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Triangle Centroid Calculator

Calculate a triangle's centroid, side lengths, perimeter, area and the three medians from its three vertex coordinates on the Cartesian plane.

Input

Output

Results
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REST API

curl -X POST https://api.iotools.cloud/v1/tool/triangle-centroid-calculator \
  -H "Authorization: Bearer YOUR_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
    "precision": "4",
    "ax": "0",
    "ay": "0",
    "bx": "6",
    "by": "0",
    "cx": "3",
    "cy": "6"
  }'

Swap in your own key from your account. The tool's fields are the body — no wrapper.

Ask an AI agent

Use the IOTools `triangle-centroid-calculator` tool (Triangle Centroid Calculator) on this input:

YOUR_INPUT_HERE

Paste this at any agent connected to the IOTools MCP server, then add your input.

Embed widget

<iframe
  src="https://iotools.cloud/embed/triangle-centroid-calculator/"
  width="100%" height="520" frameborder="0" scrolling="no" loading="lazy"
  title="Triangle Centroid Calculator — iotools.cloud"
  sandbox="allow-scripts allow-forms allow-same-origin allow-downloads allow-popups allow-popups-to-escape-sandbox"
  allow="clipboard-write"
  style="width:100%;border:1px solid #e5e7eb;border-radius:12px;overflow:hidden"></iframe>
<script src="https://iotools.cloud/embed.js" async></script>

Drop this into your own page — free, no key required, just a link back.

Cost per API/MCP callFrom 5 credits
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Guides

Enter the three vertex coordinates of a triangle on the Cartesian plane and get its centroid, side lengths, perimeter, area, and the length of each median in one pass.

What is a centroid?

The centroid is a triangle's center of mass — the point where its three medians (the line from each vertex to the midpoint of the opposite side) all intersect. It always sits at exactly 2/3 of the distance from each vertex to the midpoint of the opposite side, and it's always inside the triangle, no matter its shape.

Formulas

For a triangle with vertices A(x₁,y₁), B(x₂,y₂), C(x₃,y₃):

Centroid      = ((x₁+x₂+x₃) / 3, (y₁+y₂+y₃) / 3)
Side a (BC)   = distance from B to C     (opposite vertex A)
Side b (CA)   = distance from C to A     (opposite vertex B)
Side c (AB)   = distance from A to B     (opposite vertex C)
Area          = |x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)| / 2      (shoelace formula)
Median from A = distance from A to the midpoint of BC

(and likewise for the medians from B and C, each to the midpoint of its opposite side)

How to use it

  1. Enter the x and y coordinates for each of the three vertices, A, B, and C.
  2. Choose how many decimal places to display.
  3. Results update instantly as you type.

FAQ

What if my three points are on a straight line?

Three collinear points don't form a triangle — there's no enclosed area, so no centroid to compute. The calculator flags this rather than returning a misleading result.

Does vertex order (A, B, C) matter?

No — the centroid, area, and perimeter come out identical no matter which order you enter the vertices in. Only the side/median labels (which one is "opposite A" vs "opposite B") shift accordingly.

I have side lengths and angles, not coordinates — can I still use this?

Use the Triangle Calculator instead — it solves a triangle from any three known sides/angles (SSS, SAS, ASA, AAS, or SSA) without needing coordinates, and reports area, perimeter, heights and more.

Privacy

Everything runs locally in your browser — nothing you enter is uploaded or stored anywhere.

centroidtriangleverticescoordinatesmediancartesiancenter of massgeometrymathx y coordinates

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