Biplot Generator Tool Calculator

Enter PCA inputs

Use eigenvalues, variable loadings, and observation scores from your principal component analysis.

3-column desktop layout

PC1 eigenvalue

Higher values mean more explained variance.

PC2 eigenvalue

Used with PC1 to compute variance shares.

Total variance

For standardized data, this often equals variable count.

Vector scale multiplier

Adjust arrow lengths for clearer plotting.

Plot margin %

Adds empty space around extreme points.

Coordinates use the first two components only. Scores are plotted directly. Variable arrows are scaled from loadings and eigenvalues.

Variable loadings for PC1 and PC2

Variable Label	Loading on PC1	Loading on PC2

Observation scores for PC1 and PC2

Observation Label	PC1 Score	PC2 Score

Example data table

This sample uses six variables, six observations, two retained components, and standardized variance equal to the variable count.

Example configuration

PC1 Eigenvalue	2.95
PC2 Eigenvalue	1.65
Total Variance	6.00
Vector Scale	1.15
Plot Margin	20%

Example variable loadings

Variable	PC1	PC2
Revenue Growth	0.86	0.18
Cost Efficiency	0.74	-0.42
Customer Satisfaction	0.69	0.63
Retention Rate	0.65	0.58
Service Time	-0.48	0.72
Defect Rate	-0.71	0.36

Example observation scores

Observation	PC1 Score	PC2 Score
Segment A	2.10	0.80
Segment B	1.40	-1.10
Segment C	-0.60	1.70
Segment D	-1.80	-0.90
Segment E	0.30	2.00
Segment F	-2.20	0.20

Formula used

Explained variance for each component
Explained Variance % = (Eigenvalue of Component ÷ Total Variance) × 100

Variable vector coordinates
X-coordinate = Loading on PC1 × √(PC1 Eigenvalue) × Scale
Y-coordinate = Loading on PC2 × √(PC2 Eigenvalue) × Scale

Vector length
Length = √(X² + Y²)

Communality across two retained components
Communality = Loading on PC1² + Loading on PC2²

Observation distance from the origin
Distance = √(PC1 Score² + PC2 Score²)

Vector angle
Angle = atan2(Y, X), expressed in degrees

This page assumes you already have PCA outputs. It does not estimate principal components from raw columns directly.

How to use this calculator

Run principal component analysis in your preferred statistics workflow.
Copy the first two eigenvalues into the eigenvalue fields.
Enter total variance, usually the standardized variable count.
Fill in variable names and their loadings on PC1 and PC2.
Enter each sample, case, or segment with its PC1 and PC2 scores.
Adjust the vector scale or plot margin if the plot looks crowded.
Press Generate Biplot to show the summary above the form.
Use the CSV and PDF buttons to export the calculated result section.

FAQs

1) What does this tool actually plot?

It places observation scores as points and variable loadings as arrows on the same PC1-PC2 plane. That lets you compare case positions and variable directions together.

2) Do I need raw data to use it?

No. This page works from PCA outputs you already calculated elsewhere. You only need two eigenvalues, variable loadings, and observation scores.

3) What does a longer arrow mean?

A longer variable arrow usually signals stronger representation on the retained two-component space. Short arrows suggest weaker capture by PC1 and PC2.

4) How should I interpret angles between arrows?

Small angles suggest positive association, right angles suggest weak relation, and opposite directions suggest negative association. This reading is approximate in reduced dimensions.

5) Why do some observations sit far from the origin?

They have stronger combined scores on PC1 and PC2. Such cases stand out more clearly from the average multivariate profile shown near the center.

6) What should total variance be?

For standardized PCA, total variance often equals the number of variables. For other workflows, use the full variance basis that your PCA procedure reports.

7) Why is the vector scale multiplier useful?

It changes arrow lengths for display without changing the underlying loading signs. Use it when labels overlap or the variable vectors look too compressed.

8) Can this replace a full PCA package?

No. It is best for visualization, quick diagnostics, and exportable summaries after PCA. Use a dedicated statistics package to estimate components from raw data.