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Centre Of Mass Calculator

Work out centre of mass instantly with clear inputs, formula shown and shareable results.

About Centre Of Mass Calculator

The centre of mass is the mass-weighted average of positions, so it always lies nearer the heavier body. With 5 kg at 0.5 m and 3 kg at 2.5 m the balance point is at 1.25 m - 0.75 m from the heavy mass and 1.25 m from the light one, in inverse proportion to their masses.

Formulas

Centre of mass

x(cm) = (m1 x1 + m2 x2) / (m1 + m2)

Lever relation

m1 x d1 = m2 x d2 about the centre of mass

Worked example

With the default values below, Centre Of Mass Calculator returns Centre Of Mass Position of 1.2500. Change any input above and every figure here is recalculated in your browser.

Inputs used

First massminimum 0 kg
5 kg
Position of the first mass
0.5 m
Second massminimum 0 kg
3 kg
Position of the second mass
2.5 m

Results

Centre Of Mass Position
1.2500 m
Total Mass
8.000 kg
Distance From The First Mass
0.7500 m
Distance From The Second Mass
1.2500 m

Step by step

  1. 1Values used
  2. 2Centre of mass
  3. 3Lever relation
  4. 4Centre Of Mass Position= 1.2500 m
  5. 5Total Mass= 8.000 kg
  6. 6Distance From The First Mass= 0.7500 m
  7. 7Distance From The Second Mass= 1.2500 m

Assumptions and limits

  • The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Is the centre of mass always inside the object?

No. A ring or a boomerang has its centre of mass in empty space, which is perfectly allowed.

Why does the balance point favour the heavy mass?

Because moments must cancel. The heavier mass needs a shorter arm to produce the same moment.

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