calculate taper per foot

In the world of machining, woodworking, and engineering, precision is everything. One of the most common measurements you'll encounter when working with lathes or conical parts is the "taper per foot." Understanding how to calculate this accurately ensures that parts fit together perfectly, whether you are creating a custom spindle or setting up a machine tool.

What is Taper Per Foot?

Taper per foot (TPF) is a ratio that describes how much the diameter of a cylindrical object changes over a length of twelve inches. It is a standard unit of measurement in North American machining, used to define the steepness of a cone-shaped workpiece.

The Taper Per Foot Formula

To calculate taper per foot manually, you need three primary measurements: the diameter at the large end, the diameter at the small end, and the length over which that change occurs. The formula is as follows:

TPF = ((Large Diameter - Small Diameter) / Length of Taper) × 12

By subtracting the small diameter from the large diameter, you find the total amount of taper. Dividing that by the length gives you the "taper per inch." Multiplying by 12 converts that value to the standard "per foot" measurement.

Step-by-Step Calculation Example

Let's say you have a steel rod that needs to be turned on a lathe. You measure the following:

• Large Diameter: 2.0 inches
• Small Diameter: 1.5 inches
• Length: 4 inches

First, find the difference in diameters: 2.0 - 1.5 = 0.5 inches. Next, divide by the length: 0.5 / 4 = 0.125 (this is your taper per inch). Finally, multiply by 12: 0.125 × 12 = 1.5. Your taper per foot is 1.5 inches.

Common Standard Tapers

In industry, several standard tapers are frequently used. Instead of calculating them from scratch, machinists often refer to these known values:

• Morse Taper: Generally around 0.625 inches per foot (varies slightly by size).
• Brown & Sharpe Taper: Usually 0.500 inches per foot.
• Jarno Taper: Exactly 0.600 inches per foot.
• NMTB Taper: Exactly 3.500 inches per foot.

Why Accurate TPF Matters

If the taper per foot is incorrect, the mating parts will not seat properly. In high-pressure or high-torque applications (like a drill bit in a drill press spindle), an incorrect taper can lead to slipping, vibration, or even catastrophic tool failure. Using a calculator or the formula ensures that the friction-fit of the taper is maximized for safety and performance.