Center of Mass Calculator
Enter two masses and their positions on a line to get the center of mass — the single balance point — and see why it always leans toward the heavier mass.
The balance point in one number
Enter both masses and both positions and the calculator returns the center of mass — the point where the two-mass system would balance.
Use one axis
Measure both positions from the same origin along the same line. Positions to the left of the origin are negative — that is fine.
What is the center of mass?
The balance point of the system
The center of mass calculator finds the single point at which two point masses on a line would balance — the mass-weighted average of their positions. Give it the two masses in kilograms and their positions in metres, and it returns the center of mass in metres. This is the point where the whole system behaves, for many purposes, as if all the mass were concentrated, and it is the foundation of how seesaws, balance beams, and binary star systems behave.
Enter two masses and their positions on a line to get the exact balance point in metres — instantly.
The center of mass is the sum of each mass times its position, divided by the total mass.
x_cm = (m1 × x1 + m2 × x2) / (m1 + m2)Each mass times its position is called its moment about the origin. Add the two moments, divide by the combined mass, and you get the position where the system balances. Because the heavier mass contributes a larger moment, the result is pulled toward it.
Suppose a 2 kg mass sits at 0 m and a 3 kg mass sits at 10 m on the same line.
Compute each moment
2 × 0 = 0 and 3 × 10 = 30 — each mass times its position.
Add the moments and the masses
Moments: 0 + 30 = 30. Total mass: 2 + 3 = 5.
Divide
30 / 5 = 6 m — the center of mass, closer to the heavier 3 kg mass at 10 m.
The center of mass tells you where the two-mass system balances. The key insight is that the balance point always shifts toward the heavier mass: in the example above, the point lands at 6 m — past the midpoint of 5 m and nearer the 3 kg mass at 10 m. Make the second mass heavier still and the point slides closer to it; make the two masses equal and the point settles exactly at the midpoint, the plain average of the two positions. The position values can be negative, zero, or positive, and so can the answer — it simply marks the spot on your axis where the combined mass is balanced. This is why a lighter child sits farther from the pivot of a seesaw to balance a heavier one, and why two stars orbit a point that lies inside the more massive one.
The formula is exact for the case it describes, but it is worth knowing where it stops.
Two point masses on a single line
This calculator handles exactly two point masses arranged on a single line — a one-dimensional, two-body case. It does not extend a body's shape, three or more masses, or motion off the line into two or three dimensions, each of which needs the full multi-point or integral form of the center-of-mass formula. The equal-mass case is the special one: when both masses match, the center of mass is simply the midpoint between the two positions.