How this calculator works
The centre of mass is the position where the system would balance. It is a weighted average: each mass pulls the answer toward its own coordinates in proportion to its size. The calculator sums the mass times coordinate for every point, divides by the total mass, and repeats that division once for each axis. A mass of zero contributes nothing, which is how unused points are ignored. At least one mass must be greater than zero, otherwise the weighted average has no meaning.
Formula
X = (Σ mᵢxᵢ) / Σmᵢ, with the same pattern for Y and Z. In one dimension only X is reported.
Worked example
A 2 kg mass at x = 0 and a 3 kg mass at x = 4 give X = (2 × 0 + 3 × 4) / 5 = 2.4 m. Adding a 1 kg mass at (-2, 5) gives X = 10 / 6 ≈ 1.6667 m and Y = 11 / 6 ≈ 1.8333 m.
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Frequently asked questions
Can I enter a negative coordinate?
Yes. Coordinates are positions relative to the origin, and negative values simply place a point on the other side of the origin.
Why is my result missing a y or z value?
The 1D mode only reports x. The 2D mode reports x and y, and only the 3D mode reports all three coordinates.
What happens to a mass set to zero?
It is multiplied by its coordinates and adds zero to both the total mass and every moment. This lets you use fewer than four points without deleting fields.
Is the centre of mass the same as the centroid?
For a uniform object the two coincide. The centroid is a purely geometric average, while the centre of mass also depends on how mass is distributed.