Tailstock Offset Taper Calculator
Calculate the tailstock set-over for turning a taper between centers, then check taper per foot, included angle, offset direction, and center-height risk before making chips.
Preset dimensions are working shop references for layout and trial cuts; verify against the actual gauge or mating socket before the final pass.
Tailstock offset results
| Preset taper | Large dia | Small dia | Taper length | Taper per foot |
|---|---|---|---|---|
| Morse Taper No. 1 | 0.4750 in | 0.3690 in | 2.13 in | 0.597 in/ft |
| Morse Taper No. 2 | 0.7000 in | 0.5720 in | 2.56 in | 0.600 in/ft |
| Morse Taper No. 3 | 0.9380 in | 0.7780 in | 3.19 in | 0.602 in/ft |
| Morse Taper No. 4 | 1.2310 in | 1.0200 in | 4.06 in | 0.624 in/ft |
| Jarno No. 5 | 0.6250 in | 0.5000 in | 2.50 in | 0.600 in/ft |
| Offset direction case | Front toolpost cue | Rear toolpost cue | Shop check |
|---|---|---|---|
| Large end at headstock | Tailstock set toward operator side | Tailstock set away from operator side | Trial taper grows toward chuck |
| Large end at tailstock | Tailstock set away from operator side | Tailstock set toward operator side | Trial taper grows toward tailstock |
| Reverse from test cut | Move opposite the measured error | Move opposite the measured error | Blue or mic both ends |
| Straight correction | Offset only half the diameter error scaled by length | Same amount, opposite side if rear tool | Indicate centers first |
| Material | Finish pass | Typical SFM | Fit check |
|---|---|---|---|
| Mild steel shaft | 0.003-0.008 in | 80-140 | Mic and blue |
| Alloy steel arbor | 0.002-0.006 in | 60-110 | Blue fit |
| Brass or bronze | 0.002-0.006 in | 150-250 | Ring gauge |
| Aluminum | 0.004-0.010 in | 250-500 | Mic ends |
| Center height check | Good range | Warning range | Action |
|---|---|---|---|
| Small precision taper | 0.0000-0.0010 in | 0.0010-0.0020 in | Shim or reset tool |
| General Morse taper | 0.0000-0.0020 in | 0.0020-0.0040 in | Recheck centerline |
| Long slender work | 0.0000-0.0015 in | 0.0015-0.0030 in | Use steady support |
| Roughing trial cut | 0.0000-0.0030 in | 0.0030-0.0060 in | Correct before finish |
It turns a taper accuratley between centers. This calculator takes the taper length, work length between centers, and taper diameter and give you the proper tailstock offset for accurate between-centers taper turning.
The precise taper from center to center appears easy until you move the tailstock and observe how your cut meanders. It is unforgiving. Too much, and the angle are wrong; too little, and the part won’t fit into its socket. A few thousandths’ offset, which typicaly determines both the taper angle and overall fit, holds all weight for either success or failure. Get it right, and you have a clean seat; get it wrong and scrap hours of effort.
How to Use the Taper Calculator
This makes what seems like a complicated subject rather simple. Take half the total difference in diameter, multiply it by twice the distance between centers (the full length) and then divide that result by desired length of taper. It sounds complicated but this is what you see everywhere in old shop manuals. Even though they say that machinists will get on the shop floor arguing about it because the length of the taper isn’t the same thing as the centers distance. You can take a piece with an eight inch centers distance and have just a two-and-a-half inch section be a taper. That’s something the calculator do for you without having to scratch some number down on your chip covered hand while trying to figure out if you’re right or wrong.
Most folks don’t realize how important direction is. Does your big end go on the tailstock end or the headstock? This means you will turn the tailstock base in one direction, but then a rear toolpost turns it back in opposite direction. That’s not an academic thing: You may think you made a test cut right, but turn that part over and it’s dead wrong, backwards.
It also takes into account whatever trial offset you’ve already cut, so you can make a smart correction rather than having to start anew each time. The silent killer of taper work is center height error. A few thousandths difference in tool height throw off your effective cutting angle, particularly when working on long slender parts. Mild steel will forgive a little more than tool steel so the results panel flags this risk for you and links it to the material you selected. Aluminum can cuts cleanly at faster speeds but deflects easy if the offset pulls the part too far from centerline. Practical checks like these prevent you from chasing a perfect number while forgetting how the material actualy behaves, which will ruin finish.
History travels with tapers. Most of those used in North American shops today was developed as Morse tapers during the 19th century for rapid tool change. Some people in tool rooms favored Jarno tapers, though they still show up from time to time on older machines. All have their slight ratio difference. That’s where the reference tables comes into play to remind us that a Morse number two is about six-tenths taper per foot.
This value has guided lathe setups for generations, since each actual part has its own centers distance, its own tolerances, and its own potential to bend. Numbers in the tables are starting places, never end of the story. Every turner has been through this rite of passage: “You see those two centers? OK, make your first cut. Go lightly across them and measure each end. Adjust half the error at one end to correct the other. Got it? That is the first smart step provided by the calculator. Now the test cut will be closer.
Then it’s almost like a conversation between you and the part and between you and the micrometer and all becomes iterative until it’s done right. It is really about proper lubrication on the centers, locking down the tailstock, and making light finish passes. Avoid the disasters that could of turn a good set up into scrap.
Ultimately though it’s not a number displayed on a screen. It’s the literal trade off between material behavior, machine constraints and geometry. The taper stops being a mystery and starts to make sense because you know what the compromise is. It’s about patience, having a sharp tool and knowing the maths has been done for you.
