PCA Explained Variance Calculator

See how much variance each principal component explains, and how many you need.

Try:

Data as CSV with a header row

sepal_length,sepal_width,petal_length,petal_width,species
5.1,3.5,1.4,0.2,setosa
4.9,3.0,1.4,0.2,setosa
4.7,3.2,1.3,0.2,setosa
4.6,3.1,1.5,0.2,setosa
5.0,3.6,1.4,0.2,setosa
5.4,3.9,1.7,0.4,setosa
4.6,3.4,1.4,0.3,setosa
5.0,3.4,1.5,0.2,setosa
4.4,2.9,1.4,0.2,setosa
4.9,3.1,1.5,0.1,setosa
5.4,3.7,1.5,0.2,setosa
4.8,3.4,1.6,0.2,setosa
4.8,3.0,1.4,0.1,setosa
4.3,3.0,1.1,0.1,setosa
5.8,4.0,1.2,0.2,setosa
5.7,4.4,1.5,0.4,setosa
5.4,3.9,1.3,0.4,setosa
5.1,3.5,1.4,0.3,setosa
5.7,3.8,1.7,0.3,setosa
5.1,3.8,1.5,0.3,setosa
5.4,3.4,1.7,0.2,setosa
5.1,3.7,1.5,0.4,setosa
4.6,3.6,1.0,0.2,setosa
5.1,3.3,1.7,0.5,setosa
4.8,3.4,1.9,0.2,setosa
5.0,3.0,1.6,0.2,setosa
5.0,3.4,1.6,0.4,setosa
5.2,3.5,1.5,0.2,setosa
5.2,3.4,1.4,0.2,setosa
4.7,3.2,1.6,0.2,setosa
4.8,3.1,1.6,0.2,setosa
5.4,3.4,1.5,0.4,setosa
5.2,4.1,1.5,0.1,setosa
5.5,4.2,1.4,0.2,setosa
4.9,3.1,1.5,0.2,setosa
5.0,3.2,1.2,0.2,setosa
5.5,3.5,1.3,0.2,setosa
4.9,3.6,1.4,0.1,setosa
4.4,3.0,1.3,0.2,setosa
5.1,3.4,1.5,0.2,setosa
5.0,3.5,1.3,0.3,setosa
4.5,2.3,1.3,0.3,setosa
4.4,3.2,1.3,0.2,setosa
5.0,3.5,1.6,0.6,setosa
5.1,3.8,1.9,0.4,setosa
4.8,3.0,1.4,0.3,setosa
5.1,3.8,1.6,0.2,setosa
4.6,3.2,1.4,0.2,setosa
5.3,3.7,1.5,0.2,setosa
5.0,3.3,1.4,0.2,setosa
7.0,3.2,4.7,1.4,versicolor
6.4,3.2,4.5,1.5,versicolor
6.9,3.1,4.9,1.5,versicolor
5.5,2.3,4.0,1.3,versicolor
6.5,2.8,4.6,1.5,versicolor
5.7,2.8,4.5,1.3,versicolor
6.3,3.3,4.7,1.6,versicolor
4.9,2.4,3.3,1.0,versicolor
6.6,2.9,4.6,1.3,versicolor
5.2,2.7,3.9,1.4,versicolor
5.0,2.0,3.5,1.0,versicolor
5.9,3.0,4.2,1.5,versicolor
6.0,2.2,4.0,1.0,versicolor
6.1,2.9,4.7,1.4,versicolor
5.6,2.9,3.6,1.3,versicolor
6.7,3.1,4.4,1.4,versicolor
5.6,3.0,4.5,1.5,versicolor
5.8,2.7,4.1,1.0,versicolor
6.2,2.2,4.5,1.5,versicolor
5.6,2.5,3.9,1.1,versicolor
5.9,3.2,4.8,1.8,versicolor
6.1,2.8,4.0,1.3,versicolor
6.3,2.5,4.9,1.5,versicolor
6.1,2.8,4.7,1.2,versicolor
6.4,2.9,4.3,1.3,versicolor
6.6,3.0,4.4,1.4,versicolor
6.8,2.8,4.8,1.4,versicolor
6.7,3.0,5.0,1.7,versicolor
6.0,2.9,4.5,1.5,versicolor
5.7,2.6,3.5,1.0,versicolor
5.5,2.4,3.8,1.1,versicolor
5.5,2.4,3.7,1.0,versicolor
5.8,2.7,3.9,1.2,versicolor
6.0,2.7,5.1,1.6,versicolor
5.4,3.0,4.5,1.5,versicolor
6.0,3.4,4.5,1.6,versicolor
6.7,3.1,4.7,1.5,versicolor
6.3,2.3,4.4,1.3,versicolor
5.6,3.0,4.1,1.3,versicolor
5.5,2.5,4.0,1.3,versicolor
5.5,2.6,4.4,1.2,versicolor
6.1,3.0,4.6,1.4,versicolor
5.8,2.6,4.0,1.2,versicolor
5.0,2.3,3.3,1.0,versicolor
5.6,2.7,4.2,1.3,versicolor
5.7,3.0,4.2,1.2,versicolor
5.7,2.9,4.2,1.3,versicolor
6.2,2.9,4.3,1.3,versicolor
5.1,2.5,3.0,1.1,versicolor
5.7,2.8,4.1,1.3,versicolor
6.3,3.3,6.0,2.5,virginica
5.8,2.7,5.1,1.9,virginica
7.1,3.0,5.9,2.1,virginica
6.3,2.9,5.6,1.8,virginica
6.5,3.0,5.8,2.2,virginica
7.6,3.0,6.6,2.1,virginica
4.9,2.5,4.5,1.7,virginica
7.3,2.9,6.3,1.8,virginica
6.7,2.5,5.8,1.8,virginica
7.2,3.6,6.1,2.5,virginica
6.5,3.2,5.1,2.0,virginica
6.4,2.7,5.3,1.9,virginica
6.8,3.0,5.5,2.1,virginica
5.7,2.5,5.0,2.0,virginica
5.8,2.8,5.1,2.4,virginica
6.4,3.2,5.3,2.3,virginica
6.5,3.0,5.5,1.8,virginica
7.7,3.8,6.7,2.2,virginica
7.7,2.6,6.9,2.3,virginica
6.0,2.2,5.0,1.5,virginica
6.9,3.2,5.7,2.3,virginica
5.6,2.8,4.9,2.0,virginica
7.7,2.8,6.7,2.0,virginica
6.3,2.7,4.9,1.8,virginica
6.7,3.3,5.7,2.1,virginica
7.2,3.2,6.0,1.8,virginica
6.2,2.8,4.8,1.8,virginica
6.1,3.0,4.9,1.8,virginica
6.4,2.8,5.6,2.1,virginica
7.2,3.0,5.8,1.6,virginica
7.4,2.8,6.1,1.9,virginica
7.9,3.8,6.4,2.0,virginica
6.4,2.8,5.6,2.2,virginica
6.3,2.8,5.1,1.5,virginica
6.1,2.6,5.6,1.4,virginica
7.7,3.0,6.1,2.3,virginica
6.3,3.4,5.6,2.4,virginica
6.4,3.1,5.5,1.8,virginica
6.0,3.0,4.8,1.8,virginica
6.9,3.1,5.4,2.1,virginica
6.7,3.1,5.6,2.4,virginica
6.9,3.1,5.1,2.3,virginica
5.8,2.7,5.1,1.9,virginica
6.8,3.2,5.9,2.3,virginica
6.7,3.3,5.7,2.5,virginica
6.7,3.0,5.2,2.3,virginica
6.3,2.5,5.0,1.9,virginica
6.5,3.0,5.2,2.0,virginica
6.2,3.4,5.4,2.3,virginica
5.9,3.0,5.1,1.8,virginica

Numeric columns are used. A text column (such as species) is kept only to colour the points. Up to 5,000 rows and 30 numeric columns.

Standardise columns (unit variance)

Standardising makes PCA use the correlation matrix, so a column measured in large units does not dominate. Leave it off when all columns share a unit.

Horizontal axis

Vertical axis

Variance explained by PC1

92.46%

The first 2 components keep at least 95% of the total variance of the 4 columns. Total variance is 4.573, the sum of the eigenvalues, which also equals the trace of the covariance matrix.

Projection onto two components

setosa
versicolor
virginica

Explained variance

Component	Eigenvalue	Explained	Cumulative
PC1	4.22824	92.46%	92.46%
PC2	0.24267	5.31%	97.77%
PC3	0.07821	1.71%	99.48%
PC4	0.02384	0.52%	100%

Covariance matrix

	sepal_length	sepal_width	petal_length	petal_width
sepal_length	0.68569	-0.04243	1.27432	0.51627
sepal_width	-0.04243	0.18998	-0.32966	-0.12164
petal_length	1.27432	-0.32966	3.11628	1.29561
petal_width	0.51627	-0.12164	1.29561	0.58101

The sample covariance divides by n - 1. The eigen decomposition uses the Jacobi rotation method, which is accurate for the small symmetric matrices that PCA produces.

Eigenvectors and loadings

Eigenvector	PC1	PC2	PC3	PC4
sepal_length	0.3614	0.6566	-0.582	0.3155
sepal_width	-0.0845	0.7302	0.5979	-0.3197
petal_length	0.8567	-0.1734	0.0762	-0.4798
petal_width	0.3583	-0.0755	0.5458	0.7537

Loading	PC1	PC2	PC3	PC4
sepal_length	0.7431	0.3234	-0.1628	0.0487
sepal_width	-0.1738	0.3597	0.1672	-0.0494
petal_length	1.7615	-0.0854	0.0213	-0.0741
petal_width	0.7367	-0.0372	0.1526	0.1164

\Sigma\,v_i = \lambda_i\, v_i, \qquad \text{loading}_{ji} = v_{ji}\sqrt{\lambda_i}, \qquad \text{score} = (x-\bar x)\cdot v_i

An eigenvector gives the direction of a component. A loading scales it by the component's spread; with standardised columns it is the correlation between a variable and the component. The sign of a component is arbitrary, so this tool makes its largest entry positive.

About PCA Explained Variance Calculator

This explained variance calculator reports the share of total variance each principal component captures, as a table and a scree chart, with the cumulative total beside it. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.

Explained variance is a component's eigenvalue divided by the sum of all eigenvalues. The cumulative column tells you how many components are needed to keep a chosen share of the information, for example 95%.

The page opens on the four iris measurements without standardising. Because petal length has by far the largest raw variance, the first component alone carries most of it, and the other three add little. Compare with the standardised version of the same data in the main tool.

How to use PCA Explained Variance 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

Iris, four columns, not standardised gives 92.5%, 5.3%, 1.7%, 0.5%
Cumulative: 92.5%, 97.8%, 99.5%, 100%.

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.

How many principal components should I keep?

Common rules are to keep enough to explain 90 to 95% of the variance, or to stop at the elbow of the scree plot.

What is a scree plot?

A chart of the explained variance of each component in order. The point where it flattens out suggests how many components are meaningful.

Explained variance

Table of values

Explained variance and cumulative explained variance per principal component
Label	Explained variance %	Cumulative %
PC1	92.46	92.46
PC2	5.31	97.77
PC3	1.71	99.48
PC4	0.52	100

Component	Eigenvalue	Explained	Cumulative
PC1	4.22824	92.46%	92.46%
PC2	0.24267	5.31%	97.77%
PC3	0.07821	1.71%	99.48%
PC4	0.02384	0.52%	100%

Covariance matrix

	sepal_length	sepal_width	petal_length	petal_width
sepal_length	0.68569	-0.04243	1.27432	0.51627
sepal_width	-0.04243	0.18998	-0.32966	-0.12164
petal_length	1.27432	-0.32966	3.11628	1.29561
petal_width	0.51627	-0.12164	1.29561	0.58101

The sample covariance divides by n - 1. The eigen decomposition uses the Jacobi rotation method, which is accurate for the small symmetric matrices that PCA produces.

Eigenvectors and loadings

Eigenvector	PC1	PC2	PC3	PC4
sepal_length	0.3614	0.6566	-0.582	0.3155
sepal_width	-0.0845	0.7302	0.5979	-0.3197
petal_length	0.8567	-0.1734	0.0762	-0.4798
petal_width	0.3583	-0.0755	0.5458	0.7537

Loading	PC1	PC2	PC3	PC4
sepal_length	0.7431	0.3234	-0.1628	0.0487
sepal_width	-0.1738	0.3597	0.1672	-0.0494
petal_length	1.7615	-0.0854	0.0213	-0.0741
petal_width	0.7367	-0.0372	0.1526	0.1164

\Sigma\,v_i = \lambda_i\, v_i, \qquad \text{loading}_{ji} = v_{ji}\sqrt{\lambda_i}, \qquad \text{score} = (x-\bar x)\cdot v_i

About PCA Explained Variance Calculator

PCA Explained Variance Calculator

Variance explained by PC1

Projection onto two components

Explained variance

Covariance matrix

Eigenvectors and loadings

About PCA Explained Variance Calculator

How to use PCA Explained Variance Calculator

Features

Worked examples

Privacy: how it works

Tips

Frequently asked questions

Is it really free?

Do I need an account?

Does it run in my browser?

Is my data uploaded?

How many principal components should I keep?

What is a scree plot?

More PCA Visualizer pages

PCA Explained Variance Calculator

Variance explained by PC1

Projection onto two components

Explained variance

Covariance matrix

Eigenvectors and loadings

About PCA Explained Variance Calculator

How to use PCA Explained Variance Calculator

Features

Worked examples

Privacy: how it works

Tips

Frequently asked questions

Is it really free?

Do I need an account?

Does it run in my browser?

Is my data uploaded?

How many principal components should I keep?

What is a scree plot?

More PCA Visualizer pages