Three Dimensional Center of Mass Calculator
Calculate the center of mass of a list of point masses in three-dimensional coordinates, with distances from the combined center.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Sum all masses and each mass-weighted coordinate. Divide the three weighted sums by total mass to locate the combined center.
Center=(Σmixi, Σmiyi, Σmizi)/Σmi
Worked example
A 1 kg point at (0,0,0) and a 3 kg point at (4,0,0) have total mass 4 kg and center (3,0,0).
Assumptions and input details
One to one hundred point masses. Every mass uses the same unit and every coordinate uses the same length unit. Masses are nonnegative, total mass positive; a zero-mass row contributes nothing. Coordinate magnitudes at most 1e9. This is a point-mass balance calculation; it does not infer volume, density distribution, support stability or the center of a continuous polygon.
References: OpenStax: center of mass
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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