---
type: "thread"
name: "#3-56 UNF"
designation: "#3-56 UNF"
series: "unf"
series_name: "Unified Fine (UNF)"
system: "unified"
size_label: "#3"
tpi: 56
pitch_in: 0.017857
pitch_mm: 0.4536
basic_major_dia_in: 0.099
basic_major_dia_mm: 2.5146
basic_pitch_dia_in: 0.0874
basic_pitch_dia_mm: 2.22
basic_minor_dia_in: 0.0797
basic_minor_dia_mm: 2.0244
tap_drill: "#45"
tap_drill_dia_in: 0.082
tap_drill_dia_mm: 2.0828
tap_drill_thread_pct: 73.3
clearance_normal_drill: "#33"
tensile_stress_area_sqin: 0.00523
tensile_stress_area_sqmm: 3.374
internal_class_assumed: "2B"
standard: "ASME B1.1 (reference values based on the ASME B1.1 system; not a compliance claim)"
verified: "August 1, 2026"
url: https://shopmath.org/threads/unf/3-56
---

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

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
- **Threads per inch**: 56
- **Tap drill**: #45
- **Standard**: ASME B1.1 (reference values based on the ASME B1.1 system; not a compliance claim)

## Basic Thread Dimensions for #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 |

_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.

| Thread % | Target hole Ø (in) | Target hole Ø (mm) | Drill | Drill Ø (in) | Drill Ø (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._

## Clearance Hole Sizes for #3-56 UNF

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

| Fit | Drill | Hole Ø (in) | Hole Ø (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)._

## 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

| Limit | Class 2A (in) | Class 2A (mm) | Class 3A (in) | Class 3A (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

| Limit | Class 2B (in) | Class 2B (mm) | Class 3B (in) | Class 3B (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

| Property | in² | mm² |
| --- | --- | --- |
| Tensile stress area | 0.00523 | 3.37 |

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.

## 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.

| Thread | Series | Pitch | Tap drill |
| --- | --- | --- | --- |
| [#3-48 UNC](https://shopmath.org/threads/unc/3-48.md) | Unified Coarse (UNC) | 48 TPI | #47 |

## Sources and Method for #3-56 UNF

### Basic dimensions

- **Source**: 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)
- **Method**: computed
- **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

### Tap drill sizes

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

### Class limits

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

### Formulas

**Tap drill hole diameter, inch threads**

```text
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**

```text
%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**

```text
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 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

## 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.

## Related pages

- Smaller in Unified Fine (UNF): [#2-64 UNF](https://shopmath.org/threads/unf/2-64.md) — tap drill #50
- Larger in Unified Fine (UNF): [#4-48 UNF](https://shopmath.org/threads/unf/4-48.md) — tap drill #42
- All Unified Fine (UNF) sizes: [Unified Fine (UNF) thread chart](https://shopmath.org/threads/unf.md)
- Every thread series: [Screw thread reference](https://shopmath.org/threads.md)
- Cross-series chart: [Tap drill chart](https://shopmath.org/charts/tap-drill.md)

---

*Source: [ShopMath](https://shopmath.org/threads/unf/3-56) — data verified August 1, 2026. Reference data; verify against the governing standard before manufacture.*