# Taper Calculator

URL: https://speedycalculator.com/calculators/construction/taper/
Last updated: 2026-10-25

> The taper calculator finds the taper per inch, taper per foot, taper ratio and half and included angles of a conical part from the large diameter, small diameter and length.

## Inputs

- Large diameter (in, mm)
- Small diameter (in, mm)
- Length of taper (in, mm)

## Results

- Taper per inch
- Taper per foot
- Half angle (compound setting)
- Included angle
- Half angle (DMS)
- Taper ratio 1 :

## Formula

```
Taper per inch = (D − d) ÷ L
Taper per foot = 12 × taper per inch
Half angle = atan((D − d) ÷ 2L); included angle = 2 × half angle
Ratio = 1 : L ÷ (D − d)
```

## Explanation

Tapers lock tools into spindles (Morse, R8, CAT), seal pipe threads (NPT is ¾ in per foot) and fit pins and handles. Machinists need the angle to set the compound rest or taper attachment on a lathe, while drawings often state taper per foot or as a ratio.

### How to use the Taper Calculator

- **Large diameter**
- **Small diameter**
- **Length of taper**
- Every result field is editable: type into **Taper per inch** and **Length of taper** plus every other field update to match.

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Enter the large diameter, the small diameter and the length of the taper.

### Tips for an accurate estimate

- Keep units consistent – the calculator handles conversions, but check every field's unit before reading a result.
- Use values from standards, data sheets or test pieces whenever you have them; typical values are only a starting point.
- Apply appropriate safety factors and have structural, electrical and pressure work checked by a qualified professional.
- Record the inputs you used so the calculation can be reviewed later.

### Common mistakes to avoid

- Confusing diameter and radius, or nominal and actual sizes.
- Using allowable stresses and ultimate strengths interchangeably.
- Treating rule-of-thumb results as a substitute for code tables or an engineered design.

### Inputs explained

FieldWhat to enterLarge diameterUnits: in, mmSmall diameterUnits: in, mmLength of taperUnits: in, mm

### What each result means

- **Taper per inch** = ([Large diameter] - [Small diameter])÷[Length of taper]
- **Taper per foot** = 12×[Taper per inch]
- **Half angle (compound setting)** = deg(atan(([Large diameter] - [Small diameter])÷(2×[Length of taper])))
- **Included angle** = 2×[Half angle (compound setting)]
- **Half angle (DMS)** = [Half angle (compound setting)]
- **Taper ratio 1 :** = [Length of taper]÷([Large diameter] - [Small diameter])

### Example values

How the main result changes when **Length of taper** changes and everything else stays at the example values above:

Length of taper (in)Taper per inch (in/in)20.12530.083340.062550.0560.041780.0313

## Worked example

Inputs — Large diameter: 1 in; Small diameter: 0.75 in; Length of taper: 4 in.

Results — **Taper per inch = 0.0625 in/in**; Taper per foot = 0.75 in/ft; Half angle (compound setting) = 1.7899 °; Included angle = 3.5798 °; Half angle (DMS) = 1° 47′ 23.68″; Taper ratio 1 : = 16.

## FAQ

**What is taper per foot?**
The change in diameter over 12 in of length; NPT pipe threads are ¾ in per foot (1:16).

**How do I set a lathe compound for a taper?**
Set it to the half angle – half of the included angle.

**What is a Morse taper?**
A family of self-holding tool tapers of about ⅝ in per foot (roughly 1:20).

**What formula does the Taper Calculator use?**
Taper per inch = (D − d) ÷ L.