Metric M Screw Threads: Profile, Designation and Tolerances: The Bolt That Almost Killed a Bridge

The Bolt That Almost Killed a Bridge

the practitioner stared at the crack propagating across the steel flange plate and felt his stomach drop.

Three months earlier, his fabrication shop had landed the biggest contract in its history — structural connections for a pedestrian bridge spanning a river gorge. The specs called for M24 × 3 bolts, tolerance class 6H/6g. Simple enough, or so his team thought.

But someone in procurement had substituted bolts from a supplier who machined to "close enough" tolerances. No one checked the pitch diameter limits. No one verified the allowance. No one confirmed the coating thickness fell within the quarter-allowance rule.

Now, under cyclic loading, the threads were failing. Not catastrophically — not yet — but the fatigue cracks told a story that every engineer, machinist, and procurement specialist needs to understand:

When it comes to metric screw threads, "close enough" is the most dangerous phrase in manufacturing.

This guide exists so you never make that mistake. Every tolerance, every formula, every limiting dimension you need — extracted directly from ANSI/ASME B1.13M-1983 (R1995) and ISO 965/1 — lives in the pages ahead.

What You'll Master in This Guide

• The ISO 68 Basic M Profile — geometry, symbols, and the fundamental triangle that governs every metric thread on the planet
• Coarse and Fine Pitch Series — every standard diameter-pitch combination with selection guidance
• M Profile Data — the complete thread proportion table for all standard pitches
• Limits and Fits — the ISO tolerance system applied to threads, decoded for practical use
• Dimensional Effect of Coating — the math behind why plating destroys threads (and how to prevent it)
• All Formulas for M Profile Limiting Dimensions — internal and external, ready to calculate
• Complete Tolerance Tables — TD1, TD2, Td, Td2 across all grades
• Internal Thread Limiting Dimensions (Table 12) — full 6H class data, M1.6 through M200
• External Thread Limiting Dimensions (Table 13) — full 6g and 4g6g class data
• Designation System — how to read, write, and decode every metric thread callout
• Comparison of Maximum Metal Dimensions — metric vs. inch equivalencies
• The MJ Profile — aerospace-grade threads for high-fatigue applications

The Foundation: ISO 68 Basic M Profile

Before the practitioner could fix his bridge problem, he had to go back to fundamentals. And every metric thread on Earth starts in the same place: the ISO 68 Basic Profile.

This is the 60-degree symmetrical V-thread profile that defines the theoretical boundary between the external thread (bolt) and the internal thread (nut). All deviations, tolerances, and fits are measured from this baseline.

The Fundamental Triangle

The entire geometry of the M profile is derived from a single value: pitch (P). The height of the fundamental (sharp-V) triangle is:

$$H = 0.8660254 \times P$$

From this single relationship, every dimension of the thread cascades:

Why this matters: When the practitioner's team received the substitute bolts, the pitch diameter was off by 0.08 mm. That sounds like nothing — until you realize that 0.08 mm on the pitch diameter translates to roughly 0.04 mm of reduced flank contact per side. Under cyclic load, that gap became a stress riser.

Key Diameter Relationships

The three critical diameters — major (D/d), pitch (D2/d2), and minor (D1/d1) — are all connected through the pitch:

• Pitch Diameter = Major Diameter − $0.649519 \times P$
• Minor Diameter (Internal) = Major Diameter − $1.082532 \times P$
• Minor Diameter (External, rounded root) = Pitch Diameter − $0.616025 \times P$

General Symbols — The Language of Metric Threads

You cannot read a thread specification, tolerance table, or engineering drawing without fluency in these symbols. They are defined by ANSI/ASME B1.13M-1983 (R1995):

Convention: Capital letters = internal thread (nut). Lowercase letters = external thread (bolt). This convention is absolute and universal throughout ISO and ANSI metric thread standards.

M Crest and Root Form

The form of the crest and root determines fatigue life, gaging capability, and assembly behavior.

External Thread (Bolt)

• Crest (major diameter): Flat, truncated $0.125H$ ($= 0.108253P$) from sharp crest. Corner rounding is permitted.
• Root (minor diameter): The root profile must lie within a defined tolerance zone. For rounded root threads (mandatory for property class 8.8 and above per ISO 898/I), the profile must be a continuous, smoothly blended non-reversing curve with minimum radius $r_{min} = 0.125P$, tangential to the flanks. The profile may comprise tangent flank arcs joined by a tangential flat.

Internal Thread (Nut)

• Crest (minor diameter): Flat, truncated $0.25H$ ($= 0.216506P$) from sharp crest.
• Root (major diameter): Must not be smaller than the basic profile. The maximum major diameter must not be sharp.

Critical safety note: The rounded root requirement for high-strength fasteners (class 8.8 and above, minimum tensile strength 800 MPa) exists because sharp roots act as stress concentrators. A flat-root M10 × 1.5 bolt in property class 10.9 can lose 40% or more of its fatigue life compared to a properly rounded root. This was exactly the failure mode on the practitioner's bridge bolts.

Standard M Profile Screw Thread Series

Coarse Pitch Series — Your First Choice

The coarse pitch series per ANSI/ASME B1.13M is the standard series for general purpose equipment and mechanical fasteners. These are your first choice for any application unless a specific design requirement demands otherwise.

Note: M22 × 2.5 and M27 × 3 are designated for high-strength structural steel fasteners only.

Fine Pitch Series — When Precision Demands It

Fine pitch threads are used when you need:

• Reduced tendency to loosen under vibration
• Greater tensile stress area (higher clamping force for same torque)
• Finer adjustment capability
• Thinner wall sections

Selected Fine Pitch Combinations (ANSI/ASME B1.13M):

Note: M12 × 1.5 fine pitch is designated for wheel studs and nuts only.

Limits and Fits — The ISO Tolerance System for Threads

This is where the practitioner's story takes its critical turn. Understanding limits and fits is the difference between a thread that performs for decades and one that fails in months.

Core Concepts

The International (ISO) metric tolerance system works identically for threads as it does for cylindrical holes and shafts:

• Basic Size = the zero reference line where mating parts interface
• Upper Deviation (ES/es) = algebraic difference between maximum limit and basic size
• Lower Deviation (EI/ei) = algebraic difference between minimum limit and basic size
• Fundamental Deviation = the deviation closest to basic size (es for external, EI for internal)
• Tolerance = total permitted variation (always positive, applied toward minimum material)

How the System Works

By convention:

• The external thread lies below the zero line (tolerance is negative — thread gets smaller)
• The internal thread lies above the zero line (tolerance is positive — thread gets larger)
• This produces a clearance fit by default

Tolerance Grade

A numerical value indicating the magnitude of the tolerance. Higher numbers = larger tolerances = looser fit.

Underlined grades are used with normal length of thread engagement.

Tolerance Position

A letter indicating the allowance (fundamental deviation) — how far the tolerance zone is shifted from basic size:

• Internal threads: G, H (capital letters)
• External threads: e, f, g, h (lowercase letters)

Where H and h = zero fundamental deviation (no allowance), and G and g = positive allowance providing clearance for coating or assembly.

Tolerance Class Designation

The grade is written first, followed by the position:

• 4g = Grade 4 pitch diameter tolerance, position g → shorthand for 4g4g
• 5H = Grade 5, position H → shorthand for 5H5H
• 4g6g = Grade 4 pitch diameter tolerance + Grade 6 major diameter tolerance, both position g
• 5H6H = Grade 5 pitch diameter + Grade 6 minor diameter, both position H

Application Comparison with Inch Threads

This is the Rosetta Stone for shops transitioning from inch to metric:

Length of Thread Engagement

The tolerance system adjusts for engagement length. There are three categories — Short, Normal, and Long — determined by the diameter-pitch combination:

Rules for non-standard engagement lengths:

• Short LE: Reduce the pitch diameter tolerance grade of the external thread by one number
• Long LE: Increase the allowance (fundamental deviation) at the pitch diameter of the external thread

Table 6 — Length of Thread Engagement Classifications (Selected Sizes, mm):

Allowance (Fundamental Deviation) Table

Table 7 — ANSI Standard Allowance for Internal and External Metric Threads (ISO 965/1)

All values in millimeters. es is an absolute value.

Tolerance class crosswalk for different engagement lengths:

Dimensional Effect of Coating — The Hidden Destroyer

This is the section the practitioner wishes he had read before his bridge project. Coating thickness on threads is not a simple one-to-one relationship.

The 4× Rule for Pitch Diameter

On a cylindrical surface, coating changes the diameter by twice the coating thickness (once per side). But on a 60-degree thread flank, the coating thickness is measured perpendicular to the flank surface, while the pitch diameter is measured perpendicular to the thread axis.

The result:

The effect of uniform coating on the pitch diameter is FOUR TIMES the coating thickness on the flank.

This means a mere 0.010 mm coating thickness shifts the pitch diameter by 0.040 mm — enough to blow past tolerance limits on many thread sizes.

External Thread with No Allowance — Before-Coating Adjustments

To determine gaging limits before coating for a uniformly coated thread:

1. Max pitch diameter → decrease by 4 × max coating thickness
2. Min pitch diameter → decrease by 4 × min coating thickness
3. Max major diameter → decrease by 2 × max coating thickness
4. Min major diameter → decrease by 2 × min coating thickness

External Thread with Only Nominal/Minimum Coating Thickness

When no coating tolerance is given, assume +50% of the nominal or minimum thickness as the tolerance. Then:

1. Max pitch diameter → decrease by 6 × coating thickness
2. Min pitch diameter → decrease by 4 × coating thickness
3. Max major diameter → decrease by 3 × coating thickness
4. Min major diameter → decrease by 2 × coating thickness

Internal Threads — Before-Coating Adjustments

Standard internal threads provide no allowance for coating thickness. To determine before-coating limits:

1. Min pitch diameter → increase by 4 × max coating thickness (or 6 × nominal if no tolerance specified)
2. Max pitch diameter → increase by 4 × min or nominal coating thickness
3. Min minor diameter → increase by 2 × max coating thickness (or 3 × nominal)
4. Max minor diameter → increase by 2 × min or nominal coating thickness

The Quarter-Allowance Rule

For standard tolerance classes 6g and 4g6g, size limits apply prior to coating. The external thread allowance may accommodate the coating thickness, provided that the maximum coating thickness is no more than one-quarter of the allowance.

After coating, the thread must pass:

• A basic (tolerance position h) size GO thread gage
• A tolerance position g gage for minimum material (LO or NOT-GO)

Worked Example: Coating Calculation

Thread: M6 × 1 − 4h6h, with 0.010 mm minimum coating thickness

Before coating limits:

• Major dia = 5.780 – 5.940
• Pitch dia = 5.239 – 5.290

After coating, the thread must not transgress the basic profile and is accepted using a basic (tolerance position H/h) size GO gage.

Strength Warning

On small threads (M5 and smaller), coating thickness adjustments can push the base material toward minimum material conditions that significantly affect strength of externally threaded parts. In these cases, limit coating thickness or redesign the part.

Formulas for M Profile Screw Thread Limiting Dimensions

These are the formulas used to calculate every value in Tables 12 and 13. Memorize them, bookmark them, or tape them to your CNC controller.

Internal Threads

$$\text{Min Major Dia.} = \text{Basic Major Dia.} + EI \quad \text{(Table 7)}$$

$$\text{Min Pitch Dia.} = \text{Basic Major Dia.} - 0.649519P \quad \text{(Table 3)} + EI_{D2} \quad \text{(Table 7)}$$

$$\text{Max Pitch Dia.} = \text{Min Pitch Dia.} + T_{D2} \quad \text{(Table 8)}$$

$$\text{Max Major Dia.} = \text{Max Pitch Dia.} + 0.793857P \quad \text{(Table 3)}$$

$$\text{Min Minor Dia.} = \text{Min Major Dia.} - 1.082532P \quad \text{(Table 3)}$$

$$\text{Max Minor Dia.} = \text{Min Minor Dia.} + T_{D1} \quad \text{(Table 9)}$$

External Threads

$$\text{Max Major Dia.} = \text{Basic Major Dia.} - es \quad \text{(Table 7, absolute value)}$$

$$\text{Min Major Dia.} = \text{Max Major Dia.} - T_d \quad \text{(Table 10)}$$

$$\text{Max Pitch Dia.} = \text{Basic Major Dia.} - 0.649519P \quad \text{(Table 3)} - es_{d2} \quad \text{(Table 7)}$$

$$\text{Min Pitch Dia.} = \text{Max Pitch Dia.} - T_{d2} \quad \text{(Table 11)}$$

$$\text{Max Flat Form Minor Dia.} = \text{Max Pitch Dia.} - 0.433013P \quad \text{(Table 3)}$$

$$\text{Max Rounded Root Minor Dia.} = \text{Max Pitch Dia.} - 2 \times \text{max truncation (See Fig. 4)}$$

$$\text{Min Rounded Root Minor Dia.} = \text{Min Pitch Dia.} - 0.616025P \quad \text{(Table 3)}$$

$$\text{Min Root Radius} = 0.125P$$

Worked Example: Calculating M10 × 1.5 − 6g Limits

Given: Basic major diameter = 10.000 mm, Pitch = 1.5 mm, es(g) = 0.032 mm

External thread (6g):

1. Max major dia. = 10.000 − 0.032 = 9.968 mm
2. Min major dia. = 9.968 − Td(6) ... (from Table 10 for P=1.5: Td = 0.236) = 9.732 mm
3. Max pitch dia. = 10.000 − 0.649519(1.5) − 0.032 = 10.000 − 0.974 − 0.032 = 8.994 mm
4. Min pitch dia. = 8.994 − Td2(6) ... (from Table 11 for P=1.5: Td2 = 0.132) = 8.862 mm
5. Max flat minor dia. = 8.994 − 0.433013(1.5) = 8.994 − 0.650 = 8.344 mm
6. Min rounded root minor dia. = 8.862 − 0.616025(1.5) = 8.862 − 0.924 = 7.938 mm

✅ Cross-check with Table 13: M10 × 1.5 − 6g shows Max major = 9.968, Min major = 9.732, Max PD = 8.994, Min PD = 8.862, Max minor = 8.344, Min minor (d3) = 7.938. Perfect match.

Complete Tolerance Tables

Table 11 — Pitch Diameter Tolerances of External Metric Threads, Td2 (mm)

Tolerance Grade Comparisons — Quick Ratios

If you know the Grade 6 tolerance, you can approximate any other grade:

Minor Diameter (Internal), TD1:

• Grade 4 = 0.63 × TD1(6)
• Grade 5 = 0.80 × TD1(6)
• Grade 7 = 1.25 × TD1(6)
• Grade 8 = 1.60 × TD1(6)

Pitch Diameter (Internal), TD2 (ratios based on Grade 6 external pitch diameter tolerance):

• Grade 4 = 0.85 × Td2(6)
• Grade 5 = 1.06 × Td2(6)
• Grade 6 = 1.32 × Td2(6)
• Grade 7 = 1.70 × Td2(6)
• Grade 8 = 2.12 × Td2(6)

Major Diameter (External), Td:

• Grade 4 = 0.63 × Td(6)
• Grade 8 = 1.60 × Td(6)

Pitch Diameter (External), Td2:

• Grade 3 = 0.50 × Td2(6)
• Grade 4 = 0.63 × Td2(6)
• Grade 5 = 0.80 × Td2(6)
• Grade 7 = 1.25 × Td2(6)
• Grade 8 = 1.60 × Td2(6)
• Grade 9 = 2.00 × Td2(6)

Internal Metric Thread — M Profile Limiting Dimensions (Table 12)

Tolerance Class 6H — ANSI/ASME B1.13M-1983 (R1995)

All dimensions in millimeters.

Continued — Large Sizes:

Note: Maximum major diameter (D Max) is a reference dimension used in design of tools and is not normally specified. Major diameter acceptance is generally based upon maximum material condition gaging.