Free Lathe Taper Turning Angle Calculator

Calculate compound rest swivel angle in degrees & minutes, Taper Per Foot (TPF), and tailstock offset for manual lathe machining.

⚙️ Taper Dimensions & Presets

Standard Machine Taper Presets

Large Diameter D (in)

Small Diameter d (in)

Taper Length L (in)

Overall Workpiece Lw (in) For tailstock offset method

📊 Machining Angles & Offsets

Compound Rest Angle (α) 0.00° 0° 00' 00" swivel

Total Included Angle (2α) 0.00° 0° 00' full cone

Taper Per Foot (TPF) 0.000" / ft 0.000" / inch (TPI)

Tailstock Setover Offset 0.000" Between centers offset

Formula: tan(α) = (D - d) / (2 × L)

Tailstock Setover Formula: Offset = (Lw × (D - d)) / (2 × L)

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Frequently Asked Questions

Why is the compound rest angle half of the included angle?

Because a lathe rotates the workpiece around a central centerline axis. The tool cuts only on one side of the part at a time, removing metal symmetrically from both sides. Thus, the compound angle α must be exactly half the total included cone angle (2α).

How do you convert decimal degrees to degrees and minutes on a lathe dial?

Multiply the fractional decimal portion by 60. For example, 4.76° = 4 degrees plus (0.76 × 60 = 45.6 minutes), which reads as 4° 46'.

What is the standard Taper Per Foot for a Morse Taper?

Morse tapers vary slightly by size: MT1 is 0.5986" TPF, MT2 is 0.5994" TPF, MT3 is 0.6024" TPF, MT4 is 0.6233" TPF, and MT5 is 0.6315" TPF (~5/8 inch per foot).

What is the limit of the tailstock offset method?

The tailstock offset method is strictly limited to shallow tapers (typically less than 8 degrees). Excessive tailstock offset cocks the dead or live centers at an angle inside the center holes, destroying the bearing contact surface.