Taper Calculator
Solve any taper from three measurements. Enter the large end, small end, and taper length in inches to get taper per foot, the included and half (per-side) angles in degrees, and the 1:x taper ratio.
Example: with Large end diameter (in) 1.5 · Small end diameter (in) 0.75 · Taper length (in) 6 → Taper per foot: 1.5000 in/ft (0.1250 in/in).
- Included angle7.153°
- Angle per side (half angle)3.576° (set the compound to this)
- Taper ratio1 : 8.00 (1 in of diameter per 8.00 in of length)
Computed by the calculator below using its default values. Change any input to see your own numbers.
Taper per foot = (D − d) ÷ length × 12. Included angle = 2 × atan((D − d) ÷ (2 × length)) — the compound-slide setting is the half angle.
Reading a taper three different ways
Machinists describe the same cone three ways. Taper per foot — how much the diameter shrinks over 12 inches — is the American shop convention (a Morse taper is about 5/8 in/ft, a Jarno exactly 0.600). The taper ratio 1:x, common in metric standards, says the diameter changes one unit per x units of length (ISO spindle tapers are 1:3.429, written as 7:24). And the angle is what the machine wants: a lathe compound or a sine bar is set to the half angle, because the tool follows one side of the cone.
The trig is one triangle: half the diameter difference over the length gives the tangent of the half angle. Doubling that gives the included angle. Note that a 1 in/ft taper is 4.772°, not 4.764° — the angle is not simply proportional to TPF because tangent is nonlinear.
How it’s calculated
With large diameter D, small diameter d, and axial length L (all inches): taper per foot = (D − d) ÷ L × 12; half angle = atan((D − d) ÷ (2L)) in degrees; included angle = 2 × half angle; ratio = 1 : L ÷ (D − d). Standard machine-shop relations as tabulated in Machinery's Handbook.
Measures a straight (conical) taper on diameters — for tapers given on one side only, such as flat wedges, halve the diameter difference before comparing.
Common standard tapers
| Standard | Taper | Included angle |
|---|---|---|
| Morse (avg, MT0–MT7) | ≈ 0.625 in/ft | ≈ 2.98° |
| Jarno | 0.600 in/ft | 2.864° |
| Brown & Sharpe | 0.500 in/ft | 2.387° |
| Jacobs #33 (chuck arbor) | 0.7644 in/ft | 3.648° |
| NMTB / CAT (7:24) | 3.500 in/ft | 16.594° |
| Pipe thread (NPT) | 0.750 in/ft | 3.580° |
Machinery's Handbook standard taper tables; Morse tapers vary slightly by size (0.598–0.631 in/ft), so an average is shown.
Common mistakes
- Setting the compound to the included angle instead of the half angle — the part comes out twice as steep.
- Measuring taper on the radius but entering it as diameter difference (or vice versa); diameters are the convention here.
- Using the workpiece's overall length instead of the tapered section's length.
- Assuming angle scales linearly with taper per foot — tangent curvature makes 3 in/ft slightly less than 3× the angle of 1 in/ft.
Frequently asked questions
How do you calculate taper per foot?
Subtract the small diameter from the large, divide by the taper length, and multiply by 12. A part going from 1.5 to 0.75 in over 6 in tapers (0.75 ÷ 6) × 12 = 1.5 inches per foot.
How do I get the taper angle?
Half angle = atan((D − d) ÷ (2 × length)); double it for the included angle. The same 1.5 in/ft example gives atan(0.75 ÷ 12) = 3.576° per side, 7.153° included.
What angle do I set the lathe compound to?
The half angle (per side), not the included angle. The compound slides along one flank of the cone, so a 7.15° included taper means a 3.58° compound setting.
What does a 1:8 taper mean?
The diameter changes 1 unit for every 8 units of length — equivalent to 1.5 in/ft. Ratios and taper-per-foot are interchangeable: TPF = 12 ÷ x for a 1:x taper.