How to Measure, Identify, and Match a Morse Taper

Rowan Blake August 18, 2026 · 17 min read

What a Morse taper size tells you

A Morse taper is a shallow, self-holding machine taper. A male tool shank, arbor, or center seats in a female socket with matching geometry. As the parts wedge together, broad contact between the tapered surfaces creates the friction fit that locates and holds the tool.

The commonly listed sizes are MT0, MT1, MT2, MT3, MT4, MT4.5, MT5, MT6, and MT7. Each number identifies a distinct nominal combination of large diameter, small diameter, axial length, and taper rate. Dimensions generally increase with the number, but the family is not a simple scale: the taper rate varies slightly from size to size.

The taper surfaces provide the basic holding action. A tang may assist with ejection where the socket is designed for it, but it is not a substitute for sound taper contact and should not be treated as the primary torque carrier after the taper begins to slip. These operating principles are summarized in this overview of machine tapers.

You may see the same numbered size written in several ways:

MT2
2MT
MK2, from the German Morsekegel
Morse No. 2

These generally denote the same numbered Morse taper geometry. The CGTK metric reference specifically equates MT, number-first MT, and MK notation for a given number.

Matching notation does not guarantee that every accessory will work in every machine. Usable taper length, tang form, threads, drawbar provisions, socket depth, and ejection arrangements may still differ.

Morse should not be confused with Jacobs, Jarno, or Brown & Sharpe. These are separate taper families. A drill-chuck arbor can have a Morse taper on the machine end and a Jacobs taper on the chuck end, but the two geometries are not interchangeable. Similar appearance—or even a close diameter—is not enough to establish compatibility.

All dimensions below are nominal third-party reference values for identification and comparison. They are not manufacturing tolerances, certified gauge dimensions, acceptance limits, or substitutes for authoritative machine and tooling drawings.

Morse taper sizes chart: MT0 through MT7

The following chart normalizes the nominal inch series published in the LittleMachineShop standard-taper table. The millimeter diameters are corroborated by an independent metric table. To avoid mixing incompatible length conventions, the metric lengths shown here are direct arithmetic conversions of the listed inch lengths, using 25.4 millimeters per inch and rounding to approximately 0.1 millimeter.

Size	Nominal large diameter	Nominal small diameter	Reference length	Taper per inch	Centerline half-angle	Calculated included angle
MT0	0.3561 in / 9.045 mm	0.2520 in / 6.401 mm	2.00 in / 50.8 mm	0.0521 in/in	1.4908°	≈2.9816°
MT1	0.4750 in / 12.065 mm	0.3690 in / 9.373 mm	2.13 in / ≈54.1 mm	0.0499 in/in	1.4287°	≈2.8574°
MT2	0.7000 in / 17.780 mm	0.5720 in / 14.529 mm	2.56 in / ≈65.0 mm	0.0500 in/in	1.4307°	≈2.8614°
MT3	0.9380 in / 23.825 mm	0.7780 in / ≈19.762 mm	3.19 in / ≈81.0 mm	0.0502 in/in	1.4377°	≈2.8754°
MT4	1.2310 in / 31.267 mm	1.0200 in / 25.908 mm	4.06 in / ≈103.1 mm	0.0519 in/in	1.4876°	≈2.9752°
MT4.5	1.5000 in / 38.100 mm	1.2660 in / 32.156 mm	4.50 in / 114.3 mm	0.0520 in/in	1.4894°	≈2.9788°
MT5	1.7480 in / 44.399 mm	1.4750 in / 37.465 mm	5.19 in / ≈131.8 mm	0.0526 in/in	1.5073°	≈3.0146°
MT6	2.4940 in / 63.348 mm	2.1160 in / 53.746 mm	7.25 in / ≈184.2 mm	0.0521 in/in	1.4933°	≈2.9866°
MT7	3.2700 in / 83.058 mm	2.7500 in / 69.850 mm	10.00 in / 254.0 mm	0.0520 in/in	1.4894°	≈2.9788°

Important length note: These lengths follow one recurring published inch series. Do not assume that “reference length” means overall shank length, tang-inclusive length, socket depth, or universally available seating length. Other published tables use a shorter series.

The included angles are calculated by doubling the listed centerline half-angle. They are displayed to four decimal places only to make that relationship visible. The number of displayed digits does not imply an inspection tolerance or suggest that an ordinary shop protractor can reproduce the geometry to that precision.

A few quick comparisons help orient the chart:

MT1 has a nominal large diameter just under 0.5 inch.
MT2 is nominally 0.700 inch at its large reference plane.
MT3 is nominally 0.938 inch.
MT4.5 is a listed size between MT4 and MT5.
MT5 has a supported nominal small diameter of 1.4750 inches, not 1.457 inches.

Use the chart to narrow the possibilities, then confirm an unknown taper from more than one measurement.

How to read diameter, taper rate, and angle

The large diameter and small diameter are diameters at specified axial locations. They do not remain constant along the tapered surface.

That is why caliper placement matters. Move the jaws toward the narrow end of a male shank and the reading decreases. Move them toward the broad end and it increases. A measurement described only as “the end diameter” is ambiguous unless the physical edge or reference plane is also identified.

This is especially important when an accessory does not expose the complete theoretical taper. Its visible end may be truncated, rounded, relieved, blended into another feature, or followed by a tang. A physical edge should not automatically be treated as one of the chart’s nominal reference planes.

Taper per inch means the change in diameter over one inch of axial distance. It is not the change in radius. For two diameter measurements:

Taper per unit length = D_large-D_small ÷ L

where:

D_large is the larger measured diameter;
D_small is the smaller measured diameter; and
L is the axial separation between the measurement planes.

Suppose a shank measures 0.690 inch at one plane and 0.640 inch at another plane exactly 1.000 inch away:

0.690-0.640 ÷ 1.000 = 0.050 in/in

That result is close to the nominal MT2 taper rate. It is not sufficient by itself to classify the shank as MT2. The measured diameters must also be plausible for MT2 at the locations where they were taken.

The centerline half-angle is the angle between one tapered surface and the longitudinal centerline. The included angle is the full angle between opposing taper surfaces:

Included angle = 2 × half-angle

Confusing these values creates a factor-of-two error. A half-angle near 1.43 degrees corresponds to an included angle near 2.86 degrees.

Morse taper slopes are similar, but they are not identical. In the chart, taper rates range from approximately 0.0499 to 0.0526 inch per inch. One generic “Morse angle” is therefore unsuitable for machining every MT size.

MT2 and MT3 illustrate the distinction. Their nominal large diameters—0.700 and 0.938 inch—are readily distinguishable when measured at comparable planes. Their half-angles, however, are close: 1.4307 and 1.4377 degrees. Close does not mean interchangeable. An angular mismatch can shift contact toward one end rather than distributing it across the taper, weakening the intended self-holding fit.

How to identify a male Morse taper shank

A male shank is generally easier to identify than an internal socket because more of its surface is accessible. Even so, one rough measurement can be misleading.

Use this workflow:

Clean the shank. Remove loose chips, dust, dried residue, and loose corrosion products without altering the tapered surface.
Check for markings. Look on the body, shoulder, tang, arbor, and packaging for MT, MK, or number-first designations.
Inspect the surface. Look for raised burrs, dents, scoring, rust, wear bands, or evidence that the shank has been shortened or modified.
Measure an accessible large diameter. Record exactly where the caliper jaws contact the taper.
Compare it with the chart. Use the first reading to eliminate clearly impossible sizes.
Measure a second diameter. Select another clean, uninterrupted plane far enough away to produce a useful difference.
Measure the axial separation. Record the distance between the two diameter planes.
Calculate the taper rate. Divide the diameter difference by the axial separation.
Compare diameter and slope. Both should indicate the same chart row.
Check accessory details. Verify usable length, tang form, threads, drawbar provision, and ejection arrangement.

Diameter, length, and taper-per-inch measurements are also identified as useful comparison methods in the Travers Tool identification guide. Ordinary shop measurements remain preliminary rather than gauge inspection.

Practical diameter screens

A reading near 0.700 inch or 17.8 millimeters at a plausible large reference plane suggests MT2. A reading near 0.938 inch or 23.8 millimeters suggests MT3. The difference is large enough to make those sizes relatively easy to distinguish when the measurement location and surface condition are sound.

Approximate shop rules can also help with initial sorting:

MT1 is near 1/2 inch at the large end.
MT2 is near 3/4 inch.
MT3 is near 1 inch.

These are not precision dimensions. The Highland Woodworking measuring guide gives similar rounded comparisons and notes that caliper readings vary with position along the shank.

Record measurement planes, not just the “large end”

Do not assume that the visible ends of an accessory correspond to the nominal large- and small-diameter planes in the chart. Instead, keep a record such as:

Diameter A: 0.6842 inch, measured 0.150 inch from the visible large edge.
Diameter B: 0.6341 inch, measured 1.150 inches from the same edge.
Axial separation: 1.000 inch.

This makes the calculation repeatable and allows another person to reproduce the measurements.

If the diameter suggests one size but the calculated slope suggests another, stop rather than averaging the disagreement into the MT number you expected. Possible explanations include:

unsuitable or misidentified measurement planes;
caliper tilt;
contamination or a raised burr;
wear, corrosion, or impact damage;
a shortened or modified taper;
a different taper family;
an incorrectly machined replacement part.

When the result remains ambiguous—especially before buying an expensive arbor, center, or sleeve—check the machine manual or obtain a dimensioned drawing from the machine or tooling manufacturer.

How to identify a female socket in a spindle or tailstock

An internal taper is harder to measure. The opening is usually accessible, but the small end and complete internal length may be beyond the reach of ordinary calipers.

Begin by removing loose debris and visually inspecting the bore under good light. Measure the opening at the spindle, quill, or ram face, keeping the measuring tool square to the bore. If access permits, repeat the reading at several positions around the circumference.

Treat the opening diameter as a screening measurement, not conclusive identification. The machine face may not coincide with the nominal large-diameter reference plane. If the theoretical plane lies outside the physical face—or the cavity is recessed or truncated—the observed opening can be smaller than the chart value.

AutoDrill gives a specific example: an MT2 female cavity may measure about 0.695 inch at the accessible opening rather than the nominal 0.700-inch maximum because the cavity may not expose the full nominal plane (AutoDrill Morse taper dimensions note).

Other sources of uncertainty include:

limited measuring-jaw access;
jaws contacting the wall at different depths;
dirt packed against the socket;
rust or gummy residue;
burrs at the mouth;
wear or impact damage;
a recessed, shortened, or modified socket.

Do not alter a socket merely to identify it.

On a lathe, measure the headstock and tailstock separately. The two positions may use different sizes, so a machine description mentioning one taper does not necessarily identify both.

If the opening suggests a likely size, stronger confirmation can come from:

the machine manual or parts drawing;
another internal diameter measured at a known depth with suitable equipment;
a known, clean, undamaged shank of the suspected size;
inspection by a machine-tool service shop.

Do not force a close-looking test shank into place. If the fit appears abnormal, remove it and follow the machine or tooling manufacturer’s inspection and insertion procedure.

Matching tools, sockets, and reducing sleeves

The basic match is straightforward: a male Morse taper is intended to seat in a female socket with the same nominal size and matching angle. In practice, the MT number is only the first compatibility check.

Before purchasing or installing an accessory, verify:

machine-side Morse taper size;
tool-side Morse taper size;
usable taper length;
available socket depth;
tanged or tangless construction;
threaded or drawbar retention;
knockout slot, drift, or automatic-ejection arrangement;
clearance behind and around the tool;
intended loading and the manufacturer’s retention requirements.

A reducing sleeve allows a smaller Morse-taper shank to be used in a larger machine socket. For example, a sleeve can have MT5 geometry on its exterior and an MT3 socket inside.

Describe the direction explicitly:

MT5 machine socket accepting an MT3 tool shank
Machine side MT5, tool side MT3
MT5 outside, MT3 inside

Avoid relying on a label such as “3-to-5” unless the supplier defines its naming order.

Commonly described reductions include:

MT2 machine socket accepting an MT1 tool;
MT3 machine socket accepting an MT2 tool;
MT4 machine socket accepting an MT3 tool;
MT4 machine socket accepting an MT2 tool.

These combinations are listed in an industrial Morse taper and adapter guide, but the existence of a nominal size combination does not establish suitability for every machine or operation.

A sleeve addresses the difference between a larger machine socket and a smaller tool shank. It does not automatically solve:

insufficient working length;
a tang that cannot reach the ejection feature;
a tangless center trapped in a sleeve intended for tanged tooling;
inadequate thread or drawbar engagement;
interference with a knockout bar;
excessive tool projection;
reduced working clearance;
operation-specific retention requirements.

Because headstock and tailstock sizes can differ, select an adapter for the actual socket rather than for “the lathe” as a whole.

Do not infer that friction-only retention is appropriate for milling, transverse loading, interrupted cutting, or heavy work merely because the taper seats. Machine tapers may require a key, threaded section, or drawbar under heavier or transverse loads; follow the retention requirements specified by the machine and tool manufacturers.

Seating, holding, and diagnosing a poor fit

A nominally correct taper can still slip, run out, stick, or fail to seat. The self-holding action depends on broad contact between clean, compatible surfaces.

Before fitting a tool:

Remove loose chips, dust, and debris from both surfaces.
Inspect the male shank and female socket under good light.
Check for raised burrs without running bare fingers over sharp edges.
Look for scoring, corrosion, dents, and localized wear.
Confirm the Morse size and required retention arrangement.
If using a sleeve, confirm which side fits the machine and which fits the tool.
Follow the machine manufacturer’s insertion procedure.

Mating surfaces should ordinarily be clean, dry, smooth, burr-free, and undamaged. Oil, chips, gummy residue, or a raised defect can hold the components apart and concentrate contact over a small area.

A tang may assist with ejection in a socket designed for it. It is not a remedy for poor taper contact and should not be expected to carry the working torque after the taper slips.

Symptom	Possible causes	Useful next checks
Contact only at the large end	Angular mismatch, wrong taper family, raised mouth burr, incompatible geometry	Clean and inspect; verify nominal size and calculated slope
Contact only at the small end	Angular mismatch, obstruction at depth, modified socket or shank	Check accessible depth and accessory length; compare with a dimensioned drawing
Tool slips	Contamination, damage, poor contact, unsuitable retention, incompatible loading	Clean both parts; inspect condition; verify the required retention method
Excessive runout	Debris, burrs, wear, bent tooling, socket damage, incomplete seating	Clean and reseat; inspect arbor and socket separately
Tool will not seat fully	Wrong size, wrong taper family, excessive length, obstruction, incompatible tang or sleeve	Stop and compare geometry and accessory features
Difficult removal	Corrosion, damage, incompatible sleeve, blocked ejection arrangement	Use the specified drift, knockout bar, quill mechanism, or manufacturer procedure
Tool rocks in the socket	Major mismatch, localized damage, inadequate engagement	Remove it and identify both components again before operation

Marking compound may be used as a qualitative contact check where appropriate for the component and diagnostic method. A thin indication layer can reveal whether contact is broadly distributed or concentrated in isolated bands.

This is not a substitute for calibrated gauges. The supplied evidence does not establish a universal bearing-percentage threshold, so a contact pattern should be treated as a troubleshooting clue rather than certification that a taper is within tolerance.

For removal, use the proper drift, knockout bar, quill-retraction mechanism, or manufacturer-specified method. Retailer guidance likewise describes a drift or knockout bar as the normal removal provision for applicable Morse tooling (Zoro’s taper comparison guide).

This article does not recommend improvising with heat, aggressive hammering, grinding, cutting, or routine lapping. Precision taper tooling should not be modified without validated manufacturer guidance or qualified inspection.

Why published Morse taper lengths do not always agree

Morse taper diameter values are relatively consistent across the supplied references, but published lengths are not. Two recurring inch series illustrate the problem.

The longer reference series is:

Size	Longer published reference length
MT0	2.00 in
MT1	2.13 in
MT2	2.56 in
MT3	3.19 in
MT4	4.06 in
MT4.5	4.50 in
MT5	5.19 in
MT6	7.25 in
MT7	10.00 in

Another published series gives:

Size	Shorter published length
MT0	1.938 in
MT1	2.063 in
MT2	2.500 in
MT3	3.063 in
MT4	3.875 in
MT4.5	4.313 in
MT5	4.938 in
MT6	7.000 in
MT7	9.500 in

The longer values come from the LittleMachineShop table cited with the main chart. The shorter values are reported by Zoro. Neither source supplies enough shared dimensional definitions to establish which exact physical endpoints each table intends.

Possible explanations include:

different axial reference planes;
different definitions of where the tapered body begins or ends;
rounded values or conversions;
accessory-specific end configurations;
inclusion or omission of a relief or another feature.

These are possibilities, not established resolutions. The available references do not justify silently selecting either series as a universal inspection standard.

Several different dimensions may be involved:

Nominal taper geometry: the changing diameter and slope of the conical surface.
Taper-body length: the axial extent of a specifically defined tapered portion.
Overall shank length: the complete length of an accessory, potentially including other features.
Tang-inclusive length: a dimension extending through the tang.
Socket depth: the physical internal depth available in the machine.
Usable seating length: the portion that can engage before another feature interferes.

These terms are not interchangeable. A chart labeled only “length” may not reveal which dimension it reports.

Third-party metric references also disagree. For example, one published table lists MT2 at approximately 64.3 millimeters, while the CGTK table lists an L2 dimension of 65.087 millimeters. The references do not provide enough common definition to determine whether the difference results from rounding, different reference planes, or another dimensional convention.

The supplied sources also do not establish:

male or female manufacturing tolerances;
acceptance limits;
gauge-line conventions;
mandatory gauge methods;
the current controlling edition of a primary standard.

Use diameter and calculated taper rate for preliminary identification. When length, fit, manufacture, or inspection is critical, obtain a drawing that defines the reference planes, end features, and applicable tolerances for the specific machine or tool.

Frequently asked questions

Are MT2, 2MT, and MK2 the same size?

Generally, yes. MT2, 2MT, and MK2 refer to the same numbered Morse taper geometry.

The notation alone does not guarantee complete accessory interchangeability. Check usable length, tang or tangless construction, threads, drawbar provisions, and ejection arrangements before treating two accessories as equivalent.

Can I identify a Morse taper from the opening diameter alone?

Sometimes an opening diameter gives a strong preliminary identification, especially when the likely sizes are widely separated. It is not conclusive for every socket.

The machine face may not coincide with the nominal large-diameter reference plane. Recess, truncation, dirt, burrs, wear, restricted measuring access, or modification can affect the reading. Confirm the result with documentation, another internal measurement, or a known undamaged test shank whenever practical.

Do all Morse taper sizes use the same angle?

No. Morse taper rates and angles are close but not identical. The nominal rates in the chart range from approximately 0.0499 to 0.0526 inch per inch, while the listed half-angles range from 1.4287 to 1.5073 degrees.

Do not machine every Morse size from one generic angle. Use the geometry for the specific size and verify the resulting contact.

Is MT4.5 a listed Morse taper size?

Yes. MT4.5 appears in multiple third-party dimensional tables between MT4 and MT5. Its commonly published nominal diameters are 1.5000 inches at the large reference plane and 1.2660 inches at the small reference plane.

That does not establish informal intermediate labels as recognized sizes, nor does it prove that an unidentified socket must be MT4.5. Measure the geometry and confirm the machine documentation.

Can a reducing sleeve fit an MT3 tool into an MT5 socket?

Yes. A reducing sleeve can have an MT5 male exterior for the machine socket and an MT3 female interior for the tool. Specify it as machine side MT5, tool side MT3.

Before purchasing, confirm working length, tang clearance, thread or drawbar requirements, ejection method, tool projection, and intended loading. The sleeve adapts nominal sizes; it does not make every MT3 accessory suitable for every MT5-equipped machine.

The practical identification rule

Use a three-part process:

Screen the taper by nominal large diameter.
Confirm it with a second diameter and the measured axial separation between the two readings.
Verify machine-specific length, retention, clearance, and ejection details before buying or making tooling.

If the diameter and calculated taper rate do not indicate the same chart row—or if length and fit are critical—leave the taper classified as unresolved until an authoritative machine or tooling drawing confirms it.