Taper Per Inch Calculator
Calculate taper per inch from large diameter, small diameter, and length, then convert it to included angle, taper per foot, mm per 25.4 mm, and practical lathe setup offsets.
⚙Taper Presets
Choose a known shop taper or enter your own measured diameters and taper length.
📐Measured Taper Inputs
🔢Conversion Grid
📋Common Taper Reference
| Taper family | Typical TPI | Taper per foot | Included angle |
|---|---|---|---|
| Morse machine tapers | About 0.050 in/in | About 0.600 in/ft | About 2.86° |
| Jarno tapers | 0.050 in/in | 0.600 in/ft | 2.864° |
| Brown & Sharpe tapers | About 0.0417 to 0.0502 | About 0.500 to 0.602 | About 2.39° to 2.88° |
| 7/24 toolholder tapers | 0.2917 in/in | 3.500 in/ft | 16.594° |
| Pipe plug style tapers | 0.0625 in/in | 0.750 in/ft | 3.580° |
| Custom locating seats | From print dimensions | TPI × 12 | 2 × atan(TPI / 2) |
⚒Setup Offset Reference
| Setup method | Use this output | Shop formula | Best use |
|---|---|---|---|
| Compound rest | Half angle | atan((D - d) / (2L)) | Short external or internal tapers |
| Tailstock offset | Offset amount | Center distance × TPI / 2 | Long shafts between centers |
| Indicator check | Diameter change over span | TPI × travel | Verifying taper attachment travel |
| Sine bar | Rise over span | sin(half angle) × bar length | Grinding fixtures and inspection |
| Boring head offset | Radial change | TPI × length / 2 | Boring tapered seats |
🔧Measurement Planning Table
| Measurement span | At 0.050 TPI | At 0.0625 TPI | At 0.2917 TPI |
|---|---|---|---|
| 0.250 in travel | 0.0125 in diameter | 0.0156 in diameter | 0.0729 in diameter |
| 0.500 in travel | 0.0250 in diameter | 0.0313 in diameter | 0.1459 in diameter |
| 1.000 in travel | 0.0500 in diameter | 0.0625 in diameter | 0.2917 in diameter |
| 2.000 in travel | 0.1000 in diameter | 0.1250 in diameter | 0.5834 in diameter |
📑Unit Conversion Table
| Output | Imperial meaning | Metric meaning | Conversion note |
|---|---|---|---|
| Taper per inch | Diameter change per 1 in | Same slope basis | Use inches internally |
| mm per 25.4 mm | Same numeric as TPI | Diameter mm over 25.4 mm | Good for metric prints |
| mm per 100 mm | TPI × 100 | Diameter mm over 100 mm | Check long metric parts |
| Taper per foot | TPI × 12 | Legacy machine taper callout | Common in handbooks |
💡Shop Tips
But you look at the tapered arbor and see it doesn’t quite bottom out. You tap it hard and turn the chuck and… well it’s there a bit. Ugh! Now you’re doubting your measurements and tool. Don’t worry, this isn’t usually due to a warped part or bad metal. What happens here is naturaly always a lack of understanding how those numbers are interpreted.
On paper taper per inch sound easy. After all, it’s simply a ratio of how much diameter changes over some linear value. In the shop we convert that ratio into sine bar height, offsets, and angles. Those figures sounds like a foreign language if you haven’t broken them down yet. Let’s let the calculator do the math for us (see above). Why does it spit out those numbers? Because knowing how to interpret them will save time and materials.
How to Set Up Tapers on a Lathe
What do most machinists do? Pick up their micrometer and calipers. Measure the small end and big end of a taper. Divide the difference by the length. Multiply the answer by the length. There you have it, the taper per inch. It is a nice neat number. It tells you exactly how much it slope away from the center line.
But your tailstock doesn’t care about the half angle. Your tailstock cares about the lateral offset. And your lathe compound rest doesn’t care about the diameter change. Your lathe compound rest cares about the half angle. The tool connects the mechanics of your machine and geometry of what you’re trying to make.
One continual source of confusion lies in the difference between half angle and included angle. Setting up is then ruined by that confusion. When you draw a taper and call it a 2 degree taper, you typically mean the total included angle between both sides. You need to have the compound rest on one degree. Set it for two degrees and your cut will be too steep. Nothing will fit. It’s a little thing, but it makes a difference.
The calculator does the conversion for you automatically. It tells you exactly how much to set the compound for. Also gives you individual offset if you’re running between centers.
There’s also issue of measuring tapers. You can’t hold your caliper flat against something sloped and expect it to read correctly. It won’t. The jaws will be angled in such a way as to add error that grows rapidley. Over pins is the ideal method. Alternatively, use a sine plate height gauge. For roughs, a few checks with a micrometer in key spots are usually adequate. Inputting a slight amount of allowance for stock let’s the calculator account for all those fuzzy measurements we know happen. It reminds us that we’re working with metal, not drawing dots on a piece of paper.
The taper can be long and present other issues. If the center distance is large then the slightest offset of the tailstock results in huge changes near the end. Here is the math laid out on the table on the page. How does offset scale with length? A one/tenth offset would appear small on a two inch shaft. However, on an eighteen inch drive shaft it moves the center line so much that it will cause uneven wear or chatter. Think about the whole length of what you are machining. Think about more than just the cut you is currently cutting.
A taper that works as a good benchmark… Something to compare the rest of them against, is Morse or Jarno which are both pretty consistent (Morse is about ½ an inch per foot). So if it’s wildly off from that your probably looking at the worn surface. Or maybe you’re on a completely different standard. At least then knowing what the ballpark should be will help you spot gross error before you go cut stuff. It is nothing but a sanity check that costs nothing. Just a quick look up on this page or in a handbook.
It’s a question of abstraction: of converting the geometric expression from page to metal. That number is merely the map; the cut is the territory. Setting up the taper correctly require understanding angle in relation to length and diameter. It requires taking time with measurements. You must be precise with machine positioning. You should of double-check that set-up before the final pass. When you see that arbor fit exactly, you realize the math was worth it. And all along it goes back to that initial measurement.
