PCA Biplot Calculator

PCA Results

Results appear after calculation.

Rows used

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Variables used

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Selected variance

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Components retained

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Eigenvalues and variance

Loadings and contributions

Observation scores

Descriptive statistics

Correlation or covariance matrix

Dataset

Paste, upload, or edit a table. The first row must contain column names.

CSV or TSV file

Sample dataset

Paste tabular data

PCA configuration

Choose variables, preprocessing, components, grouping, and biplot appearance.

Numeric variables

Use Ctrl or Command for multiple selection.

Observation label Group column

Hide variable arrows

Hidden variables still participate in PCA.

Preprocessing and calculation

Variable transformation

Missing values

PCA basis

Outlier detection

Outlier threshold

Decimal precision

Remove duplicate rows

Exclude detected outliers

Components to retain

Variance target (%)

Biplot axes and scaling

Horizontal component

Vertical component

Biplot scaling

Arrow scale 1.00

Point scale 1.00

Point size 9

Point opacity 0.80

Label size 12

Chart theme

Display layers

Highlighting and interaction

Highlight observation

Highlight variable

Update plot automatically

Import settings JSON

Formula used

1. Center or standardise the data matrix X. 2. Compute S = XᵀX / (n − 1). 3. Solve S vₖ = λₖ vₖ. 4. Compute scores T = X V. 5. Compute loadings L = V √Λ. 6. Explained variance ratio = λₖ / Σλ.

How to use the PCA biplot calculator

Upload data, paste values, or load a sample dataset.
Select at least two numeric variables for PCA.
Choose preprocessing and missing-value handling settings.
Select the two principal components for the biplot axes.
Enable grouping layers such as centroids or confidence ellipses.
Calculate, inspect diagnostics, and export the results.

How to interpret a PCA biplot

Nearby observations have similar profiles across selected variables. Long arrows identify variables strongly represented by the displayed components. Small arrow angles suggest positive correlations between variables.

Opposing arrows suggest negative relationships between variables. Perpendicular arrows indicate weak linear correlation in the displayed plane. Projection toward an arrow suggests a relatively high variable value.

Example data

Sample	Group	Length	Width	Mass
A	Type 1	5.1	3.5	1.4
B	Type 1	4.9	3.0	1.4
C	Type 2	6.4	3.2	4.5

Frequently asked questions

What does a PCA biplot show?

It combines observation scores and variable loadings on two principal component axes.

Should variables be standardised?

Standardisation is usually preferred when variables use different units or scales.

What does arrow length mean?

Longer arrows indicate stronger representation on the selected component plane.

What does the angle between arrows mean?

Small angles suggest positive correlation, while opposite arrows suggest negative correlation.

Why do points appear close together?

Their selected-variable profiles are similar after the chosen preprocessing method.

What is explained variance?

It measures how much dataset variation each principal component captures.

Can categorical variables enter PCA?

Standard PCA requires numeric variables, but categories can colour or label observations.

Why can loadings change sign?

Eigenvector signs are arbitrary, so an entire component may be reflected.

What is symmetric biplot scaling?

It balances observation and variable coordinates for a readable combined display.

When should covariance PCA be used?

Use it when original units and natural variable variances are meaningful.