Slings and hitches
Sling angle from leg length and pick-point spacing
- where
- leg angle to the vertical (°)
- distance between opposite pick points, diagonal for 4-leg (m)
- sling leg length, hook to pick point (m)
- included angle between opposite legs (°)
- height of hook above the pick points (m)
- tension factor
Explain this equation
Finds the leg angle a sling will make from its leg length and the spacing of the lifting points. Use it at the planning stage to pick the right sling length and rating band, and to check headroom under the hook.
s is the straight-line distance between opposite pick points: across the diagonal for a four-leg sling. L is one leg's length from hook to pick point, including fittings. β is each leg's angle to the vertical, α is the included angle between opposite legs, h is the height of the hook above the pick points, and k is the tension factor.
Each leg, half the spacing and the vertical drop make a right-angled triangle. So sin β is half the spacing divided by the leg length, and Pythagoras gives the height. The tension factor 1/cos β shows how much harder a leg pulls than it would hanging straight.
Sense check: 2 m legs on pick points 2 m apart sit at 30°, with the hook 1.73 m above the load. When the legs are only just longer than half the spacing, the angle shoots up.
Watch out: on a four-leg sling, measuring along one side instead of across the diagonal understates the angle.
Finds the leg angle from the sling length and the spacing of the lifting points, so you can pick the right rating band and see how much headroom the sling needs.
Enter your values to see the result.
Good to know
For a two-leg sling, s is the distance between the two pick points. For a four-leg sling on a rectangular load, use the diagonal √(length² + width²) between opposite corners, as LEEA measures the angle between diagonally opposite legs. Include the length of shackles and master link in L. As a rule of thumb, legs at least as long as the pick-point spacing keep β at or below 30°.
Common mistake
Measuring s along one side of a four-leg sling instead of across the diagonal, which understates the angle.
Limits
Assumes equal leg lengths and the hook centred over the pick points. For planning only: this does not replace a lift plan prepared by a competent person under LOLER 1998 (reg. 8) and BS 7121, and the manufacturer’s WLL markings, load charts and data always govern over this result.
Sources
- LEEA COPSULE Ed. 10, 1.A5.4 Principles for the selection of slings (uniform load method: 2-leg 0–45° ×1.4, 45–60° ×1.0; 3- and 4-leg 0–45° ×2.1, 45–60° ×1.5; 4-leg rated as 3-leg; trigonometric method 2·cos β, 3·cos β, 4·cos β)
- LEEA COPSULE Ed. 10, 15.5.2 Wire rope slings (BS EN 13414-1), method of use: choke hitch ×0.8, basket hitch with both ends on the hook 0–45° ×1.4, two single slings 0–45° ×1.4
- The Lifting Operations and Lifting Equipment Regulations 1998 (SI 1998/2307), reg. 8: every lifting operation properly planned by a competent person, appropriately supervised and carried out safely
- HSE L113 Safe use of lifting equipment. Lifting Operations and Lifting Equipment Regulations 1998. Approved Code of Practice and guidance
Results are calculations from the published methods and figures shown, and depend on the data you enter. For planning and checking only. Scaffolds must be erected to NASC TG20 or a bespoke design by competent persons, and lifting operations planned under LOLER by a competent person. Never rely on these results instead of a design, a lift plan or manufacturer ratings.