Jacobs tapers (JT) and drill chuck arbors

The Jacobs taper exists for exactly one job: mounting a drill chuck on an arbor. There are nine sizes, the numbering is not in size order, and unlike Morse tapers the taper angle is not constant across the series. All three facts matter when you order.

Dimensions

Cross-checked across four independent published tables. Small end, big end and length agree everywhere; the taper-per-foot column comes from two of them.
Taper	Small end (in)	Big end (in)	Length (in)	Taper / foot (in)	Half angle
JT0	0.22844	0.2500	0.4375	0.59145	1.41°
JT1	0.33341	0.3840	0.65625	0.92508	2.21°
JT2	0.48764	0.5590	0.8750	0.97861	2.34°
JT2 short	0.48764	0.5488	0.7500	0.97861	2.34°
JT2½	0.625	0.677	1.055	—	—
JT3	0.74610	0.8110	1.21875	0.63898	1.53°
JT4	1.0372	1.1240	1.6563	0.62886	1.50°
JT5	1.3161	1.4130	1.8750	0.62010	1.48°
JT6	0.6241	0.6760	1.0000	0.62292	1.49°
JT33	0.5605	0.6240	1.0000	0.76194	1.82°

Two traps in this table.

The numbering is not size order. JT5 has a 1.413" big end, but JT6 is only 0.676" — barely bigger than JT2. And JT33 (0.624") sits between JT2 and JT3 despite the number. The 33 is not a typo; it is an odd numbering system. Never infer a size from the number.
The taper angle is not constant. Taper per foot ranges from 0.591 (JT0) to 0.979 (JT2) — roughly 1.41° to 2.34° per side. This is the opposite of the Morse series, which holds a near-constant angle. It is why a JT arbor and a JT socket of the same number must be matched, and why JT and Morse are never interchangeable.

Fitting a chuck to an arbor

Jacobs tapers are self-holding, like Morse. But because a drill chuck on its arbor is rarely removed, the joint is expected to be very tight. The method one reference gives is worth quoting because it is the opposite of what most people do:

Seat it by inertia, not by pressing. Put the male and female tapers together, then strike the opposite end of the arbor against a piece of wood. The chuck's inertia drives it onto the taper as the arbor stops suddenly. Do not use an arbor press — the controlled impact is what produces a seating force high enough to survive drilling loads.

Keep both tapers clean and dry. As with Morse tapers, do not oil them before assembly: it makes the joint lock up and difficult to remove later, and if left assembled for a long period it promotes corrosion in the joint.

Thread connections to the machine

The other end of the arbor is usually a threaded stud. 1/2"-20 is the size that appears most often in drill chuck listings, including adapters that convert a 3/4" Weldon shank to a chuck. Smaller chucks also use 3/8"-24. Measure the stud, or check the chuck's own specification — the thread is not implied by the JT number.

JT versus Morse versus R8

JT — drill chucks on arbors. Drill presses, portable drills, magnetic drills. Nine sizes, non-sequential numbering, varying angle.
Morse (MT) — taper-shank tools and spindles: drill presses, tailstocks, some mills. MT0–MT7, near-constant angle, and the MTA / MTB distinction decides whether you can mill with it.
R8 — a collet system for Bridgeport-type knee mills, held with a drawbar from the top of the head. Not a taper-mount system at all.

A very common and very sensible upgrade is an R8 shank ER collet chuck: you keep the R8 spindle and gain the whole ER range. See R8 collets.

Drill chucks, arbors and adapters

Looking for the taper that goes into the spindle rather than onto a chuck? Start at Morse taper dimensions or 7:24 tool holder tapers.