Center of Mass Calculator (Two Masses)
Find the balance point of two masses on a line from their sizes and positions — the weighted average that is the center of mass.
How it works
x_cm = (m₁·x₁ + m₂·x₂) ÷ (m₁ + m₂)
The center of mass is the mass-weighted average of the two positions — the single point where the system balances and where an external force acts as if all the mass were concentrated. It always lies on the line between the two bodies, closer to the heavier one, and the ratio of its distances to the two masses is the inverse of the mass ratio. If the masses are equal it sits exactly halfway.
Worked example
A 2 kg mass at x = 0 and a 3 kg mass at x = 5 m: x_cm = (2×0 + 3×5) ÷ (2 + 3) = 15 ÷ 5 = 3.0 m. That is 3 m from the lighter mass and 2 m from the heavier one — the distances are in the 3:2 inverse of the 2:3 masses.
Sources: Center of mass — Wikipedia
Frequently asked questions
Why is the center of mass closer to the heavier object?
It is a weighted average, so the larger mass pulls the balance point toward itself. The distances from the center of mass to each object are inversely proportional to their masses — double the mass, half the distance.
Does the choice of origin matter?
No. You can place the zero of your position axis anywhere; the center of mass comes out at the same physical point. Only the number describing it changes with the reference you pick.
What if one mass is zero?
Then the center of mass sits exactly at the other mass, since it carries all the weight in the average. The calculator handles this as long as the total mass is above zero.
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This calculator is for educational purposes. Double-check important results before acting on them.