PCA Score Calculator

Input data

Paste or upload

Paste delimited data

Use consistent columns per row. Missing values: blank, NA, NaN, null.

Or upload CSV

If uploaded, it overrides the pasted data.

Options

First row contains variable names

Missing values

Scaling for scoring

If correlation is chosen below, z-score is enforced for the matrix.

Matrix type

Controls

Number of components (k)

Must be ≤ number of variables.

Decimal places

Preview rows

Reset

Computation uses a symmetric eigen-solver optimized for small-to-medium matrices.

Example data table

You can paste this dataset into the input box.

FeatureA	FeatureB	FeatureC
2.5	2.4	1.2
0.5	0.7	0.3
2.2	2.9	1.1
1.9	2.2	0.9
3.1	3.0	1.4

Tip: Use the “First row contains variable names” option if you include headers.

How to use this calculator

Paste your numeric dataset, or upload a CSV file.
Enable the header option if your first row contains names.
Select missing-value handling (impute or drop incomplete rows).
Choose scaling and matrix type, then set the component count.
Press Submit to view explained variance, loadings, and scores.
Use the download buttons to export CSV or PDF outputs.

Formula used

Preprocessing

Centering: Xc(i,j) = X(i,j) − μ(j)
Z-score: Z(i,j) = (X(i,j) − μ(j)) / σ(j)

μ(j) is the mean of variable j, σ(j) its sample standard deviation.

PCA core equations

S = (1/(n−1)) · Zᵀ Z
S = V Λ Vᵀ
Scores: T = Z V
Use first k columns of V for k components.

Λ holds eigenvalues; V columns are eigenvectors (component weights).

Notes: When using the correlation matrix, variables are standardized before decomposition. Loadings here are computed as weights × √(eigenvalue) for each component.

Practical value of PCA scores

Principal component analysis converts many correlated variables into a smaller set of uncorrelated components. The score for an observation is its coordinate in this new component space, making clustering, trend detection, and visualization easier rapidly. This calculator estimates those scores from your dataset and summarizes how much variability each component explains. By focusing on the first few components, you reduce noise while keeping structure that supports exploratory analysis and downstream statistical modeling.

Data requirements and preparation

Reliable scoring starts with clean numeric inputs. Provide a rectangular table where each row is an observation and each column is a measured variable. Consistent units and sensible ranges improve interpretability. If your file has headers, enable the header option to preserve variable names. For missing entries, choose mean imputation to keep sample size, or drop incomplete rows when missingness is rare. Always review the preview tables for sanity before computation begins.

Scaling and matrix selection

PCA depends on how variables are scaled. When variables use different units or spreads, standardization is usually preferred; the z‑score option centers values and divides by the sample standard deviation. The correlation matrix corresponds to standardized variables and is a common default for mixed‑scale data. The covariance matrix reflects the chosen scaling and can emphasize high‑variance measurements often. Select the approach that matches your analytic goal and domain expectations.

Understanding variance, weights, and loadings

Eigenvalues indicate component strength; dividing each eigenvalue by their total yields the explained variance percentage. Cumulative variance helps you pick a suitable number of components k. Weights (eigenvectors) define the direction of each component as a linear combination of variables. Loadings, computed as weights multiplied by the square root of the eigenvalue, approximate how strongly each variable contributes. Use signs and magnitudes to interpret contrasts and shared patterns for clear, defensible interpretation.

Using scores in projects and reports

Scores can be used as compact features in regression, classification, anomaly detection, and quality control. Because components are orthogonal, multicollinearity is reduced and models can become more stable. Keep k small enough to generalize, but large enough to retain important variation. Export the full score table to CSV for further analysis, or generate a PDF summary for audits and stakeholder updates. Document scaling choices alongside results for transparency across teams and tools.

FAQs

What are PCA scores in simple terms?

They are new coordinates for each observation after rotating the data into principal component directions. Each score is a weighted sum of the centered or standardized variables, showing where the observation lies on a component axis.

When should I choose correlation versus covariance?

Use correlation when variables have different units or very different spreads, because standardization makes them comparable. Use covariance when all variables share a meaningful scale and you want higher-variance variables to carry more influence.

How do I decide the number of components k?

Review cumulative explained variance and pick the smallest k that captures the structure you need. Many workflows target 70–95% cumulative variance, but you should also consider interpretability and the stability of downstream models.

How does the calculator handle missing values?

You can drop any row containing a missing entry, or replace missing cells with the variable mean before scaling. Mean imputation preserves more rows, but dropping can be safer if missingness is minimal and not systematic.

What do negative weights or loadings mean?

The sign indicates direction, not importance. A negative loading means the component increases when that variable decreases, relative to the other variables. Interpret signs by comparing variables within the same component and focusing on magnitudes.

Can I export everything for further analysis?

Yes. The CSV download includes all observation scores plus variance summaries, while the PDF provides a compact report-style summary. Use exported scores as features in modeling, visualization, clustering, or reporting pipelines.