Tools
Centre of gravity finder
Find where the centre of gravity of a load sits, from its parts or by weighing it, and how its weight is shared between the lifting points.
How it works
How the finder works
The finder takes moments about the front left corner of the load. Each part's weight times its distance from that corner, added up and divided by the total weight, gives the distance to the centre of gravity, along the length and across the width, and up if you include height. Weighing works the same way, with each support's reading as the weight. With lifting points, it shares the weight between them with the hook over the centre of gravity.
About measuring from the corner
Every figure is measured from one corner, seen from above: the front left corner is 0, 0. x runs along the length (to the right on the drawing), y runs across the width (towards the back) and z runs up from the underside. Measure to the middle of each part, which is close to its own centre of gravity for most solid parts. The load's length and width are optional; with them the answer says how far the centre of gravity is from the middle of the load.
About finding it from the parts
For each part, multiply its weight by its distance from the corner. Add these up and divide by the total weight. For example, a 2 t motor 0.5 m from the corner and a 1 t pump 2 m from it give (2 × 0.5 + 1 × 2) ÷ 3 = 1 m. The answer is only as good as the parts' weights: take them from the maker's drawings or data plates, or from our weight estimator, and include everything that is lifted with the load.
About finding it by weighing
Set the load on load cells, or on jacks with gauges, and enter each support's reading and where it sits. The readings add up to the total weight, and the same moment sum gives the centre of gravity. Three or four supports give it both ways; two give it only along the line between them. Anything sitting on the supports with the load, such as blocking, skates or a cradle, is counted in the readings unless it is taken off.
About the share on each lifting point
With two lifting points, the weight is shared by the lever rule: with 10 t, points 4 m apart and the centre of gravity 1 m from A, A carries 7.5 t and B 2.5 t. If the centre of gravity is off the line between the two points, the load tilts sideways until it hangs under that line. Three points share the weight in one way only, found by balancing the weight and its moments both ways. If the centre of gravity is outside the points, the load will tip. The shares are the vertical load at each point; a sling leg at an angle carries more, which our rigging calculator works out.
About four lifting points
With four points the share depends on the leg lengths and how stiff the load is, so the finder only gives one for four points at the corners of a rectangle: each corner carries the total weight times its share along the length times its share across the width, each measured from the opposite side. A rigid load on a four-leg sling can end up hanging from two legs at opposite corners, because the legs are never exactly the same length. LEEA's guidance for multi-leg slings is to rate the legs as if two of them carry the load unless the share is known to be even, and the finder adds that as a check.
FAQs
Common questions
How do I find the centre of gravity of a load?
Measure from one corner. Multiply each part's weight by its distance from that corner, add these up and divide by the total weight; then do the same across the width. A 2 t motor 0.5 m from the corner and a 1 t pump 2 m from it put the centre of gravity (2 × 0.5 + 1 × 2) ÷ 3 = 1 m from the corner.
How do I find the centre of gravity by weighing?
Set the load on three or four load cells, or jacks with gauges, note each reading and where each one sits, and take moments the same way as for parts: the readings are the weights and add up to the total. Two supports only give the centre of gravity along the line between them, so weigh again with the supports turned the other way to find it across.
Why does the centre of gravity matter for slinging?
A freely hanging load turns until its centre of gravity is directly under the hook. If the lifting points are not set round the centre of gravity, the load tilts as it leaves the ground and the legs nearest the centre of gravity carry more of the weight. Knowing where it is lets the slinger choose the lifting points, leg lengths and slings so the load lifts level.
What happens if the hook is not over the centre of gravity?
As the slings take the weight the load swings sideways and tilts until its centre of gravity is under the hook. It can strike people or things nearby, and a tilted load can slide in its slings. Lift it a few centimetres first, check that it is level and steady, and land it to adjust the rigging if it is not.
How is the weight shared between lifting points?
The point nearer the centre of gravity carries more. With two points the share follows the lever rule: 10 t, points 4 m apart and the centre of gravity 1 m from A gives 7.5 t at A and 2.5 t at B. Three points share it in one way only, and with four the share depends on the leg lengths and how stiff the load is.
Does a four-leg sling share the load equally?
Rarely. The legs are never exactly the same length and a stiff load does not bend to even them out, so the weight can end up on two legs at opposite corners. LEEA's guidance is to rate the legs and lifting points as if two legs carry the load, unless you know it is shared evenly.
Where is the centre of gravity of a machine usually marked?
On the maker's general arrangement drawing or lifting instructions, often with the centre of gravity symbol: a circle in four quarters with two opposite quarters filled. Crates and packed machines often carry the symbol on the outside. If it is not marked, ask the maker, work it out from the parts, or weigh the machine.
Does the height of the centre of gravity matter?
Yes. A load whose centre of gravity is high above its lifting points can topple over in the slings, and a tall load on skates or jacks tips more easily when it is moved or the floor is uneven. Include height in the finder to see how high it is, from the height of each part.
Planning guidance only. This works out the centre of gravity from the weights, readings and positions you enter. The appointed person confirms the centre of gravity and the lifting points before the lift.
© Synergy Lifting Ltd. The centre of gravity finder and its code are our own work. You are welcome to use it to plan your lifts, but please do not copy, reproduce or reuse the tool, its code or its results without our written permission.
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