CAT, BT and SK (DIN 69871) holders all use the same 7:24 taper with the same gauge diameters (1.750 in / 44.45 mm for size 40), but their flanges and pull stud threads differ, so they are not interchangeable.

This chart gathers the key dimensions of the machine tapers you meet in a shop: steep 7:24 tapers on machining centres and mills, hollow-shank HSK, the Bridgeport R8, self-holding Morse tapers on drills and lathes, and Jacobs tapers on drill chucks. For each one you get the governing standard, the gauge (reference) diameter, flange size and the pull stud or drawbar thread where it applies. Use the search box or the family list to narrow the tables, and switch between inch and millimetres. Use the Taper Calculator to work out angles and diameters for any other taper.

7:24 steep tapers (CAT, BT, SK, NMTB)

All 7:24 tapers have a taper of 3.500 in per foot, a half angle of 8°17′50″ (8.2971°) and an included angle of 16°35′39″ (16.5943°). The size number fixes the gauge diameter, so a 40 taper has the same cone whether it is CAT, BT, SK or NMTB.

TaperStandardGauge diameterFlange ODnominalPull stud threadTaper
CAT30ASME B5.50 (V-flange)1.250 in31.75 mm—1/2-13 UNC7:24
CAT40ASME B5.50 (V-flange)1.750 in44.45 mm2.500 in63.50 mm5/8-11 UNC7:24
CAT50ASME B5.50 (V-flange)2.750 in69.85 mm3.875 in98.42 mm1-8 UNC7:24
BT30MAS 403 / JIS B 63391.250 in31.75 mm1.811 in46 mmM127:24
BT40MAS 403 / JIS B 63391.750 in44.45 mm2.480 in63 mmM167:24
BT50MAS 403 / JIS B 63392.750 in69.85 mm3.937 in100 mmM247:24
SK30DIN 69871 / ISO 7388-11.250 in31.75 mm—M127:24
SK40DIN 69871 / ISO 7388-11.750 in44.45 mm2.502 in63.55 mmM167:24
SK50DIN 69871 / ISO 7388-12.750 in69.85 mm3.839 in97.50 mmM247:24
NMTB30ASME B5.18 (manual, no V-flange)1.250 in31.75 mmno V-flangeDrawbar7:24
NMTB40ASME B5.18 (manual, no V-flange)1.750 in44.45 mmno V-flangeDrawbar7:24
NMTB50ASME B5.18 (manual, no V-flange)2.750 in69.85 mmno V-flangeDrawbar7:24

Gauge diameters per ISO 297 / ASME B5.50. Flange diameters are nominal catalogue values; a dash means it is not listed here, so check the holder maker's drawing. Pull stud length and angle (45°, 60° or 90°) vary by machine builder even within one standard.

How to tell CAT from BT

  1. Check the pull stud thread. This is the definitive test. CAT uses inch threads (1/2-13, 5/8-11, 1-8 UNC); BT and SK use metric (M12, M16, M24). Unscrew the stud and try a known nut or thread gauge.
  2. Compare the flange. A BT flange is noticeably thicker than a CAT flange of the same size. Put the holder beside one you know.
  3. Look for markings. Most holders are laser-marked CAT40, BT40, SK40 or DIN 69871 on the flange or body.
  4. SK looks like CAT. DIN 69871 (SK) holders have a V-flange close to CAT in shape but take metric pull studs, and usually have a coolant-through-flange option. Treat them as a separate type.
  5. Check the machine manual. It names the spindle taper and the exact pull stud part number, which matters as much as the taper.
Never mix them. A BT40 holder will enter a CAT40 spindle because the cone is identical, but the gripper groove, flange and pull stud are wrong, so the drawbar may not seat it properly and the tool can come loose in the cut.

HSK tapers

HSK (hollow taper shank, ISO 12164 / DIN 69893) uses a short 1:10 taper that is clamped from the inside by a drawbar collet, pulling the flange face hard against the spindle face. That two-face contact gives high stiffness and accurate axial position at high speed. The size number is the flange diameter in millimetres.

SizeFlange diameter (d1)Taper shank diameter (d2)nominalTaperCommon forms
HSK-321.260 in32 mm0.945 in24 mm1:10HSK-A32, HSK-E32
HSK-401.575 in40 mm1.181 in30 mm1:10HSK-A40, HSK-E40
HSK-501.969 in50 mm1.496 in38 mm1:10HSK-A50, HSK-E50
HSK-632.480 in63 mm1.890 in48 mm1:10HSK-A63, HSK-E63
HSK-803.150 in80 mm2.362 in60 mm1:10HSK-A80, HSK-E80
HSK-1003.937 in100 mm2.953 in75 mm1:10HSK-A100, HSK-E100
  • Form A: automatic tool change, drive keys at the end of the taper, gripper groove and coolant tube. The standard choice for machining centres.
  • Form B: like A but with a larger flange for a given shank and drive keys in the flange.
  • Forms C and D: manual-clamping versions of A and B.
  • Form E: like A with no drive keys, fully symmetrical for very high speed.
  • Form F: like E with a larger flange for a given shank (for example HSK-F63 uses the HSK-50 size shank), common on high-speed routers.

Main dimensions per ISO 12164-1. Check the full standard or the holder maker's drawing for tolerances, keyway and gripper dimensions.

R8

R8 featureValue
Taper included angle16°51′ (8°25′30″ per side)
Body (shank) diameter0.950 in24.13 mm
Drawbar thread7/16-20 UNF
LocationKey in the spindle nose engages a slot along the collet
Round collet capacityup to 3/4 in (about 20 mm) in standard R8 collets
Typical machinesBridgeport-type knee mills and many benchtop mills

Morse tapers

Morse tapers are shallow, self-holding tapers of roughly 5/8 in per foot (about 1:20). The friction of the taper alone drives drills and centres; a tang or drawbar thread stops them turning or pulling out under load. Each size has its own slightly different taper, so set the compound or taper attachment from the half angle in the chart, not a general value.

TaperTaper per footratioHalf angleDia. at gauge line (A)Dia. at small end of plug (D)Standard plug depth (P)Drawbar threadDIN 228-1 form ATypical use
MT00.62460 in/ft1:19.2121°29′27″1.4908°0.3561 in9.045 mm0.252 in6.40 mm2.0000 in50.80 mm—Small drill chucks, centres
MT10.59858 in/ft1:20.0471°25′43″1.4287°0.475 in12.065 mm0.369 in9.37 mm2.1250 in53.97 mmM6Small drill chucks and drills
MT20.59941 in/ft1:20.0201°25′50″1.4307°0.700 in17.780 mm0.572 in14.53 mm2.5625 in65.09 mmM10Drill presses, small lathe tailstocks
MT30.60235 in/ft1:19.9221°26′16″1.4377°0.938 in23.825 mm0.778 in19.76 mm3.1875 in80.96 mmM12Lathe tailstocks and spindles, larger drills
MT40.62326 in/ft1:19.2541°29′15″1.4876°1.231 in31.267 mm1.020 in25.91 mm4.0625 in103.19 mmM16Larger lathes and radial drills
MT50.63151 in/ft1:19.0021°30′26″1.5073°1.748 in44.399 mm1.475 in37.47 mm5.1875 in131.76 mmM20Heavy lathes and radial drills
MT60.62565 in/ft1:19.1801°29′36″1.4933°2.494 in63.348 mm2.116 in53.75 mm7.2500 in184.15 mmM24Very large drills and lathes
MT70.62400 in/ft1:19.2311°29′22″1.4894°3.270 in83.058 mm2.750 in69.85 mm10.0000 in254.00 mm—Very large machines

Morse taper dimensions per ASME B5.10 (Machinery's Handbook table); metric gauge-line diameters match ISO 296 / DIN 228. Half angle = arctan(taper per foot ÷ 24). D = A − taper per foot × P ÷ 12. Typical uses are general guidance only. MT is also written MK (Morsekegel) in German catalogues.

Worked example. To turn an MT3 taper on a lathe, set the compound to the MT3 half angle of 1°26′16″. The large end at the gauge line is 0.938 in (23.825 mm) and the plug tapers to 0.778 in over 3.1875 in. Check the fit with marking blue in a known MT3 socket before finishing.

Jacobs tapers

Jacobs tapers seat a drill chuck on its arbor. Press the chuck onto the arbor with a sharp tap or a press; separate them with wedges, never by hammering the chuck body.

TaperLarge end diameterSmall end diameterLengthTaper per foot
JT00.2500 in6.350 mm0.2284 in5.802 mm0.4375 in11.11 mm0.59145 in/ft
JT10.3840 in9.754 mm0.3334 in8.469 mm0.6562 in16.67 mm0.92508 in/ft
JT20.5590 in14.199 mm0.4876 in12.386 mm0.8750 in22.22 mm0.97861 in/ft
JT2 Short0.5488 in13.940 mm0.4876 in12.386 mm0.7500 in19.05 mm0.97861 in/ft
JT30.8110 in20.599 mm0.7461 in18.951 mm1.2188 in30.96 mm0.63898 in/ft
JT41.1240 in28.550 mm1.0372 in26.345 mm1.6563 in42.07 mm0.62886 in/ft
JT51.4130 in35.890 mm1.3161 in33.429 mm1.8750 in47.62 mm0.62010 in/ft
JT60.6760 in17.170 mm0.6241 in15.852 mm1.0000 in25.40 mm0.62292 in/ft
JT330.6240 in15.850 mm0.5605 in14.237 mm1.0000 in25.40 mm0.76194 in/ft

Jacobs taper dimensions as published in Machinery's Handbook. Check against the chuck maker's data for critical work.

Shop tips

  • Clean every taper. Wipe the spindle and holder before each change. A chip or film of coolant on a taper shows up as runout and fretting.
  • Match the pull stud exactly. Use the stud specified by the machine builder (thread, length, angle and through-coolant bore). A wrong stud can fail to clamp even if it screws in.
  • Torque pull studs. Tighten studs to the holder maker's torque; over-tightening can swell the taper end of a holder.
  • Check spindle condition. Blue a known-good holder into the spindle: contact should be even along the full taper length.
  • Morse tapers need a clean dry fit. Do not oil a Morse taper; oil stops it holding and lets the tool spin and score the socket.

Frequently asked questions

No. CAT40 and BT40 share the same 7:24 taper and 1.750 in (44.45 mm) gauge diameter, but the flange is a different thickness and shape and the pull stud thread differs (5/8-11 UNC on CAT40, M16 on BT40). A holder of the wrong type may seem to fit but will not be gripped correctly by the tool changer or drawbar, so use only the type your spindle is built for.

A 7:24 taper changes diameter by 7 units over 24 units of length, which is 3.5 in per foot and an included angle of about 16.59 degrees. It is a steep, self-releasing taper: it does not lock on its own, so the holder is held in by a drawbar pulling on a pull stud or thread, and drive comes from keys in the flange.

Both are hollow 1:10 tapers that clamp on the taper and the flange face at the same time. HSK-A has drive keys at the end of the taper and is the usual choice for machining centres with tool changers. HSK-E has no drive keys and is fully symmetrical for balance at very high spindle speeds, so it transmits less torque.

Most small and bench lathes use MT2 in the tailstock, mid-size lathes commonly use MT3, and larger toolroom and engine lathes use MT4 or MT5. Measure the bore at the mouth and compare it with the gauge-line diameter in the chart to confirm.

R8 is the collet and tool shank system used on Bridgeport-type knee mills. It has a 16 degree 51 minute included angle, a 0.950 in body diameter and is pulled in by a 7/16-20 drawbar, with a key in the spindle stopping it from turning. It is not self-holding, so the drawbar must always be tight.