Calculator Inputs
Example Data Table
| Component | Eigenvalue | Explained % | Cumulative % | Interpretation |
|---|---|---|---|---|
| PC1 | 4.80 | 48.00% | 48.00% | Dominant structure captured immediately. |
| PC2 | 2.50 | 25.00% | 73.00% | Two components already exceed 70%. |
| PC3 | 1.40 | 14.00% | 87.00% | Three components give strong compression. |
| PC4 | 0.70 | 7.00% | 94.00% | Useful when higher fidelity matters. |
| PC5 | 0.40 | 4.00% | 98.00% | Mostly fine-detail variation. |
| PC6 | 0.20 | 2.00% | 100.00% | Marginal additional information. |
Formula Used
For each component, explained variance ratio is calculated as:
Explained Variance Ratioi = Component Variancei / Total Variance
Cumulative variance explained through component k is:
Cumulative Variancek = Σ Explained Variance Ratioi, for i = 1 to k
Expressed as a percentage:
Cumulative Variance % = Cumulative Variance × 100
When eigenvalues are used, total variance equals the sum of all eigenvalues. When ratios are entered directly, the tool normalizes them against their total before building the cumulative curve.
How to Use This Calculator
- Choose whether you will enter eigenvalues or explained variance ratios.
- Paste component values, one per line or separated by commas.
- Optionally add component labels for clearer reporting.
- Enter thresholds such as 70, 80, 90, 95, and 99.
- Select how many components you plan to retain.
- Click the calculation button to generate summary metrics, detailed tables, and the chart.
- Review threshold analysis to see how many components satisfy each retention target.
- Download the results as CSV or PDF for documentation.
Frequently Asked Questions
1. What does cumulative variance explained mean?
It shows how much total dataset variability is retained when the first several principal components are kept. The value increases as more components are included, helping you balance dimension reduction against information loss.
2. Why is 90% cumulative variance often used?
Ninety percent is a common practical target because it usually preserves most meaningful structure while still reducing dimensionality. It is a guideline, not a rule. Some projects accept 80%, while others need 95% or more.
3. Should I enter eigenvalues or explained ratios?
Use whichever output your PCA software provides. If you have raw eigenvalues, the calculator converts them into ratios. If your tool already reports explained variance ratios, you can input them directly.
4. What is the Kaiser rule?
The Kaiser rule keeps components with eigenvalues of at least 1. It is a quick heuristic for standardized variables, but you should still inspect cumulative variance, scree patterns, and domain usefulness before finalizing components.
5. Can cumulative variance be used without PCA?
Yes, the same idea applies to any ordered decomposition where each component contributes a share of total variation. PCA is the most common case, but factor-style reductions often use similar summaries.
6. What happens if the first component dominates?
A dominant first component means a large amount of variation is captured immediately. This may suggest strong correlation structure, one main latent pattern, or heavy redundancy among original features.
7. How many components should I finally keep?
Keep enough components to satisfy performance, interpretability, and retention goals together. Compare threshold results, validation metrics, downstream model quality, and stakeholder tolerance for information loss before deciding.
8. Why do my ratios not sum exactly to 100%?
Small differences often come from rounding in exported reports. This calculator normalizes the entered values, so the cumulative curve remains internally consistent even when published ratios are slightly imprecise.