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
| Property | Value |
|---|---|
| No data yet | |
More ways to use this tool
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_HEREPaste 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 call | From 5 credits |
|---|---|
| Need more credits? | View pricing |
Also available with
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
- Enter the x and y coordinates for each of the three vertices, A, B, and C.
- Choose how many decimal places to display.
- 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.