Cumulative Variance PCA Calculator

Cumulative Variance PCA Calculator Form

Enter eigenvalues or explained variance percentages. The calculator can sort values, normalize percentages, and report the smallest set meeting your target.

Input mode

Target cumulative variance (%)

Decimal places

Component label prefix

Ordering

Normalize percentage inputs to 100%

Values list

Use commas, spaces, semicolons, or line breaks between values.

Reset

Example Data Table

This sample uses PCA eigenvalues already arranged from largest to smallest.

Component	Eigenvalue	Explained Variance %	Cumulative Variance %
PC 1	4.20	46.67	46.67
PC 2	2.10	23.33	70.00
PC 3	1.10	12.22	82.22
PC 4	0.80	8.89	91.11
PC 5	0.50	5.56	96.67
PC 6	0.30	3.33	100.00

In this example, four components retain 91.11% of the total variance, so a 90% target would keep the first four components.

Formula Used

Explained variance ratio for component i:
Explained Variance Ratio(i) = Value(i) / Sum of All Component Values

Explained variance percentage:
Explained Variance %(i) = Explained Variance Ratio(i) × 100

Cumulative variance percentage through component k:
Cumulative Variance %(k) = Sum of Explained Variance % from component 1 to k

Smallest number of retained components:
Find the first k where Cumulative Variance %(k) ≥ Target Threshold %

How to Use This Calculator

Choose whether your input list contains eigenvalues or explained variance percentages.
Paste component values using commas, spaces, semicolons, or separate lines.
Set a target cumulative variance threshold, such as 80%, 90%, or 95%.
Choose whether to sort values descending or keep your original order.
Click the calculate button to see retained variance, required components, the table, and the Plotly chart.

Frequently Asked Questions

1. What does cumulative variance mean in PCA?

Cumulative variance shows how much total dataset variation is preserved when you keep the first several principal components together. It helps decide a reduced dimension count.

2. Should I enter eigenvalues or percentages?

Use eigenvalues when your PCA output lists raw component strengths. Use percentages when your software already reports explained variance by component.

3. Why are values usually sorted from largest to smallest?

PCA components are commonly ranked by variance contribution. Sorting descending makes cumulative variance interpretation easier and matches standard PCA reporting practice.

4. What threshold should I choose?

Common thresholds are 80%, 90%, and 95%. A higher threshold keeps more information but also keeps more dimensions and model complexity.

5. Why does the calculator normalize percentages?

Rounded explained variance percentages often sum to slightly less or more than 100. Normalization prevents cumulative totals from drifting and keeps the final value exactly consistent.

6. What is the Kaiser count shown for eigenvalues?

The Kaiser rule counts components with eigenvalues above 1. It is a quick screening rule, not a universal decision standard.

7. Can this calculator replace a scree plot review?

No. It is best used alongside a scree plot, domain knowledge, and downstream model testing. Cumulative variance is only one dimension-reduction decision aid.

8. Does higher cumulative variance always mean better PCA selection?

Not always. Retaining more variance can preserve noise and extra complexity. Good PCA selection balances information retention, interpretability, and model performance.