About PCA Covariance Matrix Calculator
This calculator builds the sample covariance matrix of your columns, the matrix PCA decomposes, and shows its eigenvalues and eigenvectors. It opens on a ten-point, two-variable example. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The diagonal of a covariance matrix holds each variable's variance and the off-diagonal entries hold how pairs of variables vary together. A large positive covariance means they rise and fall together, which is what lets PCA summarise them with one component. Here the covariance of 0.615 is close to both variances, so the points hug a line.
The sample covariance divides by n - 1. The example is the standard two-variable demonstration used in many PCA tutorials, with ten points.
How to use PCA Covariance Matrix Calculator
- Pick a sample dataset, or paste your own CSV with a header row and at least two numeric columns.
- Decide on standardising. Turn it on when the columns are in different units, off when they share one.
- Read the variance explained by PC1 and the scree chart to see how many components matter.
- Choose which two components to plot, if you have more than two, and look at the projection.
- Open the covariance matrix, eigenvector and loading tables to see how each variable contributes to each component.
- Copy the component scores to use in a spreadsheet or another tool.
Features
- Covariance matrix, or correlation matrix when columns are standardised.
- Eigenvalues and eigenvectors by the Jacobi rotation method, sorted from largest to smallest.
- Explained and cumulative variance as a chart and a table.
- A projection scatter on any two components, coloured by a text column when one is present.
- Eigenvector and loading tables, with a stable sign convention.
- Component scores for every row, copyable as tab-separated text.
- Up to 5,000 rows and 30 numeric columns, with iris, a two-variable example and a marks table built in.
Worked examples
Ten points of x and y, not standardised gives covariance [[0.6166, 0.6154], [0.6154, 0.7166]]
Eigenvalues 1.284 and 0.0491; PC1 explains 96.3%.
Privacy: how it works
- Your table is parsed and analysed in your browser tab. Nothing is sent to Ulkaa or anyone else.
Tips
- A common rule of thumb is to keep enough components to explain 90 to 95% of the variance. The note under the result card tells you how many that is.
- Look for an elbow in the scree chart: components after it add little.
- Large loadings of the same sign mean the variables move together on that component; opposite signs mean a contrast between them.
- Remove ID columns and anything that is not a measurement before running PCA.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your table are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your table are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What is a covariance matrix?
A square table whose diagonal is the variance of each variable and whose other entries are the covariances between pairs of variables.
Why does PCA use the covariance matrix?
Its eigenvectors are the directions of greatest variance and its eigenvalues are the variances along them.
More PCA Visualizer pages
- PCA VisualizerPaste numeric columns and see the covariance matrix, eigenvectors, explained variance and a 2D projection.
- Eigenvalue and Eigenvector Calculator for PCAGet the eigenvalues and unit eigenvectors of the covariance matrix of your data.
- PCA Explained Variance CalculatorSee how much variance each principal component explains, and how many you need.
- PCA With StandardizationRun PCA on standardised columns, so every variable has the same weight.
- PCA: PC2 vs PC3 PlotChoose any two components for the scatter, here the second and third.
- PCA on Two VariablesSee PCA at its simplest, with two variables and the correlation matrix.