Taper Calculator
Free taper calculator: compute taper per inch, taper per foot, and taper angle from major and minor diameters. Ideal for machining, tooling, and engineering.
About This Calculator
The Taper Calculator computes key taper parameters for machining and engineering applications. A taper is a gradual reduction in the cross-section of a workpiece from one end to the other, forming a conical profile similar to a frustum or truncated cone. This calculator helps machinists, engineers, and DIY enthusiasts determine the taper per inch (TPI), taper per foot (TPF), and taper angle from the major diameter, minor diameter, and taper length.
The calculations are based on standard taper formulas. Taper per inch (TPI) is calculated as (Dl - Ds) / Tl, where Dl is the major diameter, Ds is the minor diameter, and Tl is the taper length. Taper per foot (TPF) is 12 times TPI, converting the rate to inches per foot. The taper angle θ is derived from arctan(TPI / 2), giving the angle between the centerline and the sloped side of the taper.
Regional Notes
United States: Taper per foot (TPF) is the standard specification in US machining, commonly used for Morse tapers, Brown and Sharpe tapers, and machine tool spindles. Standard Morse taper sizes range from #0 to #7 with specified TPF values.
United Kingdom: UK machining follows similar standards to the US, with Morse tapers being widely used in lathe centers, drill chucks, and toolholders. Metric tapers are also common in European-manufactured equipment.
India: Indian machine shops use both Morse tapers and metric tapers depending on the equipment origin. IS and BIS standards align with international taper specifications for interchangeability of tooling.
Tapers are essential in applications such as drill chucks, arbors, nails, bolts, screws, toolholders, and self-holding circular objects. Common taper standard series include Morse, Brown and Sharpe, Jarno, metric, and Jacobs tapers.
Frequently Asked Questions
What is a taper in machining?
A taper is a gradual reduction in the cross-section of a workpiece from one end to the other, forming a conical profile. Tapers are commonly used in drill chucks, arbors, nails, bolts, screws, and toolholders for mounting and self-holding applications.
How do you calculate taper per inch?
Taper per inch (TPI) is calculated by dividing the difference between the major diameter and minor diameter by the taper length. The formula is TPI = (Dl - Ds) / Tl, where Dl is the major diameter, Ds is the minor diameter, and Tl is the taper length.
How do you calculate taper per foot?
Taper per foot (TPF) is calculated by multiplying the taper per inch by 12. The formula is TPF = 12 × (Dl - Ds) / Tl. This converts the taper rate from inches per inch to inches per foot of length.
How is taper angle calculated?
The taper angle is the angle between the center line and the sloped side of the taper. It is calculated using the formula θ = arctan(TPI / 2), where TPI is the taper per inch. The result is expressed in degrees.
What are common types of tapers?
Common taper types include Morse tapers (used in drill chucks and machine tool spindles), Brown and Sharpe tapers, Jarno tapers, metric tapers, and Jacobs tapers. Tapers are also classified by location as internal or external, and by use as self-holding or quick releasing.
What is the difference between taper per inch and taper per foot?
Taper per inch (TPI) measures the diameter reduction per inch of length, while taper per foot (TPF) measures the reduction per foot of length. TPF is always 12 times TPI, since one foot equals 12 inches. TPF is commonly used in US machining standards.
Can a taper have negative values?
Yes, when the minor diameter is larger than the major diameter, the taper per inch becomes negative, indicating a reverse taper or expanding profile. Negative tapers are used in specific applications like release tapers where quick disassembly is needed.