Center of Mass Calculator
Center of mass calculator: find the balance point of up to three masses from their weights and x, y positions.
Editorial review: Farrow (pseudonym; identity and professional credentials are not disclosed). This page is for educational purposes, not professional advice.
Your inputs
Results update as you type. Nothing you enter leaves your device.
Results
- Total mass
- 6 kg
Example with the starting values
These results use the calculator's initial inputs. Change the values above to calculate your own estimate.
Inputs
- Mass 1
- 2 kg
- Mass 1 x
- 0 m
- Mass 1 y
- 0 m
- Mass 2
- 4 kg
- Mass 2 x
- 6 m
- Mass 2 y
- 0 m
- Mass 3
- 0 kg
- Mass 3 x
- 0 m
- Mass 3 y
- 4 m
Results
- Center of mass
- (4, 0) m
- Total mass
- 6 kg
How does the Center of Mass Calculator work?
The center of mass is the mass-weighted average position: x = Σ(m·x) ÷ Σm, and the same for y.
For example, 2 kg at x = 0 and 4 kg at x = 6 balance at (2·0 + 4·6) ÷ 6 = 4. Leave a mass at 0 to ignore it.
Frequently asked questions
What are the units of the answer?
The same length unit you enter for the positions, such as meters. Mass units cancel out.
What is the center of mass?
The point where an object or system of masses balances, and where gravity effectively acts.
Is it the same as the center of gravity?
In a uniform gravitational field, yes. They differ only for very large objects.
Can I use fewer than three masses?
Yes. Set the unused masses to 0 and they will not affect the result.
Related calculators
Practice it: Balance Beam, a free center of mass game.