The Square Knot, also called the Reef Knot, is a binding knot formed by tying two overhand knots in succession with the working ends symmetrically reversed — right over left, then left over right. Unlike the Sheet Bend used to join two ropes of different size, the Square Knot binds the ends of a single line or two equal-diameter lines around an object. Sailors use it to reef sails by gathering canvas against a boom, and surgeons use a doubled version to tie off sutures. Tied correctly it lies flat and unties easily after load.
Square or Reef Knot Interactive Calculator
Vary rope strength, knot efficiency, rope diameter, and applied load to see the square knot's retained strength and tail guidance.
Equation Used
The square knot retained strength is estimated by multiplying the rope straight-pull breaking strength by the square-knot efficiency factor. The article recommends using about 0.45 for design, with typical values from 0.40 to 0.50. Tail length is also shown using the article rule of at least 6 rope diameters.
- Square knot is used only as a binding knot, not as a bend for unequal ropes.
- Rope straight-pull breaking strength is supplied by the user.
- Efficiency is typically 0.40 to 0.50; design default is 0.45.
- Minimum tail length uses the article guidance of 6 rope diameters.
Inside the Square or Reef Knot
The Square Knot works by symmetry. You form a first overhand crossing with the right working end over the left, tuck it under, then form a second overhand crossing with the now-left end over the right and tuck it under again. Both working ends exit the knot on the same side as their own standing part. That symmetry is what makes the knot lie flat against a sail or a bandage, and it's what lets you spill the knot by pushing one standing part back through it — handy when you're freezing wet on a foredeck and need to shake out a reef in seconds.
Get the symmetry wrong and you tie a Granny Knot instead. The Granny crosses both overhands the same way rather than reversing the second, and it will either jam solid under load or capsize and slip — neither outcome is what you want with a sail tie or a parcel lashing. The other classic failure is using the Square Knot as a bend to join two ropes of unequal diameter, or two ropes of slick synthetic material like Dyneema. Under shock load the smaller or slicker rope straightens, the larger rope wraps around it, and the knot capsizes into a pair of half hitches that slide right off the working end. The Ashley Book of Knots calls this out explicitly — Clifford Ashley logged multiple drownings caused by sailors using a reef knot as a bend.
Tolerances matter even on something this simple. Both rope diameters must match within roughly 10% — a 6 mm line tied to an 8 mm line is already in capsize territory. Working ends should leave at least 6 rope diameters of tail (so 36 mm of tail on a 6 mm line) so that the knot cannot work its tail back through under cyclic loading from a flogging sail.
Key Components
- Working ends: The two free ends of the rope you actively manipulate. For a binding application around a sail or bundle, leave at least 6 rope diameters of tail past the knot — under 36 mm on a 6 mm line and the tail can work back through under flogging load.
- Standing parts: The loaded sections of rope leading away from the knot. In a correctly tied Square Knot each working end exits parallel to and on the same side as its own standing part. If a working end crosses to the opposite side, you've tied a Granny.
- First overhand (right over left): Establishes the initial crossing. This locks the bundle's circumference before the second overhand is formed and determines which way the second crossing must reverse.
- Second overhand (left over right): Reverses the first crossing's handedness. This reversal is the entire mechanism — without it the knot is a Granny that jams or slips. Dressed correctly the two overhands nest and lock against each other.
- Bight or slipped loop (optional): Tying the second working end as a bight rather than a tail produces a slipped Reef Knot. A single tug on the tail spills the knot, which is why bunt lines and shoelaces use this variant.
Industries That Rely on the Square or Reef Knot
The Square Knot earns its place anywhere you need to bind something — gather it, hold it, then release it cleanly. It is not a bend for joining two lines under serious load, and any application that treats it as one is a misuse. Where it does belong is on sail reef points, parcel lashings, bandage ties, and shoelaces. The common thread is light, balanced, symmetric load on two equal-diameter ends and a need to untie the knot quickly when the job is done.
- Traditional sailing: Reefing the mainsail on a gaff-rigged Drascombe Lugger — sail ties at each reef point are finished with slipped Reef Knots so the crew can shake the reef out with a single pull when the wind drops.
- Surgery: Square Knots tied as the second and third throws of a surgeon's knot when closing skin with 3-0 silk suture. The symmetric lay keeps the suture flat against tissue and reduces the knot profile under the dressing.
- Scouting and outdoor education: The Boy Scouts of America teach the Square Knot as the first knot in the Scout handbook and use it on the friendship knot, neckerchief slide, and bandage applications in first-aid training.
- Packaging and shipping: Tying off jute or sisal twine on a parcel or a stack of newspaper bundles — the flat profile means the parcel sits squarely on a conveyor without rocking on the knot.
- Climbing and caving (limited): Used only as a binding knot inside hauling systems — for example, lashing a coil of accessory cord to a haul bag — never as a load-bearing bend between climbing ropes.
- Textile and macramé craft: The square knot is the foundational stitch in macramé wall hangings and friendship bracelets, where alternating left-over-right and right-over-left throws produce the flat decorative pattern.
The Formula Behind the Square or Reef Knot
There's no torque equation for a knot, but there is a well-established empirical relationship for knot efficiency — the fraction of a rope's straight-pull breaking strength that survives once a knot is tied in it. For the Square Knot used as a binding knot on a single rope, efficiency sits in a usable band. At the low end of typical conditions — wet, slick, small-diameter synthetic — efficiency drops to around 0.40. Nominal dry natural-fibre or hemp rope sits around 0.45. At the high end, with well-dressed, well-set knots in dry manila, you can see 0.50. The sweet spot for design is treating the Square Knot as roughly 45% efficient and never relying on the upper end. The formula simply tells you the working strength left in the rope once the knot is in it.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Fknot | Breaking strength of the rope at the knot | N | lbf |
| ηSK | Square Knot efficiency factor (typically 0.40–0.50, design at 0.45) | dimensionless | dimensionless |
| Frope | Straight-pull tensile breaking strength of the rope | N | lbf |
Worked Example: Square or Reef Knot in a heritage canvas-tent guy-line bundle
Your historical re-enactment quartermaster's tent crew in colonial williamsburg virginia is bundling 8 mm three-strand manila guy lines for winter storage and wants to know how much load the Square Knot binding can take before the bundle ties give way during transport. The manila line has a published straight-pull breaking strength of 7.6 kN. The crew expects bundle handling loads of around 0.5 kN per tie when the bundles are tossed onto a wagon.
Given
- Frope = 7.6 kN
- ηSK,nom = 0.45 dimensionless
- Fhandling = 0.5 kN per tie
Solution
Step 1 — compute the nominal knot strength using the design efficiency of 0.45:
That nominal 3.42 kN is roughly seven times the 0.5 kN handling load — a comfortable margin for a wagon toss. The bundle ties will outlast the canvas they bind.
Step 2 — at the low end of typical efficiency (η = 0.40), as you'd see on a wet or freshly tarred manila line where the fibres slide more easily inside the knot:
Still six times the handling load. Even the worst-case efficiency leaves you with a knot that won't be the failure point.
Step 3 — at the high end (η = 0.50), dry, well-dressed manila set hard:
The 0.76 kN spread between low and high tells you the variability is real but not catastrophic for a binding application. Where you cannot tolerate that spread — for example loading a knot to 80% of its nominal strength — the Square Knot is the wrong choice and you should be using a properly dressed bend or a sewn whipping instead.
Result
Nominal knot strength is 3. 42 kN, against a handling load of 0.5 kN per tie — a working factor of about 6.8, which feels secure when you toss a bundle two-handed onto a wagon bed. The low-end value of 3.04 kN and the high-end of 3.80 kN show the efficiency band only swings the answer by ±11%, so the design sits in the sweet spot for a binding application. If a tie fails in service well below the predicted 3.04 kN floor, the three most common causes are: (1) a Granny Knot tied by mistake — check the working ends both exit on the same side as their standing parts, (2) tails shorter than 6 rope diameters letting the knot work itself loose under repeated jostling, or (3) a diameter mismatch between the two ends of a doubled-back tie greater than 10%, which capsizes the knot into sliding half hitches.
When to Use a Square or Reef Knot and When Not To
The Square Knot competes with a small handful of binding and joining knots, and the right choice depends entirely on whether you're binding around an object or joining two ropes, and whether you ever need to untie it. Compare against the Granny Knot (the classic mistying) and the Sheet Bend (the correct knot for joining unequal ropes).
| Property | Square Knot (Reef Knot) | Granny Knot | Sheet Bend |
|---|---|---|---|
| Primary use | Binding equal-diameter ends around an object | None — a mistied Square Knot | Joining two ropes of equal or unequal diameter |
| Knot efficiency (rope strength retained) | 40–50% | Unpredictable, often <30% before slipping | 50–55% |
| Behaviour as a bend (joining two ropes) | Capsizes under shock load — do not use | Capsizes or jams — do not use | Holds reliably; designed for this purpose |
| Untie after load | Easy — spills with a push on the standing part | Often jams permanently | Easy with a tail tug |
| Tolerance to diameter mismatch | Fails above ~10% mismatch | Fails immediately | Tolerates 2:1 diameter ratio |
| Tying speed (trained user) | ~2 seconds | ~2 seconds (unintentional) | ~4 seconds |
| Recommended tail length | ≥6 rope diameters | Irrelevant — knot is unsafe | ≥6 rope diameters |
Frequently Asked Questions About Square or Reef Knot
You're using it as a bend rather than a binding knot. The Square Knot relies on each working end being trapped against its own standing part by the knot's symmetric geometry. When you load the two standing parts in opposite directions — which is what happens when you join two ropes — the geometry is no longer balanced, one end straightens, the other wraps around it, and the whole knot rolls into a pair of half hitches that slide off.
The fix is not to dress the knot harder. The fix is to use the right knot. Switch to a Sheet Bend for unequal ropes or a Double Fisherman's Bend for equal ropes under serious load. Reserve the Square Knot for what it actually does — binding around an object.
Look at where the working ends exit the knot relative to their own standing parts. In a correctly tied Square Knot, each working end exits parallel to and on the same side as the standing part it came from — the knot looks symmetrical, with two clean loops nested into each other. In a Granny, the working ends exit at 90° to the standing parts and the knot looks twisted or skewed.
The other tell is behaviour under load. A Square Knot draws up flat and stays flat. A Granny rolls and either jams hard or capsizes after a couple of load cycles.
Sheet Bend, every time. A reef pendant takes pulsing load from a flogging sail and often joins a thicker pendant line to the smaller cringle webbing or becket. That diameter mismatch is exactly where the Square Knot capsizes. The Sheet Bend was developed for this geometry and tolerates a 2:1 diameter ratio cleanly.
Use the Square Knot only on the sail ties themselves, where you're binding the gathered sail against the boom with a single line — equal diameters on both ends, light symmetric load, and you want it to spill fast when you shake out the reef.
Almost always it's a Granny tied as the base, not a Square. If your first overhand goes right-over-left, your second overhand (the bight one) must go left-over-right. Most people tie the same direction twice without realising, which produces a slipped Granny — and a slipped Granny works itself loose under the cyclic load of walking within an hour or two.
Diagnostic check: when the bow is lying flat, the loops should sit perpendicular to the shoe, not parallel along its length. If they point fore-and-aft, you've tied a Granny — reverse the direction of your second throw.
Two effects compound. First, synthetic fibres like polypropylene and Dyneema have a coefficient of friction roughly half that of natural fibre, so the knot's clamping force on each crossing is lower to start with. Second, water acts as a lubricant inside the knot's contact patches and drops effective friction further.
The result is that knot efficiency drops from the 0.45 nominal toward 0.30 or below, and the knot can creep under steady load. If you must bind a wet synthetic line, double the throw on each overhand to make a Surgeon's Knot variant, or switch to a Constrictor Knot which uses a riding turn to grip far harder.
Minimum 6 rope diameters, design for 8–10 if there's any flogging involved. On a 6 mm sail tie that means leaving at least 36 mm of tail past the knot, ideally 50–60 mm. Below that threshold the cyclic flogging load works the tail back through the knot one fibre at a time, and over a few hours the tail disappears into the knot and the binding releases.
If you find your sail ties consistently coming loose during a passage, measure your tails before you cast off next time. It's the single most common cause and it's free to fix.
References & Further Reading
- Wikipedia contributors. Reef knot. Wikipedia
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