Sling Angle Calculator: Leg Tension and Reduced Capacity for a Multi-Leg Lift

The tension in each leg of a lifting sling from the load, the number of legs and the leg angle, compared with the working load limit.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Enter the mass of the load including the rigging, the number of legs that really carry it, and either the angle of each leg to the horizontal or the included angle between the legs at the hook.

Enter the working load limit of one leg for a straight vertical pull, from the sling tag. The calculator gives the tension in each leg, the capacity left at that angle and the most the set can lift.

The flatter the legs, the higher the tension in each. At 60 degrees to the horizontal the tension is 15 percent more than a straight pull, at 45 degrees it is 41 percent more and at 30 degrees it is double.

Formulas used

  • T = \frac{W}{n\,\sin\theta}
  • W_{max} = n\times\mathrm{WLL}\times\sin\theta
  • \theta = 90^\circ - \frac{\alpha}{2}\;(\alpha\text{ = included angle})

Worked example

With the default numbers in the calculator above:

  1. Angle of each leg to the horizontal: 60.00 degrees
  2. Load factor on each leg (1 / sin of the angle): 1.1547 times
  3. Tension in each leg: 1.1547 t (11.32 kN)
  4. Capacity left at this angle (sin of the angle): 86.60 percent of the vertical rating
  5. Most this set of legs can lift at this angle: 2.60 t
  6. Utilisation of each leg: 76.98 percent of the working load limit

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: Which angle do you know? The included angle between the legs (measured at the hook); Angle 90 °.

  1. Angle of each leg to the horizontal: 45.00 degrees
  2. Load factor on each leg (1 / sin of the angle): 1.4142 times
  3. Tension in each leg: 1.4142 t (13.87 kN)
  4. Capacity left at this angle (sin of the angle): 70.71 percent of the vertical rating
  5. Most this set of legs can lift at this angle: 2.12 t
  6. Utilisation of each leg: 94.28 percent of the working load limit

Common questions

Why does a sling lose capacity at an angle?

Only the vertical part of the tension in each leg holds up the load. As the legs flatten, each leg has to pull harder along its length to give the same vertical force, so the tension rises and the rating for a vertical pull no longer applies.

What sling angle should I avoid?

Many lifting plans avoid legs flatter than 45 degrees to the horizontal (more than 90 degrees included) and treat anything under 30 degrees as unacceptable. Check the sling maker tables and your lift plan.

How many legs carry the load on a 3 or 4 leg sling?

With a rigid load it is common to count only 2 legs as carrying, because the load can end up held by two of them. Your lift plan should show how the load is shared.

Does this replace a lift plan?

No. The centre of gravity, lifting points, shackles, hooks, shock loading and the hitch type all need to be checked, and the lift planned by a competent person.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: AS 4991 Lifting devices; AS 1666.1 Wire-rope slings; AS 3775 Chain slings; the sling maker working load limit tables; your lift plan.

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