Skip to main content
Calcimator

Dimensionality Reduction Calculator

Determine how many principal components to retain based on eigenvalues and target explained variance. Includes scree plot data, Kaiser criterion, and cumulative variance analysis.

Inputs

Results

Components to Keep

4

Variance Explained

95%

Dimension Reduction20%
Kaiser Criterion Components2
Total Components5
Largest Eigenvalue45
Smallest Eigenvalue5
How to Use This Calculator
  1. Enter the number of original features and target number of components.
  2. Set the minimum explained variance threshold (e.g., 95%).
  3. Review the number of components needed to reach your variance threshold.
  4. Plot the scree plot to identify the elbow and confirm the component count.
  5. Use the selected components as input features for downstream modeling.

How the result changes with Eigenvalue 1 (Largest)

Eigenvalue 1 (Largest)Components to KeepVariance Explained
100,000199.95%
350,000199.98%
650,000199.99%
900,000199.99%

What each input means

Total Variance
The total variance across all original features (sum of all eigenvalues ideally).
Eigenvalue 1 (Largest)
Eigenvalue for the first principal component (largest variance direction).
Eigenvalue 2
Eigenvalue for the second principal component.
Eigenvalue 3
Eigenvalue for the third principal component.
Eigenvalue 4
Eigenvalue for the fourth principal component.
Eigenvalue 5 (Smallest)
Eigenvalue for the fifth principal component (smallest variance direction).
Target Variance Explained (%)
The minimum percentage of total variance you want your retained components to explain. 95% is common.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Total Variance = 100, Eigenvalue 1 (Largest) = 45, Eigenvalue 2 = 25, Eigenvalue 3 = 15 = 7 input(s) provided
  2. Calculate Components to Keep
    Components to Keep
    4 = 4
  3. Calculate Variance Explained
    95 = 95
  4. Calculate Dimension Reduction
    Dimension Reduction
    20 = 20
  5. Calculate Kaiser Criterion Components
    Kaiser Criterion Components
    2 = 2

Engine last updated . Checked against 1 independently-derived test — how we verify calculators.

Related Calculators

The questions that sit next to this one — chosen by subject, including calculators filed under a different category.

Data Science

Feature Scaling Calculator

Scale raw feature values using min-max normalization, z-score standardization, robust scaling, and max-abs normalization for machine learning preprocessing.

Data Science

Clustering Quality Score Calculator

Evaluate clustering quality using silhouette score, Calinski-Harabasz index, Davies-Bouldin index, and Dunn index from cluster distance metrics.

MLOps & AI Costing

Feature Importance Calculator

Estimate how many features to keep, overfitting risk, and expected variance retention based on dataset size, model type, and correlation threshold.

Data Science

A/B Test Calculator

Determine statistical significance of A/B test results. Calculate z-score, p-value, conversion lift, and whether your variant beats the control at your chosen confidence level.

More in Math & Statistics.