📏 Taper & Angle Calculator

Understanding Tapers

A taper is a gradual change in diameter along the length of a workpiece. Tapers are everywhere in machining — Morse taper toolholders, lathe centers, valve seats, pipe threads, and precision fits. The key measurements are taper per foot (TPF), taper per inch (TPI), and the included angle — and knowing how to convert between them is fundamental shop math.

• Taper per foot (TPF): The change in diameter over 12 inches of length. This is the standard way tapers are specified in the US. A Morse #2 taper is approximately 0.5994 TPF.
• Taper per inch (TPI): Same concept scaled to 1 inch. Useful for short workpieces where TPF would be an awkwardly large number relative to the actual part.
• Included angle: The total angle between the two taper surfaces. The half angle is what you set on your compound slide or taper attachment. Don't confuse the two — setting the included angle on your compound gives you double the taper.

Practical Tips

• Sine bar setup: When using a sine bar to grind or inspect a taper, you need the gage block stack height. This calculator gives you that number directly — just make sure you're using the half angle, not the included angle.
• Compound slide: Set the compound to the half angle when turning tapers. If the taper is longer than your compound travel, use the taper attachment or offset the tailstock instead.
• Tailstock offset: For external tapers between centers, offset = (TPF × total length) / 24. This only works for full-length tapers — partial tapers need the compound or taper attachment.
• Checking with bluing: Apply layout blue to the taper, insert into the mating socket, and rotate. Contact should show as at least 80% across the bearing area. Stripes at one end mean the angle is wrong.
• Standard tapers are standardized for a reason: Morse, Brown & Sharpe, and Jarno tapers are designed for self-holding — the taper angle is shallow enough that friction locks the tool in place. Steeper tapers (like CAT/BT) need a drawbar to retain.

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