By Zencalcy Editorial TeamLast reviewed About us
The centre of mass is the point where an object would balance if supported there. For a set of point masses along a line it is the mass-weighted average of their positions, so the heavier a mass is, the more it pulls the centre toward itself.
Balance point of up to three masses along a line.
x_cm = (m₁x₁ + m₂x₂ + m₃x₃) / (m₁ + m₂ + m₃)
Positions can be negative if an object sits left of the origin. The calculation is one-dimensional; for a full 3D object, apply the same weighted average to each coordinate.
| Symbol | Meaning |
|---|---|
| x_cm | Centre-of-mass position, in metres. |
| m₁…m₃ | Masses, in kilograms. |
| x₁…x₃ | Positions of each mass, in metres. |
The moment is 2 × 0 + 3 × 4 = 12 kg·m and the total mass is 5 kg, so the centre of mass sits at 12 / 5 = 2.4 m — closer to the heavier mass.
Continue with the Hooke's Law Calculator, Hydraulic Press Calculator, or the Hydrostatic Pressure Calculator — or browse more statics tools and all physics calculators.
No. A doughnut's centre of mass is in the hole, and a bent rod's can sit outside the material. What matters is the mass distribution, not whether the point is occupied.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026