Taper Calculator MM
Calculate metric taper ratio, mm per meter, included angle, half angle, tailstock or sine offset, allowance, and tolerance band from D1, D2, and taper length.
Load a real shop taper profile, then adjust diameters, length, allowance, and tolerance for the part on your bench.
Metric Taper Results
| Reference profile | D1 mm | D2 mm | Length mm | Nominal taper |
|---|---|---|---|---|
| Morse No.1 drill shank | 12.065 | 9.373 | 54.10 | about 1:20.1 |
| Morse No.2 lathe center | 17.780 | 14.529 | 65.02 | about 1:20.0 |
| Morse No.3 mill arbor | 23.825 | 19.761 | 81.03 | about 1:19.9 |
| Morse No.4 tailstock socket | 31.267 | 25.908 | 103.12 | about 1:19.2 |
| ISO 2339 taper pin 10 x 100 | 12.000 | 10.000 | 100.00 | 1:50 |
| DIN 1 taper pin 6 x 150 | 9.000 | 6.000 | 150.00 | 1:50 |
| Metric 1:20 test arbor | 25.000 | 20.000 | 100.00 | 1:20 |
| BT30 7:24 gauge segment | 31.750 | 22.680 | 31.10 | 7:24 |
| BT40 7:24 gauge segment | 44.450 | 31.750 | 43.54 | 7:24 |
| Jarno No.6 toolroom taper | 17.780 | 15.240 | 76.20 | 1:30 |
| Taper ratio | Diameter change | mm per meter | Half angle | Included angle |
|---|---|---|---|---|
| 1:100 | 1 mm in 100 mm | 10.000 | 0.2865° | 0.5730° |
| 1:50 | 1 mm in 50 mm | 20.000 | 0.5729° | 1.1459° |
| 1:30 | 1 mm in 30 mm | 33.333 | 0.9548° | 1.9096° |
| 1:20 | 1 mm in 20 mm | 50.000 | 1.4321° | 2.8642° |
| 1:10 | 1 mm in 10 mm | 100.000 | 2.8624° | 5.7248° |
| 7:24 | 7 mm in 24 mm | 291.667 | 8.2971° | 16.5943° |
| Nominal length | Diameter tolerance | Worst diff swing | mm/m change | Use note |
|---|---|---|---|---|
| 50 mm | +/- 0.005 mm | 0.020 mm | 0.400 mm/m | short gauge plug |
| 75 mm | +/- 0.010 mm | 0.040 mm | 0.533 mm/m | small Morse check |
| 100 mm | +/- 0.010 mm | 0.040 mm | 0.400 mm/m | 1:20 arbor |
| 150 mm | +/- 0.020 mm | 0.080 mm | 0.533 mm/m | long taper pin |
| 250 mm | +/- 0.025 mm | 0.100 mm | 0.400 mm/m | between centers |
| Taper ratio | Setup span 100 mm | Setup span 250 mm | Setup span 500 mm | Typical method |
|---|---|---|---|---|
| 1:50 | 1.000 mm | 2.500 mm | 5.000 mm | tailstock offset |
| 1:30 | 1.667 mm | 4.167 mm | 8.333 mm | toolroom taper |
| 1:20 | 2.500 mm | 6.250 mm | 12.500 mm | compound slide |
| 1:10 | 5.000 mm | 12.500 mm | 25.000 mm | short socket |
| 7:24 | 14.583 mm | 36.458 mm | 72.917 mm | steep spindle |
TAPER is something you’re used to measuring. You can see it drawn and figure out what it looks like by reading a line of numbers representing diameters. Or maybe you just pick up a piece and run a cut without even glancing away.
But then there’s that moment where you encounter an angle or ratio in the drawing that doesn’t come out right in your head. That’s when the number starts to matter. Then there’s the time you have to work out how much tailstock offset to set up for a long shaft. Turns out you are not as clear on slope as you thought.
How to Use the Taper Calculator
In either of those scenarios, the calculator above will save you money by preventing mistakes. Enter your raw measurements of length, small diameter, and large diameter and it gives you a whole picture of the taper’s geometry: The included angle, the ratio, the half angle for your compound slide setup, the actual radial offset required for your setup, and the millimeters per meter. Calculator does the trigonometry so all you have to do is make the cut.
The first thing to understand is how half angle differs from included angle. Generally, an included angle refer to the entire opening of the cone (which is what’s typically shown in the drawing). Your sine bar, or lathe compound slide, however, only accounts for half of this. For example, setting the full angle on a compound slide result in a taper that is twice as steep as planned.
Half angle is the one side of the full cone angle that the tool splits out and figures for you when you swivel the tool or workpiece. If you mess this up, bad things happen.
Those with an imperial mindset find it confusing that millimeters per meter are commonly used in metric machining. For example, when talking about taper, a 1:20 taper would indicate the diameter decreases one millimeter for each twenty millimeters along its length. That’s the same as saying 50 millimeters per meter. This is a common designation on CNC programs and some European specs.
The calculator spits out that number immediately so you can match your own custom part against standard ones such as ISO pins or Morse tapers. At a glance, you’ll be able to tell if your custom job is steeper (or shallower) than, say, a standard Morse No. 2.
While these numbers matter, so does how you set up the lathe. Is it tilted on a sine bar? Does it have the tailstock offset from center? Do you use the compound and just swing it around? The answer affect the geometry differently.
You’ll enter in the setup length, which can be the length from roller to roller on the sine bar or from center to center. Then it calculates the offset in inches (or millimeters) required to make the desired slope. That’s important because the offset isn’t simply added linearly to the diameter. Rather, its a proportion of the whole length of the workpiece.
So if you’ve got a short setup span, the offset will be small. But if you’re turning something long on an arbor, the same taper need a much bigger offset to get the right angle across the length of the part.
Reality meets theory with allowance and tolerance. In practice, you’re not going to cut to final size in a single pass. So how do you tell the calculator? It allows you to specify an allowance so that it knows what diameter to start cutting from to get to the finished size. And it allows you to say how much variation you’ll have between those two diameters.
That gives you a worst case scenario of your taper per meter if your diameters change according to their allowed variation. This is important when doing precise work. If you give yourself a lot of tolerance on a long taper, you might end up with something too loose to hold or too tight to seat. Knowing the range will help you know if you have enough accuracy out of your machine to do the job.
There were also some common taper standards already programmed into it (metric, Morse, Jarno etc). It is good for verifying those. Like if you’re reaming out a Morse No. 3 socket, you load that preset and see if your diameter measurements match what should be there. Sometimes they don’t, either because of manufacturing variation or just because they’ve worn a bit over time. However, with the reference info on hand, you’ll catch any differences before you do a final pass.
That’s the deal with this thing: a guess becomes a check.
All that to say: A taper is nothing more than a line in space. But creating one takes some 3D thinking. The calculator connects what is seen as a flat drawing to what happens when the workpiece rotates into place. It provides the tolerances, offsets and angles necessary to make the cut with confidence.
Now you have to take the cut. Then measure its fit. Finally, account for runout. But now that the math is done, you’re freed to pay attention to the quality of the surface; the feel of the machine.
That’s where the true craft exists.
