Metric thread size and tolerance calculator was developed to calculate major, minor and pitch diameters of the external (bolt) and internal (nut) metric threads according to ISO 724:1993 standard. In addition to basic size calculations of metric threads, tolerance calculations of different tolerance classes can be done according to ISO 965-1:1998 and ISO 965-2:1998 standards.

There are two calculation options available, general engineering use or custom use.

In general engineering use, calculations can be done by selecting a standard metric thread size from the list which contains metric thread sizes in the diameter range from 1.6 mm (M1.6) to 64 mm (M64). Tolerance class can be selected among the alternatives 6e, 6f, 6g and 4h for bolts and 5H, 6H, 7H and 6G for nuts. 6g and 6H are default values and selected class for commercial external threads and internal threads in ISO 965-1:1998. The user shall use 6g for bolts and 6H for nuts unless there is a specific requirement to use other tolerance classes.

In custom use, thread size, pitch and tolerance classes can be independently selected for custom engineering calculations.

Some important notes from ISO metric screw threads standards:

- External Screw Thread Designation: Nominal Diameter x Pitch - Tolerance class for pitch diameter - Tolerance class for major diameter (M10 x 1 5g 6g)

- Internal Screw Thread Designation: – Nominal Diameter x Pitch - Tolerance class for pitch diameter - Tolerance class for minor diameter (M10 x 1 5H 6H)

- If the two class designations for the pitch diameter and crest diameter are the same it is not necessary to repeat the symbols. (M10 x 1 6g)

- According to ISO 1:2002 , standard reference temperature for geometrical product specification is 20  °C.

- Gauges and gauging for ISO general purpose metric threads are defined in the ISO 1502:1996 standard.

- The basic profile of ISO general purpose metric screw threads is defined in the ISO 68-1:1998 and given in the first figure below.  External (bolt) thread root profile is given the "Definitions" section.  The list of metric screw thread used in general engineering applications are given in the General Purpose Metric Screw Threads Table.

Note: For more information on Metric screw threads including thread form, definitions, limits and fits for threads, standard series and combinations, thread designation, basic dimensions, dimensional effect of coating, formulas and details of MJ profile, please refer to pages 1930 - 1967 of Machinery's Handbook, 30th.

ISO metric screw thread basic profile according to ISO 68-1

 INPUT PARAMETERS Calculation Type General Engineering Use Custom Use GENERAL ENGINEERING USE Metric Thread M1.6 x 0.35 M2 x 0.4 M2.5 x 0.45 M3 x 0.5 M4 x 0.7 M5 x 0.8 M6 x 1 M8 x 1 M8 x 1.25 M10 x 1 M10 x 1.25 M10 x 1.5 M12 x 1.25 M12 x 1.5 M12 x 1.75 M16 x 1.5 M16 x 2 M20 x 1.5 M20 x 2 M20 x 2.5 M24 x 2 M24 x 3 M30 x 2 M30 x 3.5 M36 x 3 M36 x 4 M42 x 3 M42 x 4.5 M48 x 3 M48 x 5 M56 x 4 M56 x 5.5 M64 x 4 M64 x 6 External Thread (Bolt) Tolerance Class * 6e 6f 6g 4h Internal Thread (Nut) Tolerance Class** 6G 5H 6H 7H CUSTOM USE Nominal Diameter Pitch 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.6 0.7 0.75 0.8 1 1.25 1.5 1.75 2 2.5 3 3.5 4 4.5 5 5.5 6 8 Bolt Tolerance Class Tolerance Grades Deviations Pitch Diameter Tolerance 3 4 5 6 7 8 9 e f g h Major Diameter Tolerance 4 6 8 e f g h Nut Tolerance Class Tolerance Grades Deviations Pitch Diameter Tolerance 4 5 6 7 8 G H Minor Diameter Tolerance 4 5 6 7 8 G H

Note : * 6g is normally selected for commercial external (bolt) threads. Use this tolerance class for commercial external (bolt) threads. For usage of the other classes, refer to ISO 965-1:1998.

Note : ** 6H is normally selected for commercial internal (nut) threads. Use this tolerance class for commercial internal threads. For usage of the other classes, refer to ISO 965-1:1998.

 RESULTS Parameter Value Note --- Designation -- --- --- Tolerance Class for Bolt -- --- Tolerance Class for Nut -- --- Screw Thread Series -- --- Pitch P --- mm LIMITS OF SIZES FOR EXTERNAL THREADS (BOLTS) Maximum Major Diameter dmax --- mm Minimum Major Diameter dmin --- Maximum Pitch Diameter d2max --- Minimum Pitch Diameter d2min --- Maximum Rounded Root  Minor Diameter d3max --- Minimum Rounded Root  Minor Diameter d3min --- Minimum Root Radii Rmin --- Minimum Truncation Cmin --- Maximum Truncation Cmax --- LIMITS OF SIZES FOR INTERNAL THREADS (NUTS) Minimum Major Diameter Dmin --- mm Maximum Pitch Diameter D2max --- Minimum Pitch Diameter D2min --- Maximum Minor Diameter D1max --- Minimum Minor Diameter D1min --- BASIC DIMENSIONS Basic Major Diameter d , D --- mm Basic Pitch Diameter d2 , D2 --- Basic Minor Diameter d1, D1 --- Fundamental Triangle Height H ---

Note-1: For coated threads, the tolerances apply to the parts before coating, unless otherwise stated. After coating, the actual thread profile shall not at any point transgress the maximum material limits for positions h or H. For external (bolt) threads; The actual root contours shall not at any point transgress the basic profile. Fasteners of property class 8.8 and higher (see ISO 898-1), the root profile shall have a non-reversing curvature, no portion of which shall have a radius of less than Rmin.

### Definitions:

Basic profile: The theoretical profile of a screw thread in an axial plane defined by theoretical dimensions and angles common to internal and external threads

Crest: The surface at the top of the ridge connecting its two flanks.

Gauges and Gauging: Details for the manufacture and use of gauges for checking ISO general-purpose metric screw threads are specified in the ISO 1502:1996 standard. It specifies the features of the types of gauges (Solid/adjustable GO screw ring gauges, check plugs, setting plugs, wear check plugs, screw caliper gauges, plug gauges, etc.) which are recommended for checking external and internal screw threads of workplaces and for the setting and checking of certain of the screw gauges.

Major Diameter: The maximum diameter of a thread which is diameter of the crest of a male thread or root of a female thread.

Minor Diameter: The minimum diameter of a thread which is diameter of the root of a male thread or crest of a female thread.

Root: The surface at the bottom of the groove connecting the adjacent flanks

ISO metric screw external thread root contour according to ISO 965-1 for positions e, f, g

### List of Screw Thread Equations:

 Parameter Equation Height of fundamental triangle [H] $$H=\frac { \sqrt { 3 } }{ 2 } P$$ Thread basic pitch diameter [d2 , D2] $${ d }_{ 2 }={ D }_{ 2 }=d-2\times \frac { 3 }{ 8 } H=D-2\times \frac { 3 }{ 8 } H$$ Thread basic minor diameter [d1 , D1 ] $${ d }_{ 1 }={ D }_{ 1 }=d-2\times \frac { 5 }{ 8 } H=D-2\times \frac { 5 }{ 8 } H$$ External thread minimum truncation [Cmin] $${ C }_{ min }=0.125P$$ External thread maximum truncation [Cmax] $${ C }_{ max }=\frac { H }{ 4 } -{ R }_{ min }\left\{ 1-\cos { \left[ \frac { \pi }{ 3 } -\arccos { \left( 1-\frac { { T }_{ d2 } }{ 4{ R }_{ min } } \right) } \right] } \right\} +\frac { { T }_{ d2 } }{ 2 }$$ External thread maximum major diameter [dmax] $${ d }_{ max }=d+es$$ External thread minimum major diameter [dmin] $${ d }_{ min }={ d }_{ max }-{ T }_{ d }$$ External thread maximum pitch diameter [d2max] $${ d }_{ 2max }={ d }_{ 2 }+es$$ External thread minimum pitch diameter [d2min] $${ d }_{ 2min }={ d }_{ 2max }-{ T }_{ d2 }$$ External thread maximum minor diameter [d3max] $${ d }_{ 3max }={ d }_{ 1 }-es-2y$$ External thread minimum minor diameter [d3min] $${ d }_{ 3min }={ d }_{ 1 }-es-2z$$ Dimension y $$y={ R }_{ min }\left\{ 1-\cos { \left[ \frac { \pi }{ 3 } -\arccos { \left( 1-\frac { { T }_{ d2 } }{ 4{ R }_{ min } } \right) } \right] } \right\}$$ Dimension z $$z=\frac { H }{ 4 } +\frac { { T }_{ { d }_{ 2 } } }{ 2 } -\frac { P }{ 8 }$$ Internal thread minimum major diameter [Dmin] $${ D }_{ min }=D+EI$$ Internal thread maximum pitch diameter [D2max] $${ D }_{ 2max }={ D }_{ 2min }+{ T }_{ D2 }$$ Internal thread minimum pitch diameter [D2min] $${ D }_{ 2min }={ D }_{ 2 }+EI$$ Internal thread maximum minor diameter [D1max] $${ D }_{ 1max }={ D }_{ 1min }+{ T }_{ D1 }$$ Internal thread minimum minor diameter [D1min] $${ D }_{ 1min }={ D }_{ 1 }+EI$$

 List of Parameters Symbol Definition es, EI Fundamental deviation Td Major diameter tolerance of external thread Td2 Pitch diameter tolerance of external thread TD1 Minor diameter tolerance of internal thread TD2 Pitch diameter tolerance of internal thread

### Reference:

• Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2016) . Machinery's Handbook . 30th edition.  Industrial Press Inc.
• Oberg, E. , Jones ,F.D. , Horton H.L. , Ryffel H.H., (2012) . Machinery's Handbook . 29th edition.  Industrial Press Inc.
• ISO 1:2002 - Geometrical Product Specifications (GPS) - Standard reference temperature for geometrical product specification and verification
• ISO 68-1:1998 (E) - ISO general purpose screw threads — Basic profile — Part 1: Metric screw threads
• ISO 262:1998 (E) -  ISO general purpose metric screw threads — Selected sizes for screws, bolts and nuts
• ISO 724:1993 (E) - ISO general-purpose metric screw threads - Basic dimensions
• ISO 965-1:1998 – ISO General Purpose Metric Screw Threads – Tolerances Part-1: Principles and Basic Data
• ISO 965-2:1998 – ISO General Purpose Metric Screw Threads – Tolerances Part-2: Limits of sizes for general purpose external and internal screw threads - Medium quality
• BS 3643-1:2007 – ISO General Purpose Metric Screw Threads – Tolerances Part-1: Principles and Basic Data (British Standard)