# Lathe Taper Per Foot and Tailstock Offset Calculator > Source: https://netray.co/tools/lathe-taper-per-foot-and-tailstock-offset-calculator > Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems. > Section: Free Tools ## Short answer Calculate taper per foot, taper per inch, an approximate half angle and tailstock setover from large and small diameters. ## Category manufacturing ## Industry Machining ## Audience - CNC machinist - Toolmaker - Machine shop owner ## Tool **Kind:** calculator **Inputs:** #### Large diameter **Key:** big_d **Type:** number **Default:** 1 **Min:** 0 **Step:** 0.001 **Unit:** in **Help:** Diameter at the large end of the taper. #### Small diameter **Key:** small_d **Type:** number **Default:** 0.8 **Min:** 0 **Step:** 0.001 **Unit:** in **Help:** Diameter at the small end of the taper. #### Length of the taper **Key:** taper_len **Type:** number **Default:** 4 **Min:** 0.01 **Step:** 0.01 **Unit:** in **Help:** Axial length from large to small diameter. #### Total length of workpiece between centers **Key:** total_len **Type:** number **Default:** 10 **Min:** 0.01 **Step:** 0.01 **Unit:** in **Help:** Used for tailstock setover only. **Outputs:** #### Taper per inch (on diameter) **Key:** tpi **Expr:** (big_d - small_d) / taper_len **Format:** decimal **Description:** Change in diameter per inch of length. #### Taper per foot **Key:** tpf **Expr:** tpi * 12 **Format:** decimal **Primary:** true **Description:** Change in diameter per 12 inches of length. #### Approximate half angle (degrees) **Key:** half_angle **Expr:** tpi * 28.6479 **Format:** decimal **Description:** Small angle approximation, accurate to roughly 0.1 degree for tapers under about 10 degrees included. Use it as the compound slide setting. #### Radial change over taper **Key:** radial **Expr:** (big_d - small_d) / 2 **Format:** decimal **Description:** Amount the tool moves in X across the taper. #### Tailstock setover **Key:** offset **Expr:** radial * total_len / taper_len **Format:** decimal **Primary:** true **Description:** Setover of the tailstock for the whole workpiece length when turning between centers. **Chart:** #### Tailstock setover vs taper length **Type:** line **X:** taper_len **From:** 1 **To:** 10 **Steps:** 20 **Series:** - offset **Disclaimer:** The half angle uses a small angle approximation. For steep tapers use a trigonometric calculation. Tailstock setover also changes the center contact, so use it for light tapers only and confirm with a test cut. ## Content **Intro:** Taper per foot is the standard way to specify a taper in inch drawings. This calculator turns your diameters and lengths into taper per foot, taper per inch, a compound slide angle and the tailstock setover. **Sections:** #### How to use the calculator **Body:** Enter the large and small diameters of the taper, then the length of the tapered section. The tool gives taper per inch, which is the diameter change over one inch of length, and taper per foot, which is that value times twelve. If you turn between centers, also enter the total workpiece length to get the tailstock setover. For CNC work you can use the radial change directly in your program, but this is still handy for checking drawings and manual lathes. **Bullets:** - Taper per foot = (D - d) / L x 12. - Half angle is the compound slide setting for a manual lathe. - Tailstock setover works only for external tapers between centers. #### The formulas **Body:** Taper per inch is the large diameter minus the small diameter, divided by the taper length. Multiply by twelve for taper per foot. The half angle in degrees is the arctangent of half the taper per inch, which for small tapers is close to taper per inch times 28.648. Tailstock setover is half the diameter change times the ratio of the total length to the taper length. When the taper runs the full length of the part, the setover is simply half the diameter change. #### Worked example **Body:** A shaft is 1.000 in at the large end and 0.800 in at the small end over 4 in of taper. Taper per inch is 0.05 and taper per foot is 0.6. The half angle is about 1.43 degrees. If the workpiece is 10 in long between centers, the tailstock setover is 0.100 times 10 divided by 4, which is 0.250 in. Compare this with common standard tapers: the Morse tapers run roughly 0.6 inches per foot, and Jacobs and Brown and Sharpe tapers have their own values. #### Common mistakes **Body:** Using the total length instead of the taper length for the taper per inch, forgetting that setover is a radial value (half the diameter change), and mixing up included angle with half angle on the compound slide. Another mistake is cutting a steep taper by tailstock setover, which distorts the center holes and wears them unevenly. For a CNC lathe, use a G01 move or a taper cycle with the radial change per unit length. **Cta:** If you want taper and geometry checks built into your quote or routing step, Netray can help automate checks of this kind inside your ERP. **Faq:** #### How do you calculate taper per foot? **Answer:** Subtract the small diameter from the large diameter, divide by the length of the taper in inches, and multiply by 12. For example, 1.000 and 0.800 over 4 inches gives 0.05 per inch, or 0.6 per foot. #### How do you calculate tailstock offset? **Answer:** Take half the difference between the large and small diameters, divide by the taper length, and multiply by the total length between centers. When the taper covers the full length, the offset is half the diameter change. #### What angle do I set the compound slide to? **Answer:** Set it to the half angle of the taper, measured from the lathe axis. For small tapers the half angle in degrees is about 28.65 times the taper per inch. Always verify with a test cut and a taper gauge. #### Is tailstock offset accurate for steep tapers? **Answer:** No. Offsetting the tailstock tilts the workpiece on its centers, which distorts the center hole and gives a slight error. It is best for light tapers. For steep tapers use the compound slide or a CNC taper move. ## Search terms taper per foot calculator, tailstock offset calculator, lathe taper calculator, taper per inch formula, compound slide angle taper, how to turn a taper, morse taper per foot, tailstock setover formula --- Talk to an engineer: https://netray.co/contact?intent=erp_ai | Machine catalog: https://netray.co/agent/catalog.json