Find the geometric centre (centroid) of any set of 2D or 3D points instantly. Upload thousands of coordinates via CSV/TXT, export results.
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Calculate centroids for both two-dimensional and three-dimensional point sets in a single tool.
Upload thousands of rows via CSV or TXT. Auto-detect 2D/3D format and compute the centroid in milliseconds.
Instant feedback on invalid rows, missing values, and non-numeric inputs — before you even click Calculate.
Download your point set plus centroid as a clean CSV file, or copy directly to clipboard in one click.
All calculations happen in your browser. No data is sent to any server — your coordinates stay private.
Fully responsive layout that works seamlessly on phones, tablets, and desktops without any overflow.
Add points manually or upload a CSV/TXT file. Supports 2D (x,y) and 3D (x,y,z) coordinates.
Hit the Calculate button. The tool validates inputs and computes the arithmetic mean of all coordinates.
View Cx, Cy (and Cz for 3D), then copy or download your full results as a structured CSV file.
The centroid of a set of points — often called the geometric centre or centre of mass for uniform-density objects — is one of the most fundamental concepts in mathematics, engineering, and physics. Understanding how to calculate it accurately is essential for anyone working in structural analysis, data science, computer graphics, or pure geometry.
What Is the Centroid Formula? For a collection of n points in two-dimensional space, the centroid coordinates are: Cx = (x₁ + x₂ + … + xₙ) / n and Cy = (y₁ + y₂ + … + yₙ) / n. Extend this to three dimensions by adding Cz = (z₁ + z₂ + … + zₙ) / n. The formula is an arithmetic mean applied independently across each axis — elegantly simple yet enormously powerful.
Centroid of a Triangle: A classic example is the triangle centroid. For a triangle with vertices at A(x₁,y₁), B(x₂,y₂), and C(x₃,y₃), the centroid is G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3). This point is always located one-third of the way from each side to the opposite vertex — the intersection of the three medians. For instance, triangle vertices (0,0), (6,0), (3,9) produce centroid G = (3, 3).
Real-world Usage: Engineers use the centroid to determine where a beam will balance, making it critical for structural design. In computer vision, the centroid of a set of detected pixels locates the centre of an object for tracking. Data scientists use centroids as cluster centres in k-means clustering. CAD software uses it to calculate the centre of a complex polygon for machining operations. Architects rely on centroid calculations when distributing load across irregular floor plans.
How to Use This Centroid Calculator: Our bulk centroid calculator accepts both 2D and 3D coordinate sets. You can add points manually one by one, paste a list of comma-separated coordinates, or drag and drop a CSV or TXT file. The tool auto-detects whether your data is 2D or 3D. Supported delimiters include comma (,), space ( ), and semicolon (;). After processing, the centroid coordinates are displayed prominently, and you can download a full CSV containing all input points alongside the calculated centroid.
Common Mistakes to Avoid: Always ensure all points in a dataset have the same number of dimensions — mixing 2D and 3D points in a single batch will produce unreliable results. Additionally, verify there are no missing values or typos in your CSV. Our real-time validation engine flags these issues before submission, saving you time and frustration. Whether you are a student solving geometry homework, a researcher processing point cloud data, or an engineer computing centre-of-gravity positions, this free online tool provides fast, accurate, and verifiable centroid calculations without any software installation.
The centroid is the arithmetic mean position of all points in a set. For n points, each coordinate of the centroid is the average of that coordinate across all points. It represents the geometric "balancing point" of the set.
For a triangle with vertices (x₁,y₁), (x₂,y₂), (x₃,y₃): Cx = (x₁+x₂+x₃)/3, Cy = (y₁+y₂+y₃)/3. The centroid lies at the intersection of the three medians and is always inside the triangle.
Yes. Upload a CSV or TXT file with one point per row. Use comma, space, or semicolon as delimiters. The tool supports 2D (x,y) and 3D (x,y,z) data and processes thousands of rows instantly in your browser.
For a uniform-density object, the centroid and centre of mass are identical. However, centre of mass accounts for mass distribution, while centroid is purely geometric. This calculator computes the geometric centroid.
Completely safe. All calculations run locally in your browser using JavaScript. No data is ever transmitted to any server — your coordinate data never leaves your device.
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