š Centroid Calculator
Calculate the geometric centroid of shapes
Point 1
Point 2
Point 3
How to Use This Calculator
Select Shape Type
Choose the shape type: Triangle (3 points), Rectangle (4 points), or Polygon (3+ points).
Enter Coordinates
Input the X and Y coordinates for each vertex of your shape. For polygons, you can add more points as needed.
Click Calculate
Press the "Calculate Centroid" button to find the geometric center (centroid) of your shape.
Formula
Centroid X = (xā + xā + ... + xā) / n
Centroid Y = (yā + yā + ... + yā) / n
Where:
- xįµ¢, yįµ¢ = Coordinates of the i-th vertex
- n = Number of vertices
- The centroid is the arithmetic mean of all vertex coordinates
Example (Triangle): Find centroid of triangle with vertices:
Point 1: (0, 0)
Point 2: (4, 0)
Point 3: (2, 6)
Centroid X = (0 + 4 + 2) / 3 = 6/3 = 2
Centroid Y = (0 + 0 + 6) / 3 = 6/3 = 2
Centroid = (2, 2)
About Centroid Calculator
The Centroid Calculator finds the geometric centroid (center point) of polygons by calculating the average of all vertex coordinates. The centroid is the point where all medians intersect (for triangles) or the arithmetic mean of vertices (for polygons).
When to Use This Calculator
- Geometry: Find the center point of geometric shapes
- CAD & Design: Locate center points for design and drafting
- Engineering: Calculate centroid for structural analysis
- Computer Graphics: Determine center points for transformations
- Surveying: Find center points of land parcels
- Education: Learn and practice geometric calculations
Why Use Our Calculator?
- ā Multiple Shapes: Supports triangles, rectangles, and polygons
- ā Instant Results: Get centroid coordinates immediately
- ā Flexible Input: Add points for polygons as needed
- ā Step-by-Step Display: See the calculation formula
- ā 100% Accurate: Precise geometric calculations
- ā Completely Free: No registration required
Understanding Centroid
The centroid is the geometric center of a shape. For polygons, it's calculated as the average of all vertex coordinates. For triangles, the centroid is also where all three medians intersect.
- For triangles: Centroid divides each median in a 2:1 ratio
- For regular polygons: Centroid is at the center (same as circumcenter and incenter)
- For irregular polygons: Centroid is the weighted average of vertices
- Centroid represents the balance point of a shape
- Used in structural engineering for load distribution
Real-World Applications
Construction: Find the center point of a triangular roof section to determine load distribution. For a triangle with vertices at corners of a building, the centroid helps plan support placement.
Design: When centering a logo or graphic element on a polygon-shaped area, the centroid provides the optimal center point.
Surveying: Determine the center point of an irregular plot of land by finding the centroid of its boundary coordinates.
Frequently Asked Questions
What is a centroid?
The centroid is the geometric center of a shape. For polygons, it's the arithmetic mean of all vertex coordinates. For triangles, it's also the intersection point of all three medians.
Is centroid the same as center of mass?
For uniform shapes (constant density), yes! The centroid and center of mass coincide. For non-uniform shapes, they differ. This calculator assumes uniform distribution (centroid only).
How do I calculate centroid for a triangle?
For a triangle, add all x-coordinates and divide by 3, and add all y-coordinates and divide by 3. This gives you the centroid coordinates where all three medians intersect.
Does the order of points matter?
No, the order of points doesn't affect the centroid calculation. The centroid is based solely on the arithmetic mean of coordinates, regardless of how points are ordered.
Can the centroid be outside the shape?
Yes! For concave shapes (like a crescent or L-shape), the centroid can be outside the physical shape. This is normal and represents the geometric center of the vertex coordinates.
What's the difference between centroid and circumcenter?
Centroid is the average of vertices (geometric center). Circumcenter is the center of the circumscribed circle. For regular polygons they coincide, but differ for irregular shapes.
Can I use this for 3D shapes?
This calculator works in 2D only. For 3D shapes, you'd need to add a Z coordinate and calculate: Z_centroid = (zā + zā + ... + zā) / n.