Finds the balance point of up to three point masses positioned along a line.
How it works
Each mass is multiplied by its position, those products are summed, and the total is divided by the combined mass.
What this does not include
This does not include the geometric centroid of a shape, which ignores mass entirely — for that, use this site’s centroid calculator instead.
How to use this calculator
- Enter the mass and position of two or three point masses.
A worked example
Three masses: 2 kg at x=0, 3 kg at x=4, 1 kg at x=10 → center of mass = (2×0 + 3×4 + 1×10) ÷ (2+3+1) = 22 ÷ 6 = 3.6667.
Two masses: 1 kg at x=1, 1 kg at x=5 → center of mass = 3 — exactly the midpoint, since the masses are equal.
What the variables mean
| Variable | Meaning |
|---|---|
| Mass (m1, m2, m3) | Weight of each point mass |
| Position (x1, x2, x3) | Location of each mass along a line |
Edge cases worth knowing
Equal masses put the center of mass at the plain geometric midpoint — the second example above collapses to a simple average of positions specifically because the two masses are equal.
Zero total mass makes the center of mass undefined — there’s no weight to balance, so the calculator returns no result.
Frequently asked questions
Why does a heavier mass pull the center of mass toward it?
Because it’s a weighted average — positions are weighted by mass, so a heavier object at a given position has more influence on the balance point.
What happens with two equal masses?
The center of mass falls exactly halfway between them, since both positions carry equal weight in the average.
What’s a real-world use for center of mass?
Balancing a seesaw, designing stable structures, and predicting how objects rotate or tip all rely on finding the center of mass.
