Step-by-Step Guide: How to Use the Centroid Calculator
Follow these steps carefully to find the centroid of any composite 2D shape—even if it has holes or curves. This calculator is built to give you flexibility and accuracy!
Step 1: Choose Your Reference Axes
Select two edges of your composite shape (commonly the bottom and left sides) and treat them as your global reference axes. You can choose any two perpendicular sides—just stay consistent throughout your calculation.
Step 2: Divide the Shape into Basic Components and count the number of basic shapes that you got, click on + button to add same number of basic shapes. Each row in this calculator represents one shape.
If you added more shapes by mistakes simply click on – button to remove extra shapes.
Break the composite figure into basic shapes like rectangles, triangles, circles, semicircles, trapezoids, or quarter circles.
This makes calculation easier since we have standard centroid formulas for these.
- Example 1: A complex “T” shape can be divided into two rectangles.
- Example 2: A circular cutout in a rectangle can be treated as a rectangle + negative circle.
- Example 3: A curved flange can be modeled as a quarter-circle.
Step 3: Use Standard Formulas to Find Centroids of Each Shape
Centroid Formulas for Common Shapes
| Shape | Centroid (x̄) | Centroid (ȳ) |
|---|---|---|
| Rectangle (b × h) | b/2 | h/2 |
| Right Triangle (base b, height h) | b/3 | h/3 |
| Equilateral Triangle (side s) | s/2 | (s√3)/6 |
| Circle (radius r) | r | r |
| Semi-circle (flat side at bottom) | (4r)/(3π) | r |
| Quarter Circle (corner at origin) | (4r)/(3π) | (4r)/(3π) |
| Trapezoid (bases a, b; height h) | centered horizontally | (h/3) × ((a + 2b)/(a + b)) |
These formulas assume local shape origin. Measure x̄ and ȳ from your global reference axes.
Step 4: Handle Holes and Cutouts
If your composite shape includes holes, subtract their effect by assigning a negative area in the A (Area) column. Their centroid coordinates will still be measured from the same reference axes.
- Example: A rectangular plate with a circular hole → rectangle (positive area) + circle (negative area)
Step 5: Use Integration for Curved or Custom Shapes
For any part of your shape defined by a curve or function (not a basic shape), use integration:
- A = ∫dA
- x̄A = ∫x̄A
- ȳA = ∫ȳA
Use a calculator or manual method to evaluate the integrals. Then plug the results into the form fields and leave x̄ and ȳ empty for that shape.
Step 6: Enter Data and Calculate
Now enter all the data into the calculator. For each shape, you can either:
- Enter x̄ and ȳ (coordinates from reference axis), and let the calculator compute x̄A and ȳA.
- Or, if you’ve already calculated x̄A and ȳA (e.g., by integration), just enter those and leave x̄ and ȳ blank.
Finally, click the Calculate button. The tool will compute the centroid (x̄total, ȳtotal) of your composite area!
