Math

Center of Mass Calculator

Find the 1D center of mass of up to three point masses.

Mass 1

Position 1

Mass 2

Position 2

Mass 3

Position 3

Calculated Output

Center of mass 2.4

Total mass 5

Formula: x̄ = Σ(mᵢ xᵢ) ÷ Σmᵢ

Step-by-Step Breakdown

1. Values used:

2. Mass 1 = 2

3. Position 1 = 0

4. Mass 2 = 3

5. Position 2 = 4

6. Mass 3 = 0

7. Position 3 = 0

9. Center of mass = 2.4

10. Total mass = 5

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The math behind it

x̄ = Σ(mᵢ·xᵢ) ÷ Σmᵢ. Heavier masses pull the balance point toward them.

2 kg at 0 and 3 kg at 4 → (0 + 12) ÷ 5 = 2.4.

Is it the same as the centroid?

For uniform density, yes; otherwise mass weighting differs from pure geometry.