Center of Mass Calculator
Enter each point mass and its position, one per line, as: mass, x, y
For 1D problems, just use: mass, x (leave y out).
–
Center of mass calculator
This calculator finds the centre of mass (also called the centre of gravity) of a system of point masses. Enter each mass and its position — in one dimension (mass, x) or two dimensions (mass, x, y) — and it returns the coordinates of the balance point of the whole system.
How it is calculated
The centre of mass is the mass-weighted average of all the positions: x_cm = Σ(mᵢxᵢ) ÷ Σmᵢ, and the same for the y-coordinate. In other words, each position is weighted by its mass, so heavier objects pull the centre of mass towards them. The calculator sums the moments (mass × position) and divides by the total mass.
Where it is used
The centre of mass is fundamental in physics and engineering — it determines how objects balance, rotate, and respond to forces. A system behaves, for many purposes, as though all its mass were concentrated at this single point. For force and motion calculations, see our physics calculator.
Frequently asked questions
Can the centre of mass be outside the object?
Yes. For shapes like a ring or a boomerang, the centre of mass can lie in empty space where there is no material at all.