Enter Mass Points
Use the form below to calculate a 2D or 3D center of gravity.
Example Data Table
This sample shows four mass points for a simple assembly.
| Point | Mass (kg) | X (m) | Y (m) | Z (m) |
|---|---|---|---|---|
| Battery Pack | 20 | 0.0 | 0.0 | 0.0 |
| Motor | 30 | 2.0 | 0.0 | 0.0 |
| Frame Joint | 25 | 0.0 | 1.5 | 0.5 |
| Control Unit | 15 | 1.0 | 2.0 | 1.0 |
Expected result: Total mass = 90 kg and center of gravity ≈ (0.833 m, 0.750 m, 0.306 m).
Formula Used
The calculator uses the weighted average of coordinates. First, each coordinate is shifted by the chosen reference offset:
x′i = xi − xref, y′i = yi − yref, z′i = zi − zref
Then the center of gravity is calculated with these equations:
XCG = Σ(mix′i) / Σmi
YCG = Σ(miy′i) / Σmi
ZCG = Σ(miz′i) / Σmi
In 2D mode, the calculator sets all Z values to zero. The moment terms M·X, M·Y, and M·Z help verify each weighted contribution.
How to Use This Calculator
- Select 2D or 3D mode.
- Enter your preferred length and mass units.
- Set reference offsets if your datum is not zero.
- Add one row for each component, point mass, or subsystem.
- Enter label, mass, and coordinates for every valid row.
- Choose your decimal precision.
- Press the calculate button.
- Review the result card, weighted table, and Plotly graph.
- Download the current dataset and results as CSV or PDF.
Frequently Asked Questions
1) What does this calculator measure?
It finds the weighted center location of several masses. Engineers use it to study balance, stability, lifting behavior, packaging layout, and support reactions.
2) Can I use the calculator for 2D layouts?
Yes. Choose 2D mode and the calculator treats every Z coordinate as zero. This is useful for plates, floor plans, panel layouts, and planar mechanisms.
3) What is the purpose of reference offsets?
Offsets let you report the center of gravity from a chosen datum instead of the original coordinate origin. This is helpful when drawings use shifted reference points.
4) Should all masses use the same unit?
Yes. Use one consistent mass unit across every row. Mixing kilograms and pounds without conversion will produce a wrong center of gravity.
5) Can negative coordinates be entered?
Yes. Negative coordinates are valid when components sit left, below, or behind the chosen datum. The calculator handles positive and negative positions correctly.
6) Why are weighted moments shown?
Weighted moments show each row’s mass contribution to the final center of gravity. They help with checking math, validating spreadsheets, and reviewing engineering assumptions.
7) Does this work for distributed loads?
Yes, if you first replace each distributed load with an equivalent point mass at its own centroid. Then enter that equivalent mass and coordinate.
8) When is the result unreliable?
Results become unreliable when units are mixed, masses are missing, coordinates are measured from different datums, or distributed bodies are modeled too roughly.