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How to Measure a Taper
Guide · Updated October 28, 2026
A taper is defined by how much the diameter changes over a length. Measure two diameters a known distance apart and you can calculate taper per foot (TPF) and the included angle.
Set the spacing exactly
Build the exact spacing stack between your two measuring heights with the free Gage Block Calculator.
Step by step
- Stand the part: Set the part small end down on a surface plate, square to the plate.
- Measure the first diameter: Rest the micrometer on a gage block stack to fix the first height and measure the diameter there.
- Measure the second diameter: Add a known stack, for example 2.0000 in, and measure the diameter at the new height.
- Taper per inch: Taper per inch on diameter = (large D − small D) ÷ spacing.
- Convert: TPF = taper per inch × 12. Half angle = arctan((D − d) ÷ (2 × L)); included angle = 2 × half angle.
- Confirm fit: For mating tapers, blue the male part, seat it with a light twist, and check for even contact.
Worked example
Diameters 0.9500 in and 1.0000 in measured 2.0000 in apart. Taper per inch = 0.0500 ÷ 2 = 0.025, so TPF = 0.300 in/ft.
Half angle = arctan(0.0500 ÷ 4.000) = arctan(0.0125) ≈ 0.716°; included angle ≈ 1.432° (about 1° 26′). Morse tapers, for comparison, are close to 0.600–0.630 in/ft.
Tips
- For precise angles, set the taper on a sine bar: sine bar with gage blocks and the sine bar calculator.
- Rock the micrometer to find the true diameter: reading a micrometer.
- Tapers between centers: how to use a bench center.
- Quick angle checks: bevel protractor.
FAQ
How do you calculate taper per foot?
TPF = (large diameter − small diameter) ÷ length in inches × 12.
How do you convert taper per foot to angle?
Half angle = arctan(TPF ÷ 24); double it for the included angle.
How do I measure a taper without special tools?
Measure two diameters with a micrometer at a known spacing set with gage blocks on a surface plate.
How do I check if a taper fits its socket?
Apply a thin coat of bluing to the male taper, seat it with a light twist, and look for even contact along the length.
Is there a free gage block calculator?
Yes. The Gage Block Calculator at gageblockcalc.com builds any stack, free with no login.
Related guides and calculators
- How to use a sine bar with gage blocks
- Sine bar calculator
- How to use a bevel protractor
- How to use a bench center
- How to build a gage block stack
- How to Cut a Taper on a Lathe
- How to Cut a Taper with the Compound
- How to Cut a Taper with a Taper Attachment
- How to Check a Taper with a Sine Bar
- NPT Pipe Threading Basics for Machinists
- How to Thread Pipe with a Hand Pipe Die (NPT)
- All free machinist calculators
- How to Align a Lathe Tailstock
- Morse Taper Dimensions Chart
- Jacobs Taper Chart: Drill Chuck Taper Dimensions
- Brown & Sharpe and Jarno Taper Chart
- CAT, BT, R8 and HSK Toolholder Basics
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Questions? Ask a machinist.
General shop information only — follow your tooling, machine and gage manufacturers' instructions and your quality system.