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Covariance Calculator

X Values (space/comma separated)
Y Values

✓परिणाम

Covariance
4.4286
Correlation (r)
0.9764
n
8
Correlation: Strong positive

What is Covariance Calculator?

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Covariance measures how two variables change together. Positive covariance means they tend to increase together; negative means one increases as the other decreases. It is the foundation of correlation and portfolio theory.

Calkulon makes complex calculations simple — built for students and everyday problem-solvers.

सूत्र

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f(x)Cov(X,Y) = E[(X − μₓ)(Y − μᵧ)] = (Σ(xᵢ − x̄)(yᵢ − ȳ)) / (n−1)

Variable Legend

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प्रतीकनावएककवर्णन
X, Ytwo variables/datasets——
μₓ, μᵧmeans of X and Y——
Cov(X,Y)covariance—measure of joint variability
nnumber of data points——

How to Covariance Calculator

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  1. 1Sample covariance: Cov(X,Y) = Σ(xᵢ−x̄)(yᵢ−ȳ) / (n−1)
  2. 2Positive: variables move together
  3. 3Negative: variables move oppositely
  4. 4Zero: no linear relationship

Worked Examples

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Example 1
Given:X=[2,4,4,4,5], Y=[1,3,3,4,4]
परिणाम:Cov ≈ 0.95 (positive relationship)

Real-World Applications

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🏗️

Portfolio analysis and risk management

🔬

Finance and stock correlation

📊

Machine learning (feature relationships)

🏥

Statistical analysis and regression

⚙️

Quality control and process monitoring

Covariance Interpretation

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SignMeaningExample
PositiveVariables increase togetherHeight & weight
NegativeInverse relationshipPrice & demand
ZeroNo linear relationshipShoe size & IQ
Normalised = rCorrelation coefficient−1 to +1 range

Frequently Asked Questions

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Q

What does positive covariance mean?

A

Positive covariance: when X increases, Y tends to increase. They vary together.

Q

What does zero covariance mean?

A

Zero covariance suggests no linear relationship, but nonlinear relationships may exist.

Q

How is covariance related to correlation?

A

Correlation = Cov(X,Y) / (σₓ × σᵧ). Correlation is covariance normalized to [−1, 1].

Deep Dive

Read the full guide on how to use this calculator effectively

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Formula-verified for precision
Reviewed October 2026
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