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Covariance Calculator

Math Calculators

Sample & population covariance · Pearson r

Quick Answer

Covariance Calculator: Sample & population covariance · Pearson r. Covariance Calculator uses standard math formulas to compute accurate results instantly.

7 pairs

Sample covariance (n−1)23.5
Population covariance (n)20.1429
Pearson r0.9994
Pairs n7
Direction & strengthpositive · very strong

How covariance works

  1. 1Compute the means of x and y.
  2. 2For each pair take the product of deviations: (xᵢ−x̄)(yᵢ−ȳ) and sum them.
  3. 3Divide by n−1 for the sample covariance (23.5) or by n for the population covariance (20.1429).
  4. 4Covariance sign shows direction of co-movement; magnitude depends on units — use Pearson r for scale-free strength.
  • cov(x,y) > 0: x and y tend to rise together; < 0: opposite; ≈ 0: no linear co-movement (a non-linear relationship may still exist).
  • Covariance is unit-dependent (e.g. cm·kg), so its magnitude is hard to interpret; Pearson r = cov / (sx·sy) normalizes it to [−1, 1].
  • Sample covariance divides by n−1 (Bessel correction) and is the default in statistics software; population covariance divides by n.
  • Var(x+y) = Var(x) + Var(y) + 2·cov(x,y) — covariance is the bridge for portfolio variance too.

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How to Use

  1. Enter values or expressions: type directly into the Covariance Calculator — keyboard friendly.
  2. Instant results: everything computes live as you type, no button needed.
  3. Follow the steps: the result panel shows full working and formula substitution.
  4. Copy or recompute: one-click copy; change any input to recalculate instantly.

Key Points

  • Covariance Calculator is a free online math tool — open and use, no sign-up.
  • All calculations run locally in your browser; your data never leaves the device.
  • Key capability: Sample & population covariance · Pearson r.
  • Results come with formulas and reference tables so you can verify every number.

Formula & How It Works

Covariance Calculator formula

Covariance Calculator uses standard math formulas to compute accurate results instantly.

FAQ

How do I use the Covariance Calculator?
Open the page and fill in the input fields — results update automatically. Sample & population covariance · Pearson r.
Are the results accurate?
Yes. All calculations use standard mathematical formulas and are verified for accuracy.
Is it free? Do I need to sign up?
Completely free. No registration, login or download required — just open and use.
Does it work on mobile?
Yes. The responsive design works on phones, tablets and desktops.
Is my data saved?
No. All calculations run locally in your browser. Nothing is uploaded or stored.

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Source & Updates

Standard mathematical formulas. All logic verified. Last updated: 2025-07

Last updated:

Formulas and content on this page are reviewed by the YiJianSuan team. For reference only — official sources prevail.

Maintained and periodically reviewed by the YiJianSuan editorial team — review process in ourEditorial Policy.

Cite this page: YiJianSuan. Covariance Calculator[EB/OL]. https://www.yijiansuan.com/en/c/math/covariance

Results provided by this tool are for reference only and do not constitute professional advice.