Math July 13, 2026 · 8 Min Read

Centroid Calculator – Guide & Formulas

Calculate the centroid (geometric center) of triangles, rectangles, circles, and composite shapes. Get coordinates and formulas instantly.

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Put these formulas into practice with our instant, step-by-step Centroid Calculator.

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The Centroid Calculator finds the geometric center (centroid) of common 2D shapes and composite areas. Unlike center of mass which considers mass distribution, the centroid is purely geometric—based on the shape's area distribution.

Key Takeaway

Use the free Centroid Calculator to calculate the centroid (geometric center) of triangles, rectangles, circles, and composite shapes. get coordinates and formulas instantly. Get instant results with step-by-step explanations.

How to Use the Centroid Calculator

  1. Select the shape type (triangle, rectangle, circle, composite, etc.).
  2. Enter the required dimensions or vertex coordinates.
  3. For composite shapes, add multiple sub-shapes with their properties.
  4. Review the centroid coordinates (x̄, ȳ) and the calculation steps.

The Formula

X̄ = Σ(A_i × x_i) / Σ(A_i) | Ȳ = Σ(A_i × y_i) / Σ(A_i)

Variable Definitions

  • x̄: X-coordinate of the centroid
  • ȳ: Y-coordinate of the centroid
  • A_i: Area of the i-th sub-shape
  • x_i: X-coordinate of the centroid of the i-th sub-shape
  • y_i: Y-coordinate of the centroid of the i-th sub-shape

Example: Centroid of a Triangle

Find the centroid of a triangle with vertices at (0,0), (6,0), and (3,4).

  1. Step 1: Recall the centroid formula for a triangle: (x̄, ȳ) = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3).
  2. Step 2: Calculate x̄: (0 + 6 + 3)/3 = 9/3 = 3.
  3. Step 3: Calculate ȳ: (0 + 0 + 4)/3 = 4/3 ≈ 1.33.
  4. Step 4: The centroid is at (3, 1.33).
  5. Step 5: This point divides each median in a 2:1 ratio from vertex to midpoint.

Frequently Asked Questions