What is the tap drill size for #3-56 UNF?

The tap drill for #3-56 UNF is #45 — 0.0820 in (2.083 mm). That leaves 73.3% thread engagement with a cut tap.

What is the pitch diameter of #3-56 UNF?

The basic pitch diameter of #3-56 UNF is 0.0874 in (2.220 mm). For a class 2B thread it runs 0.0874 in (2.220 mm) to 0.0902 in (2.291 mm).

What is the minor diameter of #3-56 UNF?

The basic minor diameter of #3-56 UNF is 0.0797 in (2.024 mm). That is the theoretical root of the internal thread, not the drilled hole size — see the tap drill table for the hole to drill.

What is the thread pitch of #3-56 UNF?

#3-56 UNF has 56 threads per inch, a pitch of 0.0179 in (0.454 mm).

What size clearance hole does a #3-56 UNF fastener need?

close fit #37 (0.1063 in (2.700 mm)), normal fit #33 (0.1142 in (2.901 mm)), loose fit #30 (0.1299 in (3.299 mm)). The normal fit is the general-assembly default.

What is the tensile stress area of #3-56 UNF?

The tensile stress area of #3-56 UNF is 0.00523 in² (3.37 mm²). Multiply it by the fastener material's allowable stress to get a load.

Unified Fine (UNF) · #3-56 UNF

#3-56 UNF Thread — Dimensions, Tap Drill & Clearance

https://shopmath.org/threads/unf/3-56 · data verified August 1, 2026

The tap drill for #3-56 UNF is #45 — 0.0820 in (2.083 mm) — which leaves 73.3% thread engagement with a cut tap. Basic pitch diameter is 0.0874 in (2.220 mm) and basic minor diameter is 0.0797 in (2.024 mm). Tapped-hole figures on this page assume a class 2B thread; drill sizes for 50–85% engagement are in the tap drill table below.

Series: Unified Fine (UNF)
Designation: #3-56 UNF
TPI: 56
Standard: ASME B1.1

Tap drill · 73.3% thread · cut tap

#45

Drill Ø: 0.0820in
Drill Ø: 2.083mm
Clearance (normal): #33

Assumes 75% thread engagement with a cut tap and a class 2B hole. That drill actually leaves 73.3% thread.

Basic Thread Dimensions for #3-56 UNF

Basic thread dimensions — #3-56 UNF
Property	Inch	Millimetre
Basic major diameter	0.0990	2.515
Threads per inch	56	—
Pitch	0.0179	0.454
Basic pitch diameter	0.0874	2.220
Basic minor diameter	0.0797	2.024
External thread root diameter	0.0777	1.974
Sharp V thread height (H)	0.0155	0.394

Threads per inch has no millimetre counterpart — metric threads are specified by pitch instead. Basic dimensions are the theoretical values before any tolerance class is applied.

Tap Drill Sizes for #3-56 UNF

Cut taps, from 50% to 85% thread engagement. The shop default is 75% — a #45 drill. Deeper engagement means more holding strength and more torque on the tap.

Tap drill sizes by thread engagement — #3-56 UNF, cut tap
Property	Target hole Ø		Nearest standard drill			Property
Thread %	in	mm	Drill	in	mm	Actual thread %
50%	0.0874	2.220	#44	0.0860	2.184	56.0
60%	0.0851	2.162	#44	0.0860	2.184	56.0
65%	0.0839	2.131	#45	0.0820	2.083	73.3
70%	0.0828	2.103	#45	0.0820	2.083	73.3
75%default	0.0816	2.073	#45	0.0820	2.083	73.3
80%	0.0804	2.042	#46	0.0810	2.057	77.6
85%	0.0793	2.014	#47	0.0785	1.994	88.4

Target hole Ø is the theoretical hole for the stated engagement. The drill column is the nearest size in the standard number/letter/fractional/metric index, and actual thread % is what that real drill produces — the number that matters at the machine. Values are for cut taps. Tapped-hole figures assume a class 2B hole.

Clearance Hole Sizes for #3-56 UNF

The through-hole a #3-56 UNF fastener passes freely, not the tapped hole.

Clearance hole sizes — #3-56 UNF
Property	Property	Hole Ø		Property
Fit	Drill	in	mm	Use
Close	#37	0.1063	2.700	Located joints, dowelled assemblies
Normal	#33	0.1142	2.901	General assembly — the default
Loose	#30	0.1299	3.299	Slotted or adjustable joints, weldments

Clearance holes per ISO 273 (metric) and ASME B18.2.8 (inch). The drill column is the nearest standard drill at or above the specified hole diameter.

Thread Class Limits for #3-56 UNF

Manufacturing limits for classes 2B, 3B, 2A, 3A. A gauge reading outside these bands is a reject, not a judgement call.

External thread (bolt / screw) limits — #3-56 UNF
Property	Class 2A		Class 3A
Limit	in	mm	in	mm
Major Ø max	0.0983	2.497	0.0990	2.515
Major Ø min	0.0942	2.393	0.0949	2.410
Pitch Ø max	0.0867	2.202	0.0874	2.220
Pitch Ø min	0.0846	2.149	0.0858	2.179
Pitch Ø tolerance	0.0022	0.056	0.0016	0.041
Minor Ø max	0.0751	1.907	0.0758	1.925
Minor Ø min	0.0730	1.854	0.0742	1.885
Allowance	0.0007	0.018	0.0000	0.000

Internal thread (nut / tapped hole) limits — #3-56 UNF
Property	Class 2B		Class 3B
Limit	in	mm	in	mm
Major Ø max	0.1044	2.652	0.1037	2.634
Major Ø min	0.0990	2.515	0.0990	2.515
Pitch Ø max	0.0902	2.291	0.0895	2.273
Pitch Ø min	0.0874	2.220	0.0874	2.220
Pitch Ø tolerance	0.0028	0.071	0.0021	0.053
Minor Ø max	0.0865	2.197	0.0865	2.197
Minor Ø min	0.0797	2.024	0.0797	2.024
Allowance	0.0000	0.000	0.0000	0.000

Tensile Stress Area of #3-56 UNF

The effective cross-section used to size a #3-56 UNF fastener against a load. Multiply it by the material's allowable stress — the area itself carries no strength assumption.

Tensile stress area — #3-56 UNF
Property	in²	mm²
Tensile stress area	0.00523	3.37

The formula this value comes from is in the sources section below.

Other Thread Pitches in the Same Size as #3-56 UNF

A #3 fastener is not always #3-56 UNF. These are the other standard pitches cut on the same nominal size.

Other standard pitches at nominal size #3
Thread	Series	Pitch	Tap drill
#3-48 UNC	Unified Coarse (UNC)	48 TPI	#47

Sources and Method for #3-56 UNF

Basic dimensionscomputed

NBS Handbook H28 (1969) Part I §§6-7 (public domain, 17 U.S.C. 105); normative modern reference ASME B1.1; series membership: Series membership: threadlib UIS_thread.csv (BSD-3-Clause); cross-checked against NBS H28 (1969) Part I Table 2.21; clearance holes: ISO 273 (metric) and ASME B18.2.8 (inch) via FreeCAD FeatureHole.cpp (LGPL-2.1+), cross-checked against bd_warehouse clearance_hole_sizes.csv (Apache-2.0)

Verified against NBS H28 (1969) Part I, Table 2.21 (public domain); cross-checked against FreeCAD CAM thread tables (LGPL-2.1+) — 1064 checks passed at 0.0001 in

Computed from the standard's formulas, then checked against published tables.

Tap drill sizescomputed

Machinery's Handbook %-thread formula (geometry-derived); nearest-standard-drill-to-75% rule verified at 36/39 published chart rows in docs/research/data-sourcing.md §3.4

Verified against Wikipedia Unified Thread Standard, preferred cutting tap drill size columns (CC BY-SA 4.0) — 36/39 published UNC+UNF rows reproduced

Computed from the standard's formulas, then checked against published tables.

Class limitscomputed

NBS Handbook H28 (1969) Part I §§6-7 (public domain, 17 U.S.C. 105); normative modern reference ASME B1.1

Verified against NBS H28 (1969) Part I, Table 2.21 (public domain); cross-checked against FreeCAD CAM thread tables (LGPL-2.1+) — 1064 checks passed at 0.0001 in

Computed from the standard's formulas, then checked against published tables.

Formula

Tap drill hole diameter, inch threads

hole Ø  =  D − (%thread ÷ 100) × (1.29904 ÷ n)

  D = basic major diameter (in)
  n = threads per inch

1.29904 = 2 × 0.64952, twice the engaged thread height per side on the 60° Unified profile.

Actual thread engagement of the chosen drill

%thread  =  (D − drill Ø) × n ÷ 1.29904 × 100

The drill column rounds to a real drill; this is the engagement that drill actually leaves.

Tensile stress area, Unified inch threads

At  =  0.7854 × (D − 0.9743 ÷ n)²

ASME B1.1 / NBS H28 form. Reproduces the stored value exactly for this thread.

Assumptions

The headline tap drill assumes 75% thread engagement, the general shop default. Every other engagement from 50% to 85% is in the tap drill table — change the assumption and the number moves.
Tap drill figures are for cut taps. Drill diameters are nominal; a worn or run-out drill cuts oversize and reduces engagement further.
Tapped-hole figures assume a class 2B internal thread, the general-purpose fit.
Dataset scope: Le = 1D for UNC/UNF, 9P for UNEF — determined empirically against H28 Table 2.21, resolving data-sourcing.md open item 5. EXCLUDED: form (roll) tap drills, class 1A/1B limits, class 1AR allowances, constant-pitch UN series.

Data last verified

August 1, 2026

How this data is built and checked →

How to Cite This #3-56 UNF Reference

Citation

ShopMath. "#3-56 UNF Thread — Dimensions, Tap Drill & Clearance." ShopMath, verified August 1, 2026, https://shopmath.org/threads/unf/3-56

BibTeX

@misc{shopmath-threads-unf-3-56,
  title        = {#3-56 UNF Thread — Dimensions, Tap Drill & Clearance},
  author       = {{ShopMath}},
  year         = {2026},
  howpublished = {\url{https://shopmath.org/threads/unf/3-56}},
  note         = {Data verified 2026-08-01}
}

Permanent URL

https://shopmath.org/threads/unf/3-56

Common Questions About #3-56 UNF

What is the tap drill size for #3-56 UNF?: The tap drill for #3-56 UNF is #45 — 0.0820 in (2.083 mm). That leaves 73.3% thread engagement with a cut tap.
What is the pitch diameter of #3-56 UNF?: The basic pitch diameter of #3-56 UNF is 0.0874 in (2.220 mm). For a class 2B thread it runs 0.0874 in (2.220 mm) to 0.0902 in (2.291 mm).
What is the minor diameter of #3-56 UNF?: The basic minor diameter of #3-56 UNF is 0.0797 in (2.024 mm). That is the theoretical root of the internal thread, not the drilled hole size — see the tap drill table for the hole to drill.
What is the thread pitch of #3-56 UNF?: #3-56 UNF has 56 threads per inch, a pitch of 0.0179 in (0.454 mm).
What size clearance hole does a #3-56 UNF fastener need?: close fit #37 (0.1063 in (2.700 mm)), normal fit #33 (0.1142 in (2.901 mm)), loose fit #30 (0.1299 in (3.299 mm)). The normal fit is the general-assembly default.
What is the tensile stress area of #3-56 UNF?: The tensile stress area of #3-56 UNF is 0.00523 in² (3.37 mm²). Multiply it by the fastener material's allowable stress to get a load.

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