Math

Covariance Calculator

Compute covariance for paired datasets (X and Y). Choose sample or population, see means, deviations, cross-products, and export the calculation table to CSV.

Sample / Population Means + Deviations Step Table CSV Export

Covariance of X and Y

Paste values for X and Y (same length). Separate values with commas, spaces, or new lines.

Tip: Covariance is scale-dependent. If you need a standardized strength measure, use a correlation calculator.
Item Meaning Formula Why it matters
Mean of X Average of X values x̄ = Σxi / N Baseline for deviations
Mean of Y Average of Y values ȳ = Σyi / N Baseline for deviations
Cross-product sum Total co-deviation Σ(xi−x̄)(yi−ȳ) Core quantity for covariance
Population covariance True covariance for full population Σ(xi−x̄)(yi−ȳ) / N Use when data is the whole population
Sample covariance Estimate from a sample Σ(xi−x̄)(yi−ȳ) / (N−1) Reduces bias when estimating

Quick Steps

  1. Paste your X values and Y values (must be the same length).
  2. Select sample or population covariance based on your use case.
  3. Click Calculate to view covariance and the full cross-product table.
  4. Export the table to CSV if you need it for a report or spreadsheet.
Interpretation: positive covariance means X and Y tend to move in the same direction; negative means they tend to move in opposite directions.
Your covariance history will appear here after you calculate.