Taper Turning Offset Calculator
Calculate lathe tailstock setover, compound rest setting, included angle, half angle, taper rate, and diameter change from real taper dimensions or a target angle.
Calculated taper setup
Named taper dimensions are common shop references. Verify the actual part with micrometers, taper plug/ring gauges, or bluing before a final finishing pass.
| Preset taper | Large dia | Small dia | Length | Taper per ft | Half angle |
|---|---|---|---|---|---|
| Morse Taper 1 | 0.4750 in | 0.3690 in | 2.13 in | 0.5986 in/ft | 1.4287° |
| Morse Taper 2 | 0.7000 in | 0.5720 in | 2.56 in | 0.5994 in/ft | 1.4307° |
| Morse Taper 3 | 0.9380 in | 0.7780 in | 3.19 in | 0.6024 in/ft | 1.4377° |
| Morse Taper 4 | 1.2310 in | 1.0200 in | 4.06 in | 0.6233 in/ft | 1.4876° |
| Morse Taper 5 | 1.7480 in | 1.4750 in | 5.19 in | 0.6315 in/ft | 1.5073° |
| Jacobs Taper 33 | 0.6240 in | 0.5610 in | 1.00 in | 0.7560 in/ft | 1.8048° |
| Lathe method | Best use | Main setting | Formula |
|---|---|---|---|
| Compound rest | Short accurate tapers, shoulders, chuck arbors | Half angle from axis | atan((D-d)/(2L)) |
| Tailstock setover | Long tapers between centers | Offset tailstock center | C(D-d)/(2L) |
| Taper attachment | Repeat tapers with feed carriage | Half angle or taper bar scale | Same half-angle geometry |
| Offset boring bar | Internal tapers and sockets | Compound or attachment angle | Use bore diameters |
| Material | Starter SFM | Finish DOC | Notes for taper fit |
|---|---|---|---|
| Mild steel | 80-160 | 0.003-0.010 in | Stable finish, easy to blue and scrape |
| Alloy steel | 60-120 | 0.002-0.008 in | Use rigid centers and sharp tooling |
| Stainless steel | 40-100 | 0.002-0.006 in | Avoid rubbing on final taper pass |
| Cast iron | 60-140 | 0.003-0.010 in | Check dust control and dry-tool finish |
| Aluminum | 250-600 | 0.004-0.012 in | Polish lightly only after geometry is right |
| Diameter change | Length | Taper per ft | Half angle | Setover at 8 in centers |
|---|---|---|---|---|
| 0.050 in | 2.00 in | 0.300 in/ft | 0.716° | 0.100 in |
| 0.100 in | 2.00 in | 0.600 in/ft | 1.432° | 0.200 in |
| 0.125 in | 4.00 in | 0.375 in/ft | 0.895° | 0.125 in |
| 0.250 in | 5.00 in | 0.600 in/ft | 1.432° | 0.200 in |
For metric work, the calculator converts internally and displays taper rate as diameter change per 100 mm. The same geometry is used for inch and millimeter setups.
Turning tapers on a lathe appears easy enough… but then you measure them and find one end is proud of the other by several thousandths. You can’t get it to seat in a Morse taper. The arbor can rock or fit becomes either loose or seized. Each taper is actualy a triangle wrapped around cylinder with all its attendant geometry that’s unforgiving. A small variation in angle results in a significant difference in diameter over what seems like a modest length.
What happens when you get to cutting the taper? First, you set over the tailstock to tilt entire workpiece as the carriage moves in a straight line. This is great for longer taper in-between centers but the offset you dial isn’t just half the amount of diameter different. Instead it’s the total distance between center on the calculator. And as distance gets further out toward the head stock, the actual angle flattens out making the tool path seem less steep. And if you get the center distance wrong your carefully measured diameters will still be off.
How to Cut Tapers on a Lathe
With compound rest work, however, a different approach apply: keep the tailstock on center and feed along an angled line you set up with slide positioned at half its included angle. This makes sense for when you want a clean shoulder at the big end or if you’re working some very shallow, steep tapers. Problem is, most compound protractors is lousy, with only a quarter-degree resolution. Sounds OK, but it’s going to throw off your taper rate by several thousandths per foot. That is why tool displays the closest reading it can make and how far off it is.
Some folks gets confused about taper length vs. This is the overall part length. True taper length is what calculator asks for. Why? Because if you’re supposed to have a ten-inch bar with just four inches being tapered, and you feed it into math as a full ten-incher, you’ll end up with too-shallow an angle and too-small an offset. It would of been a waste of time and materials, but it is a very common mistake in shops.
The taper rate is typically given in inches/foot on the diameter. That’s the language of many of the old tooling charts and prints. If you find out that your taper calculation come to 0.6 inch/foot, then you know that it’s Morse territory or steeper, such as a Jarno. The half angle and the included angle talk specifically to setting up machine. Depending on whether you’ll be swiveling or offsetting, one of them is more useful than the other. But they’re two ways of talking about same thing.
There’s also material selection. Stainless steel has a bad finish making every dull edge and vibration obvious. It will ruin the fit before you ever check it with bluing. Aluminum springs less, cuts cleanly, and is forgiving of small angling mistakes. You can see connection between rigidity, surface feet per minute and finish allowance in reference tables on page.
Allow for a spring pass. Don’t trust the dial alone, always indicate your tailstock movement, and be sure to test with layout dye. A single light band of blue tell you more than three micrometer readings. The trick to taper turning isn’t getting the exact number right but knowing which number adjusts what. Once you see how length, diameter difference, and center distance affect each other, numbers no longer seem random. A half degree adjustment here has a predictable feel in the cut.
Is it safer to adjust tailstock or the compound? It’s not so much math as intuition. Finally everything drops into place with a click rather than a wiggle.
