Manual machining
Tailstock offset calculator
Offset = (D - d) x L / (2 x l); a 0.100 in taper over 4.000 in on a 10.000 in part needs 0.1250 in of offset.
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Tailstock offset
in
offset = (D - d) x L / (2 x l) = (1 - 0.9) x 10 / (2 x 4) = 0.1250 in
Set the tailstock over 0.1250 in (3.18 mm). Read it with a dial indicator on the quill.
Half angle (cross-check)
°
half angle = atan((D - d) / (2 x l)) = atan((1 - 0.9) / (2 x 4)) = 0.7162°
TPF = 12 x (D - d) / l = 12 x (1 - 0.9) / 4 = 0.3000 in/ft. Half angle 0° 42' 58", for cross-checking against a gauge or the compound.
Source: Machinery's Handbook (turning tapers by tailstock offset)
The offset is a starting point. Indicate the finished taper or blue it against a gauge before you call it done.
How it works
offset = (D - d) x L / (2 x l); offset = TPF x L / 24
| Symbol | Meaning | Unit |
|---|---|---|
| D | Large end diameter | in or mm |
| d | Small end diameter | in or mm |
| l | Length of the tapered section | in or mm |
| L | Overall length of the work between center points | in or mm |
| TPF | Taper per foot, change in diameter over 12 in of length | in/ft |
When the whole part is tapered, l = L and the offset is (D - d) / 2. In metric, a taper is written as a ratio 1:k with k = l / (D - d), and the offset is L / (2 x k). The offset is half the diameter change spread over the full work length, which is why a longer part needs more offset for the same taper.
Worked example: offset from end diameters (inch)
D = 1.000 in, d = 0.900 in, taper length l = 4.000 in, work length L = 10.000 in.
- D - d = 1.000 - 0.900 = 0.100 in.
- Offset = 0.100 x 10.000 / (2 x 4.000) = 1.000 / 8.000 = 0.1250 in.
- Check by taper per foot: TPF = 12 x 0.100 / 4.000 = 0.300 in/ft; 0.300 x 10.000 / 24 = 0.1250 in.
Result: 0.1250 in (3.18 mm) of offset. Half angle 0.7162°.
Worked example: offset from end diameters (metric)
D = 30 mm, d = 28 mm, taper length l = 100 mm, work length L = 250 mm.
- D - d = 30 - 28 = 2 mm.
- Offset = 2 x 250 / (2 x 100) = 500 / 200 = 2.50 mm.
Result: 2.50 mm of offset, a 1:50 taper.
Setting the offset
- Compute the offset with the calculator above.
- Move the tailstock over by that amount. Read it with a dial indicator on the quill, not the scale on the base.
- Take a trial cut and check the taper.
- Adjust the offset and recut.
Shop notes
- Every part in a batch must be the same length and center-drilled to the same depth, or the taper changes from part to part.
- The offset tilts the centers in their center holes, so long offsets wear the center holes.
- Return the tailstock to zero after the job.
- Morse taper check: MT2 at 0.59941 in/ft, tapered over the full 6.000 in length of the work, needs 0.59941 x 6.000 / 24 = 0.1499 in of offset.
How to choose a setup
- Long, shallow tapers between centers: tailstock offset.
- Steeper or short tapers: a taper attachment or the compound.
- Short, steep tapers: set the compound to half the included angle, from the taper calculator.
FAQ
How do you calculate tailstock offset for a taper?
Offset = (D - d) x L / (2 x l). A 0.100 in taper over 4.000 in on a 10.000 in part is 0.100 x 10.000 / 8.000 = 0.1250 in.
How do you set the offset from taper per foot?
Offset = TPF x L / 24. 0.300 in/ft on a 10.000 in part is 0.300 x 10.000 / 24 = 0.1250 in.
Why did the second part come out with a different taper?
A different overall length or center hole depth changes L, and at the same offset that changes the taper. Cut every part in a batch to the same length and center-drill it to the same depth.
Tailstock offset or taper attachment?
Tailstock offset suits long, shallow tapers between centers. A taper attachment or the compound suits steeper and short tapers; for a short steep taper, set the compound to half the included angle.
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