There are numerous standards that fasteners are manufactured to, and those standards describe everything from material chemistry to surface finish to heat treatment. The most relevant numbers are “Proof Stress,” “Yield Stress” and “Tensile / Ultimate Stress.” Tensile Strength is how much stress the material can withstand before finally ripping apart. Yield Stress is the amount of stress that a material can undergo before permanently stretching. Proof stress is similar to Yield stress except that it is slightly less (about 90%), and only applies to fasteners. The thread geometry causes them to yield slightly before the Yield stress level of the material, so Proof Stress can be thought of the true yield–in other words, the fastener will behave like a spring below that stress level.

**So which of these numbers should be used?** While there are many arguments for tightening a screw past its yield point (for instance), from this author’s viewpoint, if an external load yields a screw, and if that load is ever removed, the screw will now be permanently stretched and loose. Therefore, **we recommend designing so that the combined internal and external loads stay below the proof stress to avoid any possibility of yielding.** If proof stress is unknown, 85% of Yield stress can be used as an approximation. The ultimate or tensile stress is sometimes designed to, but we do not know when this acceptable or not. Also, the ultimate stress is used in designing joints for alternating loads, but this is beyond our scope.

Several organizations publish standards for fasteners. For inch/english, this includes SAE, ASTM, ANSI, ASME and others, although the most commonly used are the SAE **“Grades.”**(standard J429). The most common metric specifications are published by the ISO. (ANSI metric specs agree with ISO for all practical purposes–Machinery’s Handbook)

### Common Inch / Imperial SAE Grades: (all values in ksi or 1000 lbs / square inch)

Head Marking | Grade | Diameter (in) | Proof Strength | Yield Strength | Tensile (Ultimate) Strength |
---|---|---|---|---|---|

2 | 1/4 to 3/4 | 55 | 57 | 74 | |

3/4 to 1-1/2 | 33 | 36 | 60 | ||

5 | 1/4 to 1 | 85 | 92 | 120 | |

1 to 1-1/2 | 74 | 81 | 105 | ||

8 | 1/4 to 1-1/2 | 120 | 130 | 150 |

Socket Head Cap Screws made from alloy steel are typically manufactured to a higher strength than SAE Grade 8: 180 ksi tensile strength for fasteners up to 1/2 inch, 170 ksi for larger sizes (ASTM A574, p. G-34).

For many more head markings and their corresponding specifications, see here.

### Metric ISO Marking

Metric fasteners are marked with two numbers separated by a decimal point, like 10.9. The 10 is 1/100 of tensile strength in MPa, and the .9 represents the ratio of yield to tensile strength. So 10.9 represents a tensile strength of 1000 MPa and yield of 900 MPa. Some strengths are stronger than this method shows, see table 10 on this page. Other references for this table: here and here.

Grade | size range | proof strength (MPa) | approx yield strength (MPa) grade dec x tensile* | tensile strength (MPa) | approx equiv. to SAE grade: |
---|---|---|---|---|---|

4.8 | M1.6-M16 | 310 | 336 | 420 | SAE 2 |

8.8 | < M16 | 580 | 640 | 800 | SAE 5 |

M16-M76 | 600 | 660 | 830 | ||

10.9 | > M5 | 830 | 940 | 1040 | SAE 8 |

12.9 | M1.6-M100 | 970 | 1100 | 1220 | ASTM-A574 alloy socket screws |

*these value aren’t necessarily from the standards, they’re calculated as described above.

### Tensile stress areas and acceptable load estimates for various grades

For applications where there is any chance of bodily or property harm, don’t rely on our external load estimates–**they are intended to give a rough approximation of what screws of various grades can hold in non-critical applications, and are based on the following assumptions:**

- We use the proof strength as the maximum stress that should be endured from the combined internal (original tightening) and external loads.
- If proof load isn’t specified in the above tables, we use 85% of yield
- It is assumed that the joint is twice as stiff as the bolt, which implies that 1/3 of the external load is seen by the bolt, and the other 2/3 goes into reducing clamping load.
**The forumla explained above and used below is 60% * proof * tensile area / 1.0 (safety factor). We recommend using a 2.5 safety factor for non-critical / costly applications–ie, divide the numbers below by 2.5.**For joints clamping aluminum, plastic, gaskets or other softer material it’s safer to assume that 100% of external load is seen by the fastener (multiply by 20% instead of 60%). **tensile stress area:**Tests have shown that the average of the minor and pitch diameters approximates the effective area of a fastener. The Machinery’s handbook has a different formula for bolts with tensile strengths over 100ksi, but due to some doubt about its origins, we don’t use it.- As far as we can tell, SAE Grades apply only to bolts at least 1/4″ in diameter. Any unmarked machine screws smaller than that are probably Grade 2; we show the higher Grades for reference only on those sizes. Alloy steel socket head cap screws will most likely have a greater strength than SAE Grade 8 unless their manufacturer says otherwise.
- We assume shear loads and torsional loads from tightening are zero.
- For alloy socket screws, yield strength is 180 ksi until 1/2″ and 170 ksi for larger diameters. We use 85% of these values to approximate proof strength.

### Inch tensile areas and loads (in lbs), both fine and coarse thread

size – threads / in | dec. major diameter (in) | tensile stress area square inches | Grade 2 (proof strength: <=3/4″: 55 ksi >3/4″: 33 ksi) | Grade 5 (proof strength: 85 ksi) | Grade 8 (proof strength: 120 ksi) | alloy socket head (ASTM A574) <=1/2″: 153 ksi >1/2″: 144.5 ksi |
---|---|---|---|---|---|---|

#0-80 | .0600 | .00180 | 59.4 | 91.8 | 129.6 | 165.24 |

#2-56 | .086 | .00370 | 122.1 | 188.7 | 266.4 | 339.66 |

#2-64 | .086 | .00394 | 130.02 | 200.94 | 283.68 | 361.692 |

#4-40 | .112 | .00604 | 199.32 | 308.04 | 434.88 | 554.472 |

#4-48 | .112 | .00661 | 218.13 | 337.11 | 475.92 | 606.798 |

#6-32 | .138 | .00909 | 299.97 | 463.59 | 654.48 | 834.462 |

#6-40 | .138 | .01015 | 334.95 | 517.65 | 730.8 | 931.77 |

#8-32 | .164 | .0140 | 462 | 714 | 1008 | 1285.2 |

#8-36 | .164 | .01474 | 486.42 | 751.74 | 1061.28 | 1353.132 |

#10-24 | .190 | .0175 | 577.5 | 892.5 | 1260 | 1606.5 |

#10-32 | .190 | .0200 | 660 | 1020 | 1440 | 1836 |

1/4-20 | .250 | .0318 | 1049.4 | 1621.8 | 2289.6 | 2919.24 |

1/4-28 | .250 | .0364 | 1201.2 | 1856.4 | 2620.8 | 3341.52 |

5/16-18 | .3125 | .0524 | 1729.2 | 2672.4 | 3772.8 | 4810.32 |

5/16-24 | .3125 | .0580 | 1914 | 2958 | 4176 | 5324.4 |

3/8-16 | .375 | .0775 | 2557.5 | 3952.5 | 5580 | 7114.5 |

3/8-24 | .375 | .0878 | 2897.4 | 4477.8 | 6321.6 | 8060.04 |

7/16-14 | .4375 | .1063 | 3507.9 | 5421.3 | 7653.6 | 9758.34 |

7/16-20 | .4375 | .1187 | 3917.1 | 6053.7 | 8546.4 | 10896.66 |

1/2-13 | .5 | .1419 | 4682.7 | 7236.9 | 10216.8 | 13026.42 |

1/2-20 | .5 | .1599 | 5276.7 | 8154.9 | 11512.8 | 14678.82 |

9/16-12 | .5625 | .182 | 6006 | 9282 | 13104 | 15779.4 |

9/16-18 | .5625 | .203 | 6699 | 10353 | 14616 | 17600.1 |

5/8-11 | .625 | .226 | 7458 | 11526 | 16272 | 19594.2 |

5/8-18 | .625 | .256 | 8448 | 13056 | 18432 | 22195.2 |

3/4-10 | .75 | .334 | 6613.2 | 17034 | 24048 | 28957.8 |

3/4-16 | .75 | .373 | 7385.4 | 19023 | 26856 | 32339.1 |

7/8-9 | .875 | .462 | 9147.6 | 23562 | 33264 | 40055.4 |

7/8-14 | .875 | .509 | 10078.2 | 25959 | 36648 | 44130.3 |

1-8 | 1.0 | .606 | 11998.8 | 30906 | 43632 | 52540.2 |

1-12 | 1.0 | .663 | 13127.4 | 33813 | 47736 | 57482.1 |

alternative load carrying recommendations: here.

### Metric coarse thread tensile stress areas and estimated loads (**in N**)

Fine pitch information and more can be found here. Formula for tensile stress area: pi/4* (Nominal_Diameter-.938194*pitch)^2

Formula for load: 60% * tensile area * proof stress / (safety_factor = 1.0)

size x pitch | tensile stress area square mm | Grade 4.8 (proof strength: M1.6-M16: 310 MPa) | Grade 8.8 (proof strength: < M16: 580 MPa >= M16: 600 Mpa) | Grade 10.9 (proof strength: > M5: 120 MPa) | Grade 12.9 (proof strength: 970 MPa) |
---|---|---|---|---|---|

2x.4 | 2.0732 | 386 N | 721 N | n/a | 1207 N |

2.5x.45 | 3.3908 | 631 | 1180 | n/a | 1973 |

3x.5 | 5.0308 | 936 | 1751 | n/a | 2928 |

4x.7 | 8.7787 | 1633 | 3055 | n/a | 5109 |

5x.8 | 14.183 | 2638 | 4936 | n/a | 8255 |

6×1 | 20.123 | 3743 | 7003 | 10021 N | 11712 |

8×1.25 | 36.609 | 6809 | 12740 | 18231 | 21306 |

10×1.5 | 57.99 | 10786 | 20181 | 28879 | 33750 |

12×1.75 | 84.267 | 15674 | 29325 | 41965 | 49043 |

16×2 | 156.67 | 29141 | 56401 | 78022 | 91182 |

20×2.5 | 244.79 | n/a | 88124 | 121905 | 142468 |

24×3 | 352.5 | n/a | 126900 | 175545 | 205155 |

### Nut and tapped hole strength – How much thread engagement is needed?

If a screw / bolt fails because the threads strip, it can be hard to detect both during installation and later because the threads will still have some grip on the screw. If the bolt breaks, however, it will be completely loose, be easy to detect and remove, and usually fail during installation when additional torsional loads are present (torsional loads usually dissipate within minutes after tightening if you’re wondering why we didn’t take them into account before). Because of this, fasteners are designed to fail in the bolt, not the threads, so most nuts are more than adequate–just make sure you use a similar grade of nut compared to the screw.

**How much thread engagement is needed in a tapped hole**, then? According to “Fundamentals of Machine Component Design”, 3rd addition, by Juvinall and Marshek, p. 413, if the bolt and nut are of similar material the thread stripping stength will equal the bolt tensile strenth when the nut is .47 * diameter. Standard nuts are 7/8 of a diameter, for comparison.

Interestingly, more than a third of the load is held by the first thread in a nut according to this. As the bolt tightens, its threads stretch and the nut’s threads compress, which reduces force on the far threads.

The .47*dia calculation above takes this imbalance into account, but it will certainly be different for other material combinations. This offers some formula (also found in machinery’s handbook) for calculating the shear area of threads, but it’s uncertain how one would apply that formula given the imbalanced thread load. The Machinery’s handbook suggests at least 3 threads of engagement. We recommend 1 diameter depth for steel and 1.5-2 diameters for aluminum. The referenced formulas may at least provide a rough estimate for sheet metal, where thread engagement is limited. Unbrako’s Engineering guide has several charts showing experimental testing of various sized holes. According to their guide, formulas have performed poorly at predicting thread strength.