Center of Mass Calculator
Find the mass-weighted average position of up to three point masses along a line.
How it works
- 1Enter the mass and position of each point along the line (up to three). Set a mass to 0 to exclude that point.
- 2The calculator converts inputs to SI and applies x_cm = Σ(mᵢxᵢ) ÷ Σmᵢ — each mass times its position, divided by total mass.
- 3The result is converted back to your unit system and shown with the total mass.
Use cases
- Structural engineering — locating the centroid of a beam with concentrated loads.
- Physics problems — finding where a system of particles balances on a pivot.
- Robotics — estimating the balance point of a multi-segment arm.
Frequently asked questions
What is the centre-of-mass formula?
For point masses along a line, x_cm = Σ(mᵢxᵢ) ÷ Σmᵢ. For example, a 2 kg mass at x = 0 and a 3 kg mass at x = 5 m give x_cm = (0 + 15) ÷ 5 = 3 m.
What happens if I set a mass to 0?
A zero mass adds nothing to the numerator or the denominator, so that point is ignored. This lets you work with just one or two active points.
Do positions have to be positive?
No. Positions can be negative, zero, or positive along an arbitrary number line. The centre of mass lands between the extreme positions of the non-zero masses.
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