Enter Point Data
Add one point per line. Use x,y,w for weighted mode. Use x,y for simple mode.
Example Data Table
| Point | X | Y | Weight | Meaning |
|---|---|---|---|---|
| P1 | 2 | 3 | 1 | Light contribution |
| P2 | 4 | 7 | 2 | Moderate contribution |
| P3 | 6 | 5 | 1 | Balanced contribution |
| P4 | 8 | 9 | 3 | Strong contribution |
Paste these four rows into the calculator using comma-separated values.
Formula Used
For unweighted points, the centroid is the arithmetic mean of x and y coordinates.
Cx = Σx / n and Cy = Σy / n
For weighted points, each coordinate is multiplied by its weight before averaging.
Cx = Σ(w·x) / Σw and Cy = Σ(w·y) / Σw
This method finds the balance point of a 2D point set. It is useful in statistics, clustering, spatial summaries, and weighted location analysis.
How to Use This Calculator
- Enter one point on each line.
- Choose the correct delimiter.
- Enable weight mode if each row has a third value.
- Set the number of decimal places.
- Click Calculate Centroid.
- Review the result card above the form.
- Inspect the graph and computed table.
- Download the output as CSV or PDF if needed.
Frequently Asked Questions
1. What does a 2D centroid represent?
A 2D centroid is the balance point of a set of planar coordinates. It summarizes the central location of points using average x and average y values.
2. What is the difference between weighted and unweighted centroid?
An unweighted centroid treats every point equally. A weighted centroid gives stronger influence to rows with larger weights, shifting the final center toward more important observations.
3. Can I use negative coordinates?
Yes. Negative x and y values are valid. The calculator handles them normally, which is useful for coordinate systems centered around an origin.
4. Why must weights be positive?
Positive weights keep the interpretation consistent with influence, mass, or frequency. Zero or negative weights can distort the location and may not match standard centroid analysis.
5. Is this useful for clustering work?
Yes. Centroids are widely used in clustering, especially when summarizing grouped observations. They help describe central tendency in two-dimensional point clouds.
6. What file format does the CSV export use?
The CSV export creates a plain comma-separated file containing each point, weight, weighted products, and a final summary block with centroid values.
7. What does the graph show?
The graph plots every input point as a marker and highlights the centroid with a separate marker. This makes the center easy to compare visually.
8. Can I paste large datasets?
Yes. You can paste many rows at once. Keep the delimiter consistent across lines so the parser can read each coordinate correctly.