Find the combined centre of gravity of an assembly from each component's mass and position. Returns total mass, weight, X and Y coordinates and a percentage contribution breakdown — with negative masses supported for holes and cut-outs.
| Component | Mass (kg) | X (mm) | Y (mm) | |
|---|---|---|---|---|
The centre of gravity of a group of bodies is the mass-weighted average of their positions. Each component's coordinate is weighted by how much mass it contributes, so a heavy part near the origin pulls the answer far more than a light part far away.
mi mass of component i (kg) ·
xi, yi its coordinates ·
M total mass ·
X̄, Ȳ combined centre of gravity
A pump skid carries a motor, gearbox and pump on a fabricated baseframe. Coordinates are measured from the bottom-left corner of the frame.
The baseframe is 44 % of the mass and sits low at Y = 100, which is what pulls the combined height down to 277 mm despite the machinery sitting at 380–450 mm. Lifting lugs should straddle X = 665 mm, not the geometric middle of the frame — a common and expensive mistake when a skid tilts on first lift.
| Quantity | Symbol | Unit | Notes |
|---|---|---|---|
| Component mass | mi | kg | Negative for cut-outs |
| X position | xi | mm | Any consistent length unit |
| Y position | yi | mm | Any consistent length unit |
| Total mass | M | kg | Must be non-zero |
| Total weight | W | N | M × 9.81 |
| Centre of gravity | X̄, Ȳ | mm | Same unit as inputs |
Coordinates are unit-agnostic — millimetres, metres or inches all work, provided every component uses the same unit and the same origin. The result comes back in that unit. Weight is the only output tied to a specific unit, since it assumes mass in kilograms.
| Application | Suggested origin | Why |
|---|---|---|
| Machine skid | Bottom-left of baseframe | Matches fabrication drawings and lifting layout |
| Rotating assembly | Shaft centreline | Radial offset is the imbalance |
| Vessel or tank | Bottom tangent line | Height above support governs overturning |
| Transport load | Front axle or trailer kingpin | Determines axle load distribution |
Multiply each component's mass by its coordinate, add those products together, and divide by the total mass. Doing this separately for the X and Y directions gives the coordinates of the combined centre of gravity. The result is a mass-weighted average position, so heavy components pull the answer toward themselves far more strongly than light ones.
Yes. Entering a negative mass at the position of a hole, pocket or cut-out subtracts that material from the calculation, which is the standard composite-body method. Model the part as if it were solid, then add a negative entry for each removed volume at the centroid of that volume. The total mass must remain positive or the calculation has no physical meaning.
Centre of mass is the mass-weighted average position of a body. Centre of gravity is where the resultant weight acts, and it coincides with centre of mass whenever the gravitational field is uniform — which it effectively is for anything of engineering size. Centroid is the purely geometric average position of a volume or area, and it equals the centre of mass only when density is uniform throughout.
Lifting points must straddle the centre of gravity or the load will tilt and swing when it leaves the ground. For road transport the position determines axle loading and the height determines rollover threshold. For a machine skid or a vessel the centre of gravity sets the tipping angle and governs how anchor bolts and supports are loaded.
Any origin works because the calculation is a weighted average, but choosing a physically meaningful datum makes the result easier to act on. Common choices are the bottom-left corner of a baseframe, the centreline of a shaft, or a machined reference face. Use the same origin and the same length unit for every component, and record which datum you used alongside the answer.