Calculator
Choose an input method, paste values, then calculate explained variance and cumulative totals.
Example data table
A quick example using four eigenvalues. Try pasting them into the calculator.
| Component | Eigenvalue | Explained variance ratio | Cumulative ratio |
|---|---|---|---|
| PC1 | 3.20 | 0.6275 | 0.6275 |
| PC2 | 1.10 | 0.2157 | 0.8431 |
| PC3 | 0.60 | 0.1176 | 0.9608 |
| PC4 | 0.20 | 0.0392 | 1.0000 |
Formula used
How to use this calculator
- Select an input method: eigenvalues, ratios, or singular values.
- Paste your values using commas, spaces, or new lines.
- Optionally add labels to keep components organized.
- Set a target cumulative variance percentage, like 90%.
- Press Submit to view results above the form.
- Use Download CSV or Download PDF to save outputs.
Why explained variance matters
Explained variance summarizes how much information each principal component preserves from your original features. When the first component captures a large share, the dataset has strong shared structure. When variance spreads across many components, patterns are weaker or more diverse. This calculator converts component strength into comparable ratios and cumulative totals so you can justify dimensionality reduction decisions with numbers, not guesses, and communicate results to stakeholders.
Input choices and data quality
Use eigenvalues when available, because they directly represent component variance after PCA on centered data. If you already have ratios, the calculator accepts them as decimals or percents and normalizes to ensure they sum to one. For singular values from SVD, the calculator uses squared singular values, because variance is proportional to s2. Always standardize variables when units differ; otherwise, high‑scale features can dominate the first components.
Reading ratios and cumulative totals
The explained variance ratio for component i is λi divided by the sum of all λ values. The cumulative ratio adds ratios from the top component downward. For example, ratios of 0.52, 0.24, and 0.14 yield a cumulative of 0.90 by the third component, meaning 90% of total variance is retained. The table and chart highlight both the marginal gain of each component and the running total.
Selecting components with targets
Common retention targets are 80%, 90%, or 95%, but the right threshold depends on error tolerance and interpretability. In exploratory analytics, 80% may be enough to visualize clusters. In modeling pipelines, 90–95% often balances compactness and predictive stability. Use the “components needed” metric to document the smallest k that meets your chosen target. If you enable sorting, components are ranked by contribution to support a clearer retention rule.
Reporting and validation tips
Export results to CSV for audits, experiments, and reproducible reports. Pair the table with a short note describing preprocessing, scaling, and the chosen target. Validate decisions by re‑running PCA with cross‑validation folds or time splits; stable ratios across samples suggest robust latent structure. If the first component exceeds 60% variance, consider whether a single dominant factor is driving outcomes and whether feature engineering could improve interpretability.
FAQs
1) What if my eigenvalues include negative numbers?
For covariance-based PCA, eigenvalues should be non‑negative. Small negatives can come from rounding. If values are meaningfully negative, recheck centering, scaling, and the PCA output before interpreting explained variance.
2) Can I paste explained variance in percentages?
Yes. In ratio mode you can enter values like 42, 28, 18, 12. The calculator converts them to proportions and normalizes so the final ratios sum to one.
3) How are singular values converted to explained variance?
Variance is proportional to squared singular values. The calculator computes ratios from s2. If you provide sample size n, it also reports eigenvalue scaling via s2/(n−1), while ratios stay unchanged.
4) Should I enable sorting by contribution?
If your inputs are already ordered by largest component first, sorting is optional. If you are unsure of ordering, enable sorting to rank components correctly and get an accurate “components needed” count.
5) Which cumulative variance target is best?
Typical targets are 80% for quick visualization, 90% for many modeling tasks, and 95% for higher‑fidelity compression. Choose the smallest target that keeps downstream performance and interpretability acceptable.
6) Why doesn’t the cumulative total reach 100% sometimes?
If you set “Show first N components,” the displayed cumulative total stops at the last shown component. Set N to 0 to display all components and see the cumulative total approach 100%.