How much load does each leg of a sling carry?

Formula, assumptions, and limits

Each leg of a sling pulls along its own line toward the hook, and only the vertical part of that pull holds the load up. The ILO code of practice Safety and health in ports (Revised 2016) turns this into its trigonometric method in chapter 5, paragraph 128: the SWL of a two-leg sling is 2 × the SWL of a single leg × cos α, and of a three- or four-leg sling 3 × the single-leg SWL × cos α, with α the angle of the leg from the vertical. The calculator solves the same equation both ways.

Formula

• $T$: tension in each leg, in tonnes. A leg’s SWL must be at least $T$; the wire rope SWL calculator gives a wire rope leg’s SWL from its breaking load.
• $W$: the load, in tonnes, with anything hung below the sling.
• $n_e$: legs counted: 2 for two legs, 3 for three legs and 3 for four legs (ILO chapter 5, paragraph 128).
• $\alpha$: leg angle from the vertical. From the horizontal angle $\beta$, $\alpha = 90^\circ - \beta$; from the angle between the legs $\varphi$, $\alpha = \varphi/2$ for two legs or opposite legs of four; for three legs evenly spaced, from the angle $\psi$ between two of them, $\cos^2\alpha = (\cos\psi + 0.5)/1.5$.
• $\mathrm{SWL}_{\mathrm{leg}}$: the SWL marked for one leg in a straight vertical pull.
• $1/\cos\alpha$: the angle factor.

From the sling’s measurements, with $L$ the leg length from the hook to a pick point and $R$ the horizontal distance from the hook vertical to that pick point (half the spread for two legs, half the diagonal for four on a rectangle, the distance between two pick points ÷ √3 for three evenly spaced):

where $H$ is the height of the hook above the pick points.

Derivation

Take one leg of a two-leg sling holding a centered load $W$. The leg’s tension $T$ acts along the leg at $\alpha$ to the vertical. Resolving it, the vertical part is $T\cos\alpha$ and the horizontal part is $T\sin\alpha$. The two horizontal parts are equal and opposite and cancel; the two vertical parts together carry the load, so $2T\cos\alpha = W$. With $n_e$ legs sharing, $n_e T\cos\alpha = W$, which is the formula. Setting $T$ to the leg’s SWL and solving for $W$ gives paragraph 128’s form.

The horizontal part does not vanish at the load: each leg pulls its pick point toward the hook vertical with $T\sin\alpha$, which squeezes the load or a lifting frame. Lloyd’s Register’s Code for Lifting Appliances in a Marine Environment (July 2021), Chapter 8, 4.2.5, requires a lifting frame slung this way to be designed for those compressive forces.

Assumptions

• The load’s center of gravity is under the hook and the pick points sit evenly around it, so each counted leg takes the same tension.
• All legs are the same length and at the same angle.
• The load is static. A snatch, a swing or wind adds load the formula does not see.
• Four legs are counted as three. ILO chapter 5, paragraph 128, gives the reason: most loads are not uniform. Four legs to a stiff load leave one leg more than statics needs, and the lengths of the legs decide which three carry it.

Worked example

A 10 t load hangs on a two-leg sling, each leg 30° from the vertical, which is 60° between the legs.

1. cos 30° = 0.8660; the angle factor is 1 ÷ 0.8660 = 1.155.
2. Tension in each leg: 10 ÷ (2 × 0.8660) = 5.77 t, or 56.6 kN.
3. Each leg’s SWL must be at least 5.77 t.
4. Each leg pulls its pick point inward with 5.77 × sin 30° = 2.89 t.
5. The uniform load method in ILO paragraph 127, factor 1.4 for two legs up to 45°, asks for legs of at least 10 ÷ 1.4 = 7.14 t SWL.

ILO Figure 63 gives the same case: 0.58 t in each leg for a 1 t load at 60° between the legs.

Edge cases and limits

• Past 45° from the vertical. Paragraph 129 keeps this for cases where it becomes necessary, and paragraph 127’s uniform load factors stop at 45°, so only the trigonometric figure applies.
• At 60° from the vertical each leg of a two-leg sling carries the whole load (paragraph 129). At 80° each leg carries 2.88 times it, and the calculator refuses angles past 85°.
• ILO Figure 55 prints the same factor for union purchase cargo falls, $1/(2\cos\alpha)$. Its 80° entry reads 2.800; the arithmetic gives 2.879.
• Within 5° of the vertical, 29 CFR 1910.184(b) lets the lift count as vertical. The factor there is at most 1.004.

Regulatory basis

The ILO code of practice Safety and health in ports (Revised 2016, published 2018) sets out both methods in chapter 5: the mode factors in paragraphs 124, 125 and 127 and Figure 62, the trigonometric method in paragraphs 126 and 128, and the angle limits in paragraph 129. The UK MCA Code of Safe Working Practices for Merchant Seafarers (2025 edition), paragraph 28.5.14, limits the angle between the legs to 90° normally and 120° for slings designed for it.

In the United States, 29 CFR 1910.184(f)(1) and (h)(1) require a wire rope or fiber rope sling’s marking to show the safe working load for the hitches used, the angle the load is based on and the number of legs. The rated-capacity tables that once stood in 1910.184 were removed by 76 FR 33590 on 8 June 2011; OSHA’s angle tables now sit in its advisory guidance on safe sling use. HSE L113, the LOLER Approved Code of Practice and guidance, guidance paragraph 275, lists the angle of a sling’s legs among the ways a sling’s rated load is reduced. On ships, IMO MSC.1/Circ.1663, paragraph 4.4.2, asks lifting beams, spreaders and frames to be marked with their allowable sling angles.

Common errors

1. A horizontal angle in the vertical formula. 30° from the horizontal is 60° from the vertical, factor 2.000; the vertical formula fed 30° gives 1.155 and puts 5.77 t on legs that carry 10 t.
2. The angle between the legs taken as the leg angle. 60° between the legs is 30° per leg from the vertical. Used whole, it doubles the angle and overstates the tension, 10 t a leg where 5.77 t is right.
3. Dividing by four for a four-leg sling. For 12 t at 45° that gives 4.24 t a leg against ILO’s 5.66 t, 25% short.
4. Rating the sling and not the fittings. ILO paragraph 202 asks a shackle in a sling to have the sling’s SWL, allowing for the extra stress the angle puts on it.

Sling angle chart: factor and leg tension

The angle factor adds 15.5% to each leg’s share at 30° from the vertical, 41.4% at 45° and 100% at 60°; ILO chapter 5, paragraph 129, makes 45° the limit for normal use and 60° the ceiling. Read across from the angle in whichever form you have it; the last column is a 10 t load on two legs.

ILO uniform load and trigonometric methods

The ILO code gives two ways to rate a multi-leg sling, and they agree, to the rounding, only at 45°. The uniform load method of chapter 5, paragraph 127, multiplies the single-leg SWL by a mode factor for any angle up to 45° from the vertical:

The factors 1.4 and 2.1 are 2 × cos 45° and 3 × cos 45° rounded down. A sling used at 30° is therefore rated as if it were at 45°: a two-leg sling of 3 t legs lifts 4.20 t by the uniform load method and 5.20 t by the trigonometric one. Past 45° paragraph 127 gives no factor, and the rating is the trigonometric figure or the one the sling’s marking states for that angle.

Sling angle from leg length and spread

Two figures that are easy to get give the angle: the leg length, from the sling’s tag or a tape, and the spread across the pick points. Half the spread divided by the leg length is the sine of the angle from the vertical.

• Spread equal to the leg length: the legs and the spread make an equilateral triangle, 30° from the vertical and 60° between the legs.
• Spread 1.41 times the leg length: 45° from the vertical, the limit for normal use.
• Spread 1.73 times the leg length: 60° from the vertical, which ILO paragraph 129 says should never be exceeded.

For four legs on a rectangular load use the diagonal between opposite pick points as the spread. For three legs evenly spaced, divide the distance between two pick points by √3, 1.73, instead of halving it: a spread equal to the leg length then puts each leg 35.3° from the vertical.

ILO chapter 6, paragraph 139, asks a four-leg sling on an empty container to keep no more than 90° between the legs at the hook. Read as the angle between opposite legs, the stricter reading, that is a diagonal of at most 1.41 times the leg length. The load is the figure from the shipper or the lift plan, plus the spreader, frame or shackles below the sling’s master link; the leg SWL is on the sling’s tag.