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Covariance Calculator

Updated Sep 2026 Used 0 times
Enter X values in pair order.
Enter matching Y values.
Choose the required denominator.

Guest calculations stay on this device. Signed-in results sync privately.

Your result

Covariance

Enter your values, then calculate to see a verified result.

Inputs usedReview the information used for this result.
Full calculation and sourcesSample covariance divides the cross-deviation sum by n - 1; population covariance divides by n.

Versioned calculationFormula v1.0.0

Formula definitionUnit-normalized calculationFormula v1.0.0

What this result means

Calculate sample or population covariance from paired X and Y lists and inspect the cross-deviation sum.

Method used

Sample covariance divides the cross-deviation sum by n - 1; population covariance divides by n.

Important limitation

The result is only as reliable as the inputs and stated method.

Result actions
1
Enter the inputsUse values with the units and definitions shown beside each field.
2
Apply the methodSample covariance divides the cross-deviation sum by n - 1; population covariance divides by n.
3
Inspect the bridgeReview the primary result and supporting outputs before using it.
4
Check limitationsConfirm the assumptions, date, jurisdiction or population match your use case.

Interpretation

X 1,2,3 and Y 2,4,6 have sample covariance 2.

Sample covariance divides the cross-deviation sum by n - 1; population covariance divides by n.

The result is only as reliable as the inputs and stated method.

Use this result

Keep exploring

2 available tools
Coefficient of Determination CalculatorCalculate R squared from observed and predicted values with SSE, SST and negative-result support.Descriptive Statistics CalculatorGenerate an audit-ready summary of center, spread and quartiles with visible sample/population and quartile conventions.
Public verification recordFormula v1.0.0
Review scope
Covariance Calculator Formula, Input Validation, Edge Behavior And Result Presentation.
Review team
CalculatorGeek Expert Review Team
Verified
2026-09-21
Next source review
2027-09-21
Automated fixtures
1 cases

Review method

Package reconciliation, primary-source mapping, competitor feature comparison, deterministic fixtures, PHP/JavaScript parity and responsive preview QA.

Known limitations

  • The result is only as reliable as the inputs and stated method.
  • Changing legal, medical, exam or statistical conventions must be checked at the source.

Primary sources

Latest update

2026-09-21 ยท

On this page

Direct answer

Calculate sample or population covariance from paired X and Y lists and inspect the cross-deviation sum.

Continue with the Coefficient of Determination Calculator when that method matches your next question.

Continue with the Descriptive Statistics Calculator when that method matches your next question.

Formula and methodology

Sample covariance divides the cross-deviation sum by n - 1; population covariance divides by n.

X 1,2,3 and Y 2,4,6 have sample covariance 2.

Continue with Coefficient of Determination Calculator or Descriptive Statistics Calculator for the next calculation.

Worked example

X 1,2,3 and Y 2,4,6 have sample covariance 2.

The calculator retains working precision and rounds only the displayed values.

Interpret the result carefully

Method boundary: The result is only as reliable as the inputs and stated method.

Inputs, boundary behavior and JavaScript/PHP parity are covered by deterministic release tests.

Use the result for the named task only. Do not stretch it into a legal, clinical, safety or causal conclusion the formula does not support.

Inputs, outputs and result meaning

Calculates covariance, mean X, mean Y, and cross-deviation sum from x values, y values, and covariance basis with visible method, validation, precision, and limitations.

Inputs

X values
Enter X values in pair order.
Y values
Enter matching Y values.
Covariance basis
Choose the required denominator. Available choices are Sample (n - 1) and Population (n).

Outputs

Covariance
This is the primary result. The visible value uses up to 6 decimal places according to the output rule.
Mean X
The visible value uses up to 4 decimal places according to the output rule.
Mean Y
The visible value uses up to 4 decimal places according to the output rule.
Cross-deviation sum
The visible value uses up to 4 decimal places according to the output rule.
Pairs
The visible value is displayed without decimal places.

The calculator applies the documented method after validating and normalizing the inputs. Keep the result label, unit, selected mode, and stated limitations together when sharing the answer.

Frequently asked questions

What method does this calculator use?

Sample covariance divides the cross-deviation sum by n - 1; population covariance divides by n.

How should I round the result?

Keep full precision during the calculation and round only the final display unless a governing standard says otherwise.

What is the main limitation?

The result is only as reliable as the inputs and stated method.

Can I reproduce the answer?

Yes. The formula, inputs, supporting outputs and worked example are displayed on the page.

Sources

Source research refreshed September 21, 2026. No rankings, review credentials or official affiliation are implied.