PCA: PC2 vs PC3 Plot

Choose any two components for the scatter, here the second and third.

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: PC2 vs PC3 Plot

This page opens the PCA scatter on the second and third components of the iris data instead of the first two, using the axis menus under the data box. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.

The first components hold the most variance, but not necessarily the structure you are looking for. On iris, PC1 separates setosa from the other species. PC2 and PC3 carry far less variance, so the points are squeezed into a much smaller range, which shows how much of the spread lived in PC1.

Use the horizontal and vertical axis menus to look at any pair. Each axis label shows the share of variance that component explains.

How to use PCA: PC2 vs PC3 Plot

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, PC2 against PC3, not standardised gives PC2 5.3%, PC3 1.7%
Small shares, so the plot shows little spread compared with the PC1 axis.

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.

Why plot components other than PC1 and PC2?

Later components can reveal structure the first two miss, or confirm that they carry only noise.

Do later components always explain little variance?

By construction, each explains no more than the one before. How quickly the shares fall depends on the data.

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: PC2 vs PC3 Plot

Use the horizontal and vertical axis menus to look at any pair. Each axis label shows the share of variance that component explains.

PCA: PC2 vs PC3 Plot

Variance explained by PC1

Projection onto two components

Explained variance

Covariance matrix

Eigenvectors and loadings

About PCA: PC2 vs PC3 Plot

How to use PCA: PC2 vs PC3 Plot

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?

Why plot components other than PC1 and PC2?

Do later components always explain little variance?

More PCA Visualizer pages

PCA: PC2 vs PC3 Plot

Variance explained by PC1

Projection onto two components

Explained variance

Covariance matrix

Eigenvectors and loadings

About PCA: PC2 vs PC3 Plot

How to use PCA: PC2 vs PC3 Plot

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?

Why plot components other than PC1 and PC2?

Do later components always explain little variance?

More PCA Visualizer pages