Where the breaking load number actually comes from

This article explains where the Minimum Breaking Load (MBL) on a rope or piece of hardware comes from. The number is not the force at which one sample happened to snap. It is worked out from a set of break tests using a method called three-sigma, and this is how that method produces the single figure you read off the tag.

Most riggers meet the breaking load as a given. You read the MBL off the product, divide it down by a factor of safety, and get the working load you can actually use. That last step is covered in our factor-of-safety article. This one is about the step before it: how the MBL itself gets set, and why it sits well below the force the part really breaks at.

You break several, not one

Start with the obvious problem. If you break one rope and it snaps at 30 kN, you cannot mark every rope off that line as a 30 kN rope. The next one might snap at 28. Manufactured parts vary, and the test destroys the part it measures, so you are always making a statement about a production run from a sample you have broken.

So you break several identical specimens and work with two numbers from the results.

The first is the mean, the average breaking force across the specimens. The second is the standard deviation, written with the Greek letter sigma (σ). Standard deviation is a measure of spread: how far the individual results sit from the average. Break ten identical ropes and if they all snap at almost the same force, the standard deviation is small. If the results are scattered, some early and some late, it is large. It is, roughly, the typical distance of a single result from the average.

The published MBL is then set at:

MBL = mean − 3 standard deviations (mean − 3σ)

You take the average breaking force and come down three standard deviations below it. That is the number that gets marked.

Why subtract three

The point of coming down from the average is that half of all parts break below the average. A floor at the average would fail half the time, which is useless. You want a published figure that nearly every real part beats.

Break results, like a lot of measured things, tend to cluster around the average in the shape of a bell curve. Under that curve there is a well-known pattern for how the results spread out from the mean:

• about 68% of results sit within 1 standard deviation of the mean,
• about 95% within 2,
• about 99.7% within 3.

This is the reason three is the number people reach for. If you set the floor at mean − 3σ, then under the bell curve only about 0.135% of parts, roughly one in 740, would be expected to fall below it. So the published MBL is a deliberately low figure that almost every part off the line will beat.

There is a limit to that maths. The 99.7% pattern is exact only if the results follow a perfect bell curve, and real break data is only approximately that shape. So the figure is a conservative convention, chosen because it is practical and lands the floor low enough that nearly every part beats it. It is not a guarantee that exactly so-many parts will pass.

How many tests, and what a test involves

The number of specimens depends on which standard you are testing to.

The clearest figure comes from the Cordage Institute, the North-American rope standards body. Its life-safety rope standard, CI 1801, covering low-stretch and static kernmantle life-safety rope, requires the breaking strength to be set at three standard deviations below the mean of five or more specimens broken. So that standard pins both numbers: three sigma below the mean, and a minimum of five specimens. For ordinary, non-life-safety rope, a general test-method floor of three specimens applies. The life-safety standard is the stricter one, and it is the relevant one for rope that holds a person.

The US fire-service standard for life safety rope, NFPA 1983, writes its requirement directly as a "3σ MBS", for example a 3σ minimum breaking strength of not less than 20 kN for one rope grade. It is a published safety standard that states its minimum strength as three sigma below the mean in so many words.

A single break test runs roughly like this:

• Conditioning. The specimen is brought to standard laboratory temperature and humidity first, using new rope of standard construction.
• Termination. Each end is gripped so the machine can pull it without the grip itself causing the failure, using an eye splice, a resin socket, a drum wrap, or a machine clamp. A poor grip makes the rope fail at the grip and understates its strength, so the termination is chosen to be strong.
• The pull. The specimen is loaded on a tensile testing machine at a steady, defined pulling speed, with the force recorded the whole way.
• Failure. The rope is pulled all the way to destruction, and the machine captures the peak force at the moment it ruptures. That peak is this specimen's breaking force.
• Repeat and calculate. This is done across the required number of specimens, then the mean and standard deviation of the peak forces are worked out and mean − 3σ is published as the MBL.

The specimens are destroyed in the process. You cannot break-test the exact rope you then sell, which is why the published figure is a statistical statement about the run, inferred from a destroyed sample of it.

The European and international side is less tidy. The method standard for fibre-rope breaking force, ISO 2307, defines how the pull is done, the constant pulling speed, the peak force at failure, spliced and unspliced specimens. I have not been able to confirm from open sources the exact specimen count it requires, or whether it mandates the mean − 3σ calculation itself. The cleanest pinned figure is the Cordage Institute's five-or-more.

How it reaches the rigger

The chain, end to end, runs like this. A test house takes a sample from a production run. Each specimen is terminated and pulled to destruction, and the peak load at failure is recorded. Across the sample, the lab works out the mean and standard deviation and publishes mean − 3σ as the MBL. That figure is what gets marked or specified on the product, in kilonewtons for climbing and PPE hardware.

The rigger then applies the factor of safety on top, dividing the MBL down to a working load: working load limit = MBL ÷ factor of safety. So there are two separate layers of conservatism here. Three-sigma sets the floor of the breaking number, well below the average a part actually breaks at. Then the factor of safety divides that down again to a working number. The rigger usually sees only the second layer, but the first is already built into the MBL before it is divided.

The most useful way to hold it: the MBL is not the force at which one rope happened to break. It is a deliberately low figure, set three standard deviations below the average of several destroyed samples, so that essentially every rope off that line is stronger than its own rating. Then the factor of safety is applied below that again to get the working load.

This is not the only way an MBL is ever set

Three-sigma is the method the cordage and life-safety bodies use, the Cordage Institute and NFPA above. It is not a universal rule that every breaking load is set this way. The European standards that cover metal connectors, the karabiners and shackles a circus rigger handles, set the number by a different philosophy, and it is worth seeing how.

Under three-sigma, the standard does not name the breaking load. It tells you how to work it out from a sample, and the number falls where the test results land. A European connector standard does the reverse. It names a fixed minimum breaking strength up front, a figure every conforming part must beat, and then the part is proven against that fixed figure by destroying a small sample in a type test, with ongoing checks on production, and for lifting gear a proof test on top. So a karabiner stamped 24 kN, or a shackle with a stated rating, is a declared minimum that has been type-tested and production-controlled. It is not the mean minus three standard deviations of a sample. The cordage standard derives the number; the connector standard declares it and then proves the part clears it.

Which standard a connector sits under depends on what it is for.

Karabiners are personal protective equipment

A karabiner used to protect a person against a fall from height is personal protective equipment (PPE). In Great Britain and the EU it falls under the PPE Regulation (EU) 2016/425, which is retained in GB law after EU-exit, with UKCA marking and a GB Approved Body in place of CE marking and a Notified Body. Protection against falls from a height is named in the Regulation as Category III, the highest-risk category, and that is the point that matters: Category III triggers the most rigorous conformity route. The design is type-examined by an independent Notified Body, and production is then kept under ongoing control. That is why a conforming karabiner carries the CE mark followed by the four-digit identification number of the body that controls its production. The number on the karabiner is a declared minimum that an independent body has type-examined and that production is checked against, not a statistical figure the maker computed alone.

The figures themselves come from two connector standards.

EN 362 covers PPE connectors for work at height. Its headline requirement is a major-axis strength of at least 20 kN with the gate closed and locked (a screwlink class is held higher, at 25 kN), and a minor-axis strength of at least 7 kN. The minor axis is the across-the-gate direction, and a connector specifically designed to be loaded that way is held to a higher minor-axis figure.

EN 12275 is the mountaineering sister standard, the one most climbing karabiners are made to. Its basic type is held to the same shape: at least 20 kN on the major axis with the gate closed (an oval is the exception at 18 kN, a via-ferrata type is uprated to 25 kN), at least 7 kN on the minor axis, and a gate-open strength between 5 and 8 kN depending on the type.

The reason the marked figure is always the major-axis, gate-closed case is that it is the strongest way to load the connector, and every other way is weaker. Load a karabiner across the minor axis, or three ways at once, and the breaking load can drop by as much as 45 per cent. That is the quantified reason behind the long-standing rule to load a karabiner along its spine with the gate shut, and it is why the number stamped on the back is the best case, not a figure you can count on in any orientation.

Bow shackles are lifting accessories

A bow shackle used to lift a load is not PPE. It is a lifting accessory, and it sits under the Machinery Directive 2006/42/EC, put into GB law as the Supply of Machinery (Safety) Regulations 2008, the same regulations the factor-of-safety article cites. A lifting accessory declares a Working Load Limit (WLL) and is built from a coefficient of utilisation, the European term for a factor of safety, applied to its breaking force. The harmonised standard that gives one accepted way of meeting the Directive for shackles is EN 13889.

Reading EN 13889 directly clears up the breaking-load margin on a bow shackle, and it turns out to be three numbers, not one. They stack from the legal floor up to what a real shackle gives you:

• 4:1 is the statutory floor. The Supply of Machinery (Safety) Regulations set the minimum a forged-metal lifting item must meet at four times the working load. That is the least the part is allowed to be.
• 5:1 is the shackle standard's own minimum. EN 13889 sets the minimum breaking force at five times the WLL, with a proof force of twice the WLL, and proves each size by type-testing three samples. That is the harmonised shackle standard's floor, above the bare statutory one.
• About 6:1 is the typical actual. Makers such as Green Pin and Crosby round the breaking force up above the standard's minimum and publish 6:1, which the standard explicitly permits in a note under its own table.

These three numbers are a minimum-versus-typical stack, not a set of rival answers: a 4:1 statutory floor, a 5:1 shackle-standard minimum, and a typical real shackle that comes in nearer 6:1 because the maker rounds the breaking force up. Take a bow shackle marked WLL 1 tonne: its breaking load is at least 4 tonnes by law, at least 5 tonnes under the shackle standard, and on a typical shackle nearer 6 tonnes. The earlier connector article on this site quotes that typical 6:1, and it holds; the point here is only that 6:1 is what makers usually provide, not the standard's own minimum, which is 5:1.

The caution from that article stands without change. Do not assume a margin for a given shackle and work backwards to a breaking load. The number you can rely on is the marked WLL and the maker's own documentation for that part, not a rule of thumb.

How the connector is proven, and what that shows

EN 13889 is the clearest worked example of the declare-then-prove philosophy, because it sets out the steps. To prove the design, three samples of each size are pulled to destruction and must reach at least the standard's minimum breaking force, and they must fail gracefully, bending rather than shattering, rather than simply meeting a number. Every production shackle is then proof-loaded to twice its working load with no lasting deformation, production is sampled and the parts given a non-destructive examination for hidden cracks. At no point does the standard break a sample and compute a mean minus three standard deviations. It names a fixed minimum every shackle must beat, proves the design on three destroyed samples, and then guarantees production by proof-testing and inspection. The number on the shackle is a declared, type-tested, production-controlled minimum, which is a different piece of bookkeeping from the cordage figure earlier in this article.

How many samples are pulled is itself standard-specific, and it is worth understanding the differences between them. EN 13889 states three samples per size for its shackle type tests. For the karabiner standards, EN 362 and EN 12275, the exact number of connectors pulled for a type examination sits in the standard's test-method clauses and I have not been able to read it from open sources, so I will not put a number on it. What is clear is the shape: each of these frameworks reaches its published number a different way, and there is no single sample size or sigma figure that runs across all of them. Cordage life-safety rope breaks five or more specimens and publishes a statistical mean minus three standard deviations. Lifting shackles set a fixed minimum and prove three type-test samples against it. PPE karabiners set a fixed minimum and prove it by independent type-examination and production control. Three frameworks, three ways of arriving at the number on the part.

So three-sigma is one route to a published minimum, the one the cordage and life-safety bodies use. The European connector standards reach a published minimum too, but they declare the figure and prove the part against it rather than computing it from a sample.

Where three-sigma came from

The idea behind 3σ has a history to it.

The term "standard deviation" was coined by the English mathematician Karl Pearson, one of the founders of modern statistics, in a lecture of 1893. Pearson named the concept rather than inventing it; the underlying idea of root-mean-square spread predates him. He gave it the term we still use, in place of clumsier older names like "mean error", and popularised it.

Using three sigma as an industrial accept-or-reject line came later, from Walter Shewhart. Working in the inspection engineering department at Western Electric, and from 1925 at the newly founded Bell Telephone Laboratories, Shewhart wrote a short memo in 1924 containing a diagram we would now call a control chart. He drew limits three standard deviations above and below a process average, having found across a range of manufacturing processes that three-sigma limits struck an economic balance between chasing problems that were not really there and missing ones that were. That is the root of using three-sigma as the line between accept and reject, the same logic later used to set a three-sigma minimum breaking load.

Three-sigma became the standard industrial way to set a conservative threshold after Shewhart, and rope life-safety standards use the same convention. There is no documented record of CI 1801's drafters taking it directly from Shewhart, so the connection is a shared convention rather than something we can cite as a direct line.

The same sigma-counting idea went further in 1986, when Bill Smith at Motorola introduced Six Sigma, counting how many standard deviations of margin sit between a process average and the nearest specification limit and pushing for a much tighter target. Six Sigma is not used to set rope breaking loads. It is the next chapter of the same statistical thinking, not part of the rope story.

So the story line: Pearson names the standard deviation, Shewhart turns three-sigma into an industrial accept-or-reject threshold, and the rope and life-safety standards adopt mean − 3σ to set a published minimum breaking strength.

Sources: Cordage Institute CI 1801 (life-safety kernmantle rope) and NFPA 1983 for the five-specimen, mean − 3σ requirement; ISO 2307 for the break-test method; the 68–95–99.7 statistical rule; EN 1891 and EN 892 for the fixed-strength rope comparison. For the metal connectors: PPE Regulation (EU) 2016/425 (retained in GB law) for the karabiner conformity route; EN 362 and EN 12275 for karabiner strengths and the off-axis loss; the Machinery Directive 2006/42/EC and Supply of Machinery (Safety) Regulations 2008, harmonised through EN 13889, for the bow-shackle figures and the 4:1 / 5:1 / ≈6:1 stack. History from published biographies and standards history: Karl Pearson on "standard deviation" (1893), Walter Shewhart on three-sigma control limits (1924), and the later Six Sigma at Motorola (1986). Accessed June 2026.