Calculator
Example data
These eigenvalues illustrate how cumulative variance grows as components are added.
| Component | Eigenvalue | Explained variance | Cumulative variance |
|---|---|---|---|
| PC1 | 4.2 | 50.00% | 50.00% |
| PC2 | 2.1 | 25.00% | 75.00% |
| PC3 | 1.1 | 13.10% | 88.10% |
| PC4 | 0.6 | 7.14% | 95.24% |
| PC5 | 0.4 | 4.76% | 100.00% |
Formula used
If eigenvalues are provided, each component’s explained variance ratio is:
Cumulative variance after k components is the running sum:
If ratios are provided directly, the calculator optionally normalizes them to sum to 1, then computes the same cumulative sum.
How to use this calculator
- Choose Eigenvalues or Explained variance ratios as your input type.
- Paste values into the list box, using commas or new lines.
- Enter one or more target thresholds, such as 80, 90, 95.
- Submit to view the table, cumulative curve, and required components.
- Use the download buttons to export your results for reporting.
Purpose of cumulative variance
Principal component analysis summarizes variance across many correlated variables into ordered components. Cumulative explained variance tells you how much information is retained as you keep PC1, PC2, and beyond. In practice, teams review the curve to decide whether 3, 5, or 10 components are enough for visualization, modeling, or compression. For example, reaching 85% by PC3 often signals strong redundancy. In many datasets, five components retain over 90% variance often.
From eigenvalues to ratios
When PCA is computed on a covariance or correlation matrix, each eigenvalue represents variance captured by a component. The explained variance ratio for component i equals λi divided by the sum of all λ values, and the cumulative ratio is the running total. If you already have ratios from software output, you can paste them directly and optionally normalize to handle rounding. Their sum equals total variance for the analyzed feature space.
Choosing a target threshold
Common retention targets are 80%, 90%, and 95%, but the right value depends on risk and downstream use. Exploratory dashboards may be fine at 80%, while regulated reporting or reconstruction tasks often push toward 95%. A pragmatic approach is to test several thresholds, compare model metrics, and select the smallest component count that meets performance and interpretability needs. For denoising, stop before tiny components amplify measurement noise unnecessarily.
Interpreting diminishing returns
Cumulative variance typically rises quickly, then flattens as later components contribute small increments. If PC1 explains 45%, PC2 adds 22%, and PC3 adds 12%, you reach 79% with three components; adding PC4 at 6% brings you to 85%. Once each new component adds under 2%–3%, gains may reflect noise rather than structure, especially when inputs were not scaled consistently. Look for an elbow where added PCs barely raise totals.
Reporting and reproducibility
For clear communication, report a table with component number, eigenvalue, explained variance, and cumulative variance, plus the chosen threshold and resulting k. Also document preprocessing: missing value handling, scaling choices, and whether components were sorted. Exporting CSV and PDF makes reviews auditable, and printing the chart helps stakeholders see where the curve bends. Record scaling, feature list, and software version for reproducible reporting.
FAQs
What should I enter as values?
Paste PCA eigenvalues from your output, one per line or separated by commas. If you only have explained variance percentages, switch to ratios mode and enter values like 42%, 18%, and 9%.
Do I need to sort components?
If your software already orders components by decreasing variance, leave sorting enabled or disabled consistently. If you paste unsorted values, enable sorting so cumulative variance reflects the largest components first.
Why normalize ratios?
Some tools round explained variance ratios, so they may sum to 0.99 or 1.01. Normalization rescales ratios to sum to 1, keeping cumulative variance interpretable and ensuring thresholds like 90% are evaluated correctly.
What if cumulative variance never reaches 100%?
With ratios, cumulative should reach 100% after the last component if inputs are complete. If it does not, check for missing components, filtering, or rounding. With eigenvalues, negative or zero values are invalid for PCA variance.
Is 95% always the best target?
Not always. Higher targets keep more components but may add noise and reduce interpretability. Many workflows start with 80%–90% for exploration, then validate performance and stability before choosing a final retention level.
Can I compare results across datasets?
Yes, but only after consistent preprocessing. Use the same scaling method, feature set, and handling of missing values. Comparing cumulative variance curves is most meaningful when variance units and data quality are aligned.