How do you calculate the centre of gravity of a load?

As the mass-weighted average of its parts' positions, one axis at a time: multiply each part's mass by its own centre of gravity coordinate, add those up, and divide by the total mass. Each part needs only its mass and where its own centre of gravity sits; the shape it happens to be is irrelevant to the arithmetic. Everything else in the method is bookkeeping around that one line, and the difficulty is getting honest masses into it.

How accurate does a centre of gravity need to be?

Accurate enough that the worst position inside its tolerance still works, which is a question you answer with a sensitivity calculation rather than a rule. Take each part in turn, assume its mass is wrong by a realistic fraction, and recompute. On this article's worked package a 15 percent error in the heaviest part moves the answer 67 mm while the same error in the lightest moves it 2 mm, which tells you both what tolerance to declare and which single part is worth weighing.

What does a centre of gravity error do to sling tensions?

It redistributes them, roughly in proportion to the offset. On the worked 6 m spreader, moving the centre of gravity 300 mm off midspan put the two leg tensions 15 percent apart, and 600 mm put them 33 percent apart. The geometric margin tightens too, because the hook has to sit over the centre of gravity and the sling angles stop being symmetric.

Why does it matter whether the centre of gravity is above the lift points?

Because that decides stability rather than load share. A suspended load hangs with its centre of gravity below the hook; if the centre of gravity is below the lift points, a tilt is self-correcting, and if it is above them, a tilt keeps going until the load has turned over. Sling tension calculations are equilibrium and say nothing about it, so a load picked near or above its own centre of gravity needs that question asked explicitly.

What if the centre of gravity cannot be calculated?

Three options, in order. Weigh it at the lift points with load cells or load pins and recover the position from the shares by statics. Do a trial lift a few hundred millimetres off the ground, look at whether it hangs level, and treat that as the measurement it is. Or bound it: state an envelope you can defend from the sensitivity analysis, and design for the worst position inside that envelope. What is not an option is a drawing value used as a point with no note that it was an estimate.

How to calculate centre of gravity of a load

The short answer

The centre of gravity of an assembly is the mass-weighted average of its parts' positions. Everything else in the method is bookkeeping around that one line.
Compute the sensitivity, not just the position. On the worked package a 15 percent error in the heaviest single part moves the centre of gravity 67 mm, and a 15 percent error in the lightest moves it 2.
A centre of gravity is an envelope, not a point. Give it a tolerance and check the worst position inside it, because the governing case is at the edge.
300 mm of offset on a 6 m spreader moved the leg tensions 15 percent apart. 600 mm moved them 33 percent apart, and the load never changed.
The vertical position decides stability, not load share. A centre of gravity above the lift points is the flag to stop: whether it actually rolls depends on where the sling lines converge, and no amount of tension calculation tells you either way.

The method, for anything you can weigh in parts

Mass-weighted average of the parts' positions, done once per axis. It is one line of arithmetic and the whole difficulty is getting honest inputs into it.

For a set of parts with masses $m_{i}$ and positions $x_{i}$ , the assembly's centre of gravity is the mass-weighted average.

Centre of gravity from parts

\overset{x}{ˉ} = \frac{\sum m _{i} x _{i}}{\sum m _{i}}

$m_{i}$: is the mass of part i
$x_{i}$: is that part's own centroid, from a stated datum

Do it once for each axis. Nothing about the shape of the parts matters as long as you know where each part's own centre of gravity is.

The worked package: a skid-mounted process module, 23.0 t in six parts, measured from a datum at the corner of the skid.

Part	Mass	x	y	z	$m_{i} x_{i}$
Skid frame	4,200 kg	3.00 m	1.20 m	0.30 m	12600
Separator vessel	9,800 kg	1.80 m	1.10 m	1.85 m	17640
Filter vessel	3,100 kg	4.40 m	0.90 m	1.60 m	13640
Pump set	2,600 kg	4.90 m	1.80 m	0.75 m	12740
Pipework and valves	1,900 kg	3.20 m	1.30 m	1.40 m	6080
Structure, ladders, misc	1,400 kg	3.10 m	1.25 m	1.10 m	4340
Total	23,000 kg	2.915 m	1.196 m	1.326 m	67040

The centre of gravity is at (2.915, 1.196, 1.326) m from the datum. Note that it is not at the geometric centre of the skid in any axis, and that the separator vessel, at 43 percent of the mass, has dragged it well to one end.

The number worth computing that almost nobody does

Not where the centre of gravity is, but how far it moves if one input is wrong. That tells you which part to go and weigh.

Every mass in that table is an estimate until somebody weighs it. The useful question is therefore not "where is the centre of gravity" but "which of these numbers would change the answer if it were wrong?"

Take each part in turn, imagine its mass is 15 percent higher than stated, and recompute:

Part	Share of total mass	Shift if 15% heavy
Skid frame	18.3%	2 mm
Separator vessel	42.6%	-67 mm
Filter vessel	13.5%	29 mm
Pump set	11.3%	33 mm
Pipework and valves	8.3%	3 mm
Structure, ladders, misc	6.1%	2 mm

Read that table as an instruction. The separator vessel is the only part worth weighing. A 15 percent error in it moves the centre of gravity 67 mm; the same error in the pipework moves it 3.

Notice also the sign. The heavy part sits below the current centre of gravity in x, so making it heavier pulls the centre of gravity towards it, which is the negative shift in the table. Parts on the far side push it the other way. A sensitivity table that ignores sign tells you the size of the risk and not its direction.

The two things this table gives you that a position alone does not:

Where to spend money. Weighing costs time. This says which weighing is worth it.
A defensible tolerance. If the biggest realistic error in any single part moves the centre of gravity by 70 mm, then plus or minus 100 mm is an envelope you can justify, rather than a number somebody picked because it sounded careful.

What an offset actually costs downstream

It redistributes the load between the lift points, and the redistribution is roughly linear in the offset. On the worked spreader, 300 mm cost 15 percent and 600 mm cost 33.

Take the 10 t, 6 m spreader arrangement and move the centre of gravity along the beam. Nothing else changes.

Spreader Beam Design Calculator · computed at page render

Centre of gravity at midspan

The reference: the load hanging symmetrically between two lift points 6 m apart.

Tension, left top sling	60.1kN
Tension, right top sling	60.1kN
Difference between legs	0.0%
Peak moment in the beam	8.2kN·m
Sling angle limit	75.9%

Governing check: Sling angle within declared limits75.9% utilisationPass

Open this example in the calculator

Spreader Beam Design Calculator · computed at page render

Centre of gravity 300 mm off

Five percent of the span, which is the sort of error a careful estimate on an unweighed package still carries.

Tension, left top slingagainst 60.1 kN centred	55.8kN
Tension, right top sling	64.3kN
Difference between legs	15.2%
Sling angle limitagainst 75.9% centred	79.0%

Governing check: Sling angle within declared limits79.0% utilisationPass

The worse leg gained more than the better leg lost, and the geometry limit tightened too, because the hook has to move over the centre of gravity and the sling angles are no longer symmetric.

Open this example in the calculator

Spreader Beam Design Calculator · computed at page render

Centre of gravity 600 mm off

Ten percent of the span, which is what an unweighed package with an under-estimated vessel routinely delivers.

Tension, left top sling	51.2kN
Tension, right top slingagainst 60.1 kN centred	68.3kN
Difference between legs	33.3%
Sling angle limit	82.2%

Governing check: Sling angle within declared limits82.2% utilisationPass

One leg carrying a third more than the other. Neither number is dramatic on its own, which is exactly the problem: nothing on the result page says the assumption behind it was an estimate.

Open this example in the calculator

Not a failure, and not nothing either. Every 300 mm of offset takes another three percentage points out of the arrangement's geometric margin, before any of it reaches the steel.

The vertical position, which decides something different

The horizontal position decides load share. The vertical position decides whether the load stays the way up you left it.

Two of the three coordinates redistribute load. The third does something categorically different.

A suspended load hangs with its centre of gravity directly below the hook. Roll it slightly and whether gravity restores it or keeps going depends on one comparison: is the centre of gravity below the point where the sling lines, extended, meet?

That convergence point is not the lift points. Legs running up to a single hook meet well above the load, and a centre of gravity below that meeting point is stable even if it sits above the lift points themselves. What removes the margin is legs that are parallel - vertical drops from the ends of a spreader beam, for instance - because then the lines never converge and the effective pivot falls back to the lift-point line itself.

So the practical rule is: a centre of gravity above the lift points is the flag to stop and check, not a verdict on its own. The engine's own diagnostic puts it the same way, warning that the hang can roll over unless the out-of-plane sling geometry provides a restoring moment, and telling you to verify in three dimensions or lower the attachments.

Three practical consequences.

Know whether you are above or below. For a spreader beam picking a squat item, the centre of gravity is normally well below the beam and nobody thinks about it. For a tall slender item picked near the top, for a lifting frame carrying a light load high, or for anything picked by lugs near its own centre of gravity, this question is the first one to ask.

Marginal is worse than either. A load whose centre of gravity is a little below its lift points is stable but soft: it will hang at whatever angle the sling length tolerance produces, and it will move if anything about the rigging changes. That is where the surprises come from.

No amount of tension calculation reveals it. Sling tensions are equilibrium; stability is about what happens when equilibrium is disturbed. They are separate questions and only one of them is on most calculation sheets.

What to do when you genuinely cannot calculate it

Three options, in the order they should be considered. All three are better than an assumption nobody wrote down.

Weigh it, at the lift points. Load cells or load pins in the rigging give the shares directly, and the shares give the centre of gravity by simple statics. This is the best answer and it is more available than it sounds, because the equipment is standard rigging hardware.

Do a trial lift. Take the load a few hundred millimetres off the ground and look at it. A load that hangs level is telling you the hook is over its centre of gravity, and that is a measurement. Note the position, land it, adjust, repeat. Slow, and it is real data.

Bound it, and design for the worst case in the bound. Where neither of the above is possible, state an envelope you can defend from the sensitivity analysis and check the worst position inside it. This is the honest version of an assumption, and the difference between it and a guess is the word "envelope".

What is not an option: taking a value from a general arrangement drawing, using it as a point, and not writing down that it was an estimate.

Before a centre of gravity leaves the calculation

01Say where the datum isA drawing reference and an orientation. A coordinate with no datum is not a position.
02Say where each mass came fromWeighed, calculated from a model, or estimated, part by part. The mixed case is normal and it has to be visible.
03Compute the sensitivityThe shift for a realistic error in each part, with its sign. The largest one sets the tolerance.
04State a toleranceAn envelope, not a point, justified by the sensitivity rather than by a round number.
05Check the worst position in that envelopeThe governing case is at the edge. It is the one whose results go on the drawing.
06State whether it is above or below the lift pointsIn one sentence, with the consequence for stability named.
07Say how it will be confirmedTrial lift, load cells, or accepted as designed. Decided before the lift, not during it.

Seven ways this goes wrong

Most of them are about treating an estimate as a measurement.

1. A drawing value used as a fact. General arrangement drawings carry centres of gravity that were computed before the equipment list settled.

2. No tolerance. A centre of gravity without an envelope cannot produce a governing case, because there is nothing to take the worst of.

3. The tolerance not checked. An envelope stated on the front sheet and a calculation run at the nominal position. Common, and it makes the envelope decorative.

4. Sensitivity never computed. Somebody weighs the pipework because it is easy to get to, and the vessel that actually moves the answer stays an estimate.

5. Only one axis calculated. Along the load is the obvious one. Across it decides whether the load hangs square, and above or below the lift points decides whether it stays the right way up.

6. Fluids, insulation and contents forgotten. A vessel with residual liquid, a package with its packing, a skid with its lagging. All of them are mass and all of them are somewhere.

7. The trial lift not used as data. A load lifted 200 mm that hangs visibly out of level has just given you a measurement, and the usual response is to shorten a sling and carry on rather than to write it down.

Common questions

How do you calculate the centre of gravity of a load?: As the mass-weighted average of its parts' positions, one axis at a time: multiply each part's mass by its own centre of gravity coordinate, add those up, and divide by the total mass. Each part needs only its mass and where its own centre of gravity sits; the shape it happens to be is irrelevant to the arithmetic. Everything else in the method is bookkeeping around that one line, and the difficulty is getting honest masses into it.
How accurate does a centre of gravity need to be?: Accurate enough that the worst position inside its tolerance still works, which is a question you answer with a sensitivity calculation rather than a rule. Take each part in turn, assume its mass is wrong by a realistic fraction, and recompute. On this article's worked package a 15 percent error in the heaviest part moves the answer 67 mm while the same error in the lightest moves it 2 mm, which tells you both what tolerance to declare and which single part is worth weighing.
What does a centre of gravity error do to sling tensions?: It redistributes them, roughly in proportion to the offset. On the worked 6 m spreader, moving the centre of gravity 300 mm off midspan put the two leg tensions 15 percent apart, and 600 mm put them 33 percent apart. The geometric margin tightens too, because the hook has to sit over the centre of gravity and the sling angles stop being symmetric.
Why does it matter whether the centre of gravity is above the lift points?: Because that decides stability rather than load share. A suspended load hangs with its centre of gravity below the hook; if the centre of gravity is below the lift points, a tilt is self-correcting, and if it is above them, a tilt keeps going until the load has turned over. Sling tension calculations are equilibrium and say nothing about it, so a load picked near or above its own centre of gravity needs that question asked explicitly.
What if the centre of gravity cannot be calculated?: Three options, in order. Weigh it at the lift points with load cells or load pins and recover the position from the shares by statics. Do a trial lift a few hundred millimetres off the ground, look at whether it hangs level, and treat that as the measurement it is. Or bound it: state an envelope you can defend from the sensitivity analysis, and design for the worst position inside that envelope. What is not an option is a drawing value used as a point with no note that it was an estimate.

Sources

Every document below is linked at its publisher or regulator. Xarpis reproduces no standard text; where a clause is named, the identifier is given so you can find it in your own copy.

LOLER 1998Lifting Operations and Lifting Equipment Regulations
UK Health and Safety Executive · free to read
The UK duty framework for lifting operations: planning by a competent person, supervision, and thorough examination of lifting equipment and accessories. Like OSHA's rules it governs the process, not the arithmetic.
ASME B30.5Mobile and Locomotive Cranes
ASME · paid document
Construction, installation, operation, inspection and maintenance of mobile cranes in the US, including load rating and the requirement to operate within the manufacturer's chart. It governs the machine; the ground it stands on is 29 CFR 1926.1402 and the calculation is yours.
29 CFR 1926 Subpart CCCranes and Derricks in Construction
US Occupational Safety and Health Administration · free to read
The whole US construction crane subpart, free in full: ground conditions, assembly and disassembly, power line clearance, operator qualification, signals, inspection and multiple-crane lifts. The index page, because the duty a reader needs is usually two sections away from the one they searched for.
DNV-ST-N001Marine operations and marine warranty
DNV · paid document
The marine warranty standard behind most offshore lift factor sets: dynamic amplification, skew load and consequence factors, and the load cases a marine operation is planned against. Widely applied onshore by contract even though its scope is marine.

Run the check properly

Reading about a calculation is not the same as being able to hand one over. These tools produce the traceable record.

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