Taper Length Calculator
Calculate shop-ready taper length from major and minor diameters using side angle, included angle, taper rate, or taper ratio.
Taper Length Results
| Taper standard | Common callout | Diameter rate | Included angle |
|---|---|---|---|
| Morse taper family | MT1 through MT7 | About 0.60 in per ft | About 2.9° |
| Jarno taper | Numbered machine arbors | 0.600 in per ft | 2.862° |
| NPT pipe taper | ANSI pipe thread taper | 0.750 in per ft | 3.576° |
| 7:24 steep taper | CAT, BT, ISO toolholders | 3.500 in per ft | 16.594° |
| ER collet seat | Typical collet chuck seat | Angle callout preferred | 16.000° |
| Drawing input | Formula for length | Use when | Watch point |
|---|---|---|---|
| Side angle A | L = (D - d) / (2 tan A) | Compound slide or cone angle shown | Angle must be from centerline |
| Included angle B | L = (D - d) / (2 tan B/2) | Print shows full cone angle | Divide by two for compound |
| Taper per foot | L = 12(D - d) / TPF | Imperial machine taper standard | TPF is diameter change |
| Millimeters per meter | L = 1000(D - d) / rate | Metric taper callout | Use same length units for D and d |
| Ratio 1:N | L = N(D - d) | Pipe, fixture, and quick shop ratios | Ratio is normally diameter taper |
| Material | Finish allowance | Rigidity note | Typical taper work |
|---|---|---|---|
| Softwood | 0.010 in or 0.25 mm | Support long legs or spindles | Furniture legs, plugs, knobs |
| Hardwood | 0.008 in or 0.20 mm | Cut light near the small end | Chair legs, tool handles |
| Aluminum | 0.006 in or 0.15 mm | Use sharp tool and stable setup | Adapters, cones, bushings |
| Mild steel | 0.004 in or 0.10 mm | Check tailstock and carriage lock | Arbors, pins, centers |
| Stainless steel | 0.003 in or 0.08 mm | Avoid rubbing at the small end | Precision sleeves, medical parts |
| Project setup | Large to small diameter | Common taper spec | Practical result to check |
|---|---|---|---|
| Morse socket cleanup | 0.700 to 0.572 in | About 0.60 in per ft | Short taper needs accurate lands |
| 7:24 toolholder seat | 1.750 to 1.250 in | 7:24 ratio | Gauge line controls fit |
| NPT male thread prep | 1.050 to 0.940 in | 1:16 diameter taper | Thread length should match standard |
| Hardwood table leg | 1.750 to 0.875 in | Project length driven | Long slender stock needs support |
| Aluminum cone adapter | 2.000 to 1.250 in | 10° included cone | Check set-over before cutting |
Until you realize you have four options of how to write down the same taper angle, and you look up drawing numbers and ask yourself… do I put number in as a radius or as a diameter? We all stands in front of a lathe with chunk of steel with not enough confidence to know what to do.
Once you plug your numbers into calculator above (shown below), it does the math for you. It also spares you from guessing which coefficient to use for your specific setup. Where the real effort come in is understanding what those numbers mean for your actualy cut.
How to Calculate Taper Angles for Machining
When you see a taper on most shop drawings, they lists either the included angle (which is whole cone) or a side angle (used to tell you what your compound slide should of be). One tells you the whole cone and other tells you where to position your compound slide. Most folks gets this wrong, but that’s only if your print is showing the included angle. In that case, you divide it in half and then go touch your machine.
When you pick your input mode on the tool, it figure this out for you automatically, but you’ll still want to know which number you’re seeing. Typically on a lathe, the compound would be set to side angle measured from centerline of spindle. Using the included angle directly would give you twice the slope than you were expecting.
Before you begin cutting any metal, it’s good to check your inputs with a reference table. The other popular one that throws people off is taper rate. This also can be confusing if you bounce from metric to imperial. For example, a Jarno taper has same rate (inches/foot), just a different size.
The 0.NPT pipe threads run at 0.75 inches per foot. Means there is no thread interference, but rather a seal by friction. 75 inches per foot This represents amount of change in diameter across some fixed distance. Plug it into calculator to find total length needed to connect your small and large diameters.
This means it’s simply a linear relationship. A high rate, meaning a short taper, is difficult to make precisely and its steep. Any angle deviation are magnified. A low rate creates a long, gentle taper that is forgiving of small angle errors, but it takes more time and material.
How you tackle this work also depend on the material. Rough saws and warped blanks require woodworkers to incorporate large stock allowance, occasionaly as much as 15 percent or even more. By contrast, machinists working in mild steel may requires just a few thousandths of an inch for cleanup.
For parts that must function, it’s important to specify land allowances at each end of the taper. At the large end of a Morse socket, there should be a straight gauge face so part seats correctly onto milling machine spindle. At small end of an NPT thread, there should be a relief to allow clearance when the part is seated in a pipe joint. Without these lands, the part looks right on paper but fails in practice.
Long Taper Without Compound Slide, This is done by using the tailstock to set over on the part; it’s a classic lathe method that uses the carriage’s main lead screw. Based off your taper rate and center distance, the calculator will work out the set-over required at the tailstock. It’s stiffer and faster than compound work, since the main lead screw of the carriage take the load.
The drawback: If you don’t have enough bed length to allow for the set-over, you won’t be able to reach it. Your math may tell you you need an ideal set-over, but there isn’t enough physical room for the tailstock to go that far. So again, compare what the calc tells you with what you can do on your machine.
The bottom line is that tapering math isn’t so much an art as an exercise in seeing. You’re describing a cone that has to fit onto some other cone or surface. A precise description will result in a precise fitting part, whether you’re boring out a hardened steel arbor or shaping a wooden table leg. Knowing how much the taper changes the diameter and how that change affect the length saves money on scrap. And the tool tells you what those numbers are, while your judgement makes sure they fit the real world of the shop floor. Feed it accurate stuff, double check your allowances and lands, and then let your hand follow where the geometry takes it instead of guessing.
