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
| Field | What to enter |
|---|---|
| Large diameter | Units: in, mm |
| Small diameter | Units: in, mm |
| Length of taper | Units: 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) |
|---|---|
| 2 | 0.125 |
| 3 | 0.0833 |
| 4 | 0.0625 |
| 5 | 0.05 |
| 6 | 0.0417 |
| 8 | 0.0313 |
Formula
Taper per inch = (D − d) ÷ LTaper per foot = 12 × taper per inchHalf angle = atan((D − d) ÷ 2L); included angle = 2 × half angleRatio = 1 : L ÷ (D − d)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.
Frequently asked questions
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.