 1.49°. This shallow angle creates tremendous wedging friction that locks drill chucks into drill presses without slipping.