How to Use Taper Calculator
The Taper Calculator needs only three measurements.
- Choose a unit — mm, cm or inch.
- Enter large diameter (D), small diameter (d) and length (L) — Use the projected length along the axis.
- Read the result — Taper ratio, taper per inch, taper per foot, half angle, included angle.
Formula & Theory — Taper Calculator
The Taper Calculator is rooted in plane trigonometry:
Ratio = (D - d) / L
TPI = (D - d) / L (if L in inches)
TPF = 12 × TPI
HalfAngle = arctan((D - d) / (2 × L))
IncludedAng = 2 × HalfAngle| Symbol | Meaning |
|---|---|
| D | Large diameter |
| d | Small diameter |
| L | Axial length over which taper occurs |
Common machine tapers include Morse, Jacobs and NMTB; each is defined by a known taper ratio that the Taper Calculator can verify.
Tapers and self-holding
Self-holding tapers (Morse, Brown & Sharpe) rely on small included angles (≈ 3°). Self-releasing tapers (CAT, BT) use larger angles for quick changeover.
Use Cases for Taper Calculator
- Lathe setup — Match the compound slide angle to a target taper.
- Tool calibration — Verify Morse or Jacobs taper geometry on tool shanks.
- Machine repair — Recalculate worn or modified spindle tapers.
- Mechanical design — Specify drift pins, plug gauges and reamers.
- Education — Reinforce the link between linear taper and trigonometric angle.
- Quality control — Inspect parts against drawings using calculated angles.
The Taper Calculator turns three measurements into the complete geometric specification of any taper.