Covariance measures the joint variability of two random variables. This calculator supports both the sample covariance formula with divisor n - 1 and the population covariance formula with divisor n.
⚠Both datasets must have the same number of values. Covariance is scale-dependent; use correlation for standardized comparison.
Population Covariance Formula
Population covariance divides the sum of paired deviations by n: Cov(X,Y) = sum((xi - meanX)(yi - meanY)) / n. Sample covariance uses the same numerator but divides by n - 1 to estimate the population value from a sample.
What is Covariance?
Covariance measures how two variables change together. A positive covariance indicates that larger values of one variable tend to be associated with larger values of the other. A negative covariance indicates the opposite.
Positive Covariance
Cov > 0: Variables tend to increase together (e.g., height & weight)
Negative Covariance
Cov < 0: When one variable increases, the other decreases
Zero Covariance
Cov = 0: No linear relationship between variables
Sample vs Population
Sample uses n-1 (unbiased), population uses n (biased)
Covariance measures how two variables vary together. Positive covariance means variables tend to increase together. Negative covariance means when one increases, the other tends to decrease.
Population vs sample covariance?▼
Population covariance divides by n. Sample covariance divides by n-1 (Bessel's correction) to give an unbiased estimator of population covariance.
How is covariance related to correlation?▼
Correlation = Covariance / (σₓ × σᵧ). Correlation normalizes covariance to range -1 to +1, making it easier to interpret strength of relationship.
What does covariance value mean?▼
Magnitude depends on variable scales. Sign matters: positive = variables move together, negative = move opposite. Use correlation for standardized comparison.
Free online calculators and tools covering mathematics, unit conversion, text processing, and daily life. Accurate, fast, mobile-friendly, and completely free to use.