Calculator Inputs
Enter mass points, choose dimensional mode, then compute weighted coordinates for the system.
Example Data Table
This sample shows a four-point 3D system. Its center of mass is approximately (2.8571, 1.5714, 0.2857).
| Point | Mass | X | Y | Z |
|---|---|---|---|---|
| A | 2 | 0 | 0 | 0 |
| B | 3 | 4 | 0 | 0 |
| C | 5 | 4 | 2 | 0 |
| D | 4 | 2 | 3 | 1 |
Formula Used
For point masses:
xcm = Σ(mixi) / Σmi
ycm = Σ(miyi) / Σmi
zcm = Σ(mizi) / Σmi
The calculator multiplies each coordinate by its mass, adds the weighted terms, then divides by total mass. In 1D, only x is used. In 2D, x and y are used. In 3D, all three coordinates are included.
How to Use This Calculator
Frequently Asked Questions
1. What does the center of mass represent?
It is the weighted average position of all mass in the system. If supported at that point, the modeled body would balance under uniform gravity.
2. Can I use negative coordinates?
Yes. Negative coordinates are valid and often necessary when the chosen origin lies between points or outside the body.
3. Must all masses use the same unit?
Yes. Use one consistent mass unit across every point. Mixing kilograms, grams, or pounds without conversion gives incorrect weighted averages.
4. Must all coordinates use the same length unit?
Yes. Keep all coordinates in one length unit, such as meters or feet. The output center uses that same coordinate unit.
5. Why does the calculator reject zero total mass?
The formulas divide by total mass. If total mass is zero, the weighted average position becomes undefined and cannot be computed.
6. Is this suitable for rigid bodies?
Yes, when the body can be approximated by point masses or segmented parts. Finer segmentation usually improves the approximation.
7. What does the graph show?
The graph plots each entered mass point and highlights the computed center of mass. Larger markers correspond to larger masses.
8. Can I export the results?
Yes. After calculation, use the CSV and PDF buttons to save a compact report containing summary values and the detailed contribution table.