Master the COVAR Function: Complete Guide to Calculating Covariance in Excel
=COVAR(array1, array2)The COVAR function is a statistical tool in Excel that measures the covariance between two data arrays, helping you understand how two variables move together. Covariance is a fundamental concept in statistics and finance, indicating whether two datasets tend to increase or decrease together. When covariance is positive, the variables move in the same direction; when negative, they move in opposite directions. This function is particularly valuable for financial analysts, researchers, and data scientists who need to assess relationships between variables such as stock prices and market indices, or sales figures and marketing expenses. The COVAR function was introduced in Excel 2007 and has been a staple for statistical analysis. However, it's important to note that this function is considered legacy in modern Excel versions (2010 and later), as Microsoft introduced COVARIANCE.P and COVARIANCE.S as more explicit alternatives. Understanding COVAR remains essential for working with older spreadsheets and maintaining compatibility across different Excel versions. This comprehensive guide will walk you through the syntax, practical applications, and best practices for using COVAR effectively in your data analysis projects.
Syntax & Parameters
The COVAR function uses a straightforward two-parameter syntax: =COVAR(array1, array2). The first parameter, array1, represents the first data range or dataset you want to analyze. This must be a continuous range of cells containing numerical values. The second parameter, array2, is the second data range that you're comparing against the first array. Both parameters are required, and both arrays must contain the same number of data points for the function to calculate correctly. When you use COVAR, Excel calculates the average deviation of each point in array1 from its mean, multiplies it by the average deviation of the corresponding point in array2 from its mean, and then averages these products. The result is a single number representing the covariance. It's crucial to ensure that both arrays have identical lengths; if they don't, Excel will return a #N/A error. Additionally, COVAR treats the data as a population covariance (similar to COVARIANCE.P), meaning it divides by n rather than n-1. For sample covariance calculations, you should use COVARIANCE.S instead. The function ignores empty cells, text values, and logical values within your arrays, automatically filtering them out during calculation.
array1array2Practical Examples
Stock Performance Analysis
=COVAR(B2:B13, C2:C13)B2:B13 contains Company A's monthly stock prices ranging from $45 to $68, while C2:C13 contains the corresponding market index values from 2500 to 2750. The COVAR function calculates how these two variables move together over the year.
Marketing Spend vs Sales Revenue
=COVAR(D2:D7, E2:E7)D2:D7 contains monthly marketing budgets ($5,000 to $15,000), and E2:E7 contains corresponding monthly sales revenue ($50,000 to $180,000). This analysis reveals whether increased marketing spending correlates with higher sales.
Temperature vs Ice Cream Sales
=COVAR(F2:F11, G2:G11)F2:F11 contains daily temperatures in Fahrenheit (72°F to 92°F), and G2:G11 contains corresponding daily ice cream sales in units (120 to 450 units). This helps the business understand seasonal demand patterns.
Key Takeaways
- COVAR calculates population covariance between two arrays, indicating how variables move together directionally and magnetically
- Both arrays must have identical lengths; mismatched dimensions return #N/A error, requiring data validation before formula application
- COVAR is legacy in Excel 2010+; use COVARIANCE.P for population or COVARIANCE.S for sample data in modern spreadsheets
- Covariance values lack standardization; combine with STDEV to calculate correlation coefficient for better interpretability across datasets
- COVAR ignores empty cells and text values automatically, but ensure arrays are clean and contain primarily numerical data for accurate results
Pro Tips
Always verify array dimensions before applying COVAR. Use the Name Manager to create named ranges for both arrays, making formulas more readable and reducing reference errors.
Impact : Prevents #N/A errors and makes spreadsheets more maintainable. Named ranges automatically adjust when data is inserted or deleted within the defined range.
Use COVARIANCE.S instead of COVAR for sample data analysis. The n-1 denominator provides statistically unbiased estimates crucial for accurate hypothesis testing and confidence intervals.
Impact : Improves statistical accuracy and validity of conclusions drawn from sample data. Prevents systematic underestimation of population variance.
Combine COVAR with correlation analysis using PEARSON function to get both raw covariance and standardized correlation. This dual approach provides complete relationship insights.
Impact : Enables comprehensive understanding of both the magnitude and strength of variable relationships, supporting better decision-making in financial and business analysis.
Document the source and meaning of covariance results in adjacent cells using formulas like =COVAR(A2:A11, B2:B11) with descriptive labels. Add comments explaining whether values represent population or sample data.
Impact : Enhances spreadsheet clarity and prevents misinterpretation of results. Makes spreadsheets more professional and audit-ready for compliance requirements.
Useful Combinations
Covariance with AVERAGE for Normalized Analysis
=COVAR(A2:A11, B2:B11) / (STDEV(A2:A11) * STDEV(B2:B11))This combination calculates the correlation coefficient by dividing covariance by the product of standard deviations. This standardizes the relationship measure to a -1 to 1 scale, making it more interpretable and comparable across different datasets. Useful for comprehensive statistical analysis.
COVAR with IF for Conditional Analysis
=COVAR(IF(C2:C11>100, A2:A11), IF(C2:C11>100, B2:B11))This array formula calculates covariance only for rows where a condition is met (e.g., values in column C exceed 100). Enter with Ctrl+Shift+Enter in older Excel versions. Enables segmented analysis of relationships within specific data subsets, useful for conditional statistical studies.
COVAR with OFFSET for Dynamic Range Analysis
=COVAR(OFFSET($A$1, 0, 0, COUNTA($A:$A)-1, 1), OFFSET($B$1, 0, 0, COUNTA($B:$B)-1, 1))This combination uses OFFSET to create dynamic ranges that automatically adjust when new data is added. The formula expands or contracts based on the number of non-empty cells in each column, eliminating the need to manually update range references when datasets grow.
Common Errors
Cause: The two arrays have different lengths. For example, =COVAR(A1:A10, B1:B12) attempts to compare a 10-cell range with a 12-cell range.
Solution: Ensure both arrays contain exactly the same number of cells. Verify the row counts before entering the formula. Use =COVAR(A1:A10, B1:B10) with matching dimensions.
Cause: One or both arrays contain non-numeric values that cannot be ignored, such as text strings mixed with numbers in a way that prevents calculation.
Solution: Check both arrays for text values, special characters, or formatting issues. Clean the data by removing non-numeric entries or converting them to numbers. Ensure cells contain only numerical data or empty cells.
Cause: Rarely occurs with COVAR, but can happen if both arrays contain only a single value or if calculation parameters are invalid.
Solution: Verify that each array contains at least two data points. Check that neither array is empty. Ensure the data range references are correct and point to actual numerical values.
Troubleshooting Checklist
- 1.Verify both arrays contain exactly the same number of data points by counting rows or using COUNTA function
- 2.Check that both arrays contain numerical values; convert text-formatted numbers to actual numbers using VALUE function
- 3.Ensure neither array is completely empty; COVAR requires at least two data points in each array
- 4.Confirm array references are absolute ($A$1:$A$10) if copying formulas to prevent reference shifting
- 5.Test with a simple known dataset to verify COVAR is calculating correctly before applying to complex data
- 6.Use Find & Replace to remove any hidden characters, spaces, or formatting issues that might prevent recognition of numerical values
Edge Cases
One array contains all identical values (no variance)
Behavior: COVAR returns 0, as there is no deviation from the mean in that array, resulting in zero covariance regardless of the other array's values
Solution: This is mathematically correct. If you need to identify such cases, add a check using VAR or STDEV to detect zero-variance arrays before analysis
This edge case is valid and expected behavior, not an error
Arrays contain very large numbers (millions or billions) that exceed typical data ranges
Behavior: COVAR calculates correctly but may display in scientific notation. Results may have reduced precision due to floating-point arithmetic limitations
Solution: Format cells to display appropriate decimal places. Consider scaling data (dividing by 1000 or 1,000,000) before calculation, then scaling results back
Excel handles large numbers but precision decreases with magnitude
Arrays contain negative numbers, zeros, or mix of positive and negative values
Behavior: COVAR handles all value types correctly, producing positive, negative, or zero results based on directional relationship. Negative covariance indicates inverse relationships
This is normal behavior. Negative covariance is valid and indicates variables move in opposite directions
Limitations
- •COVAR calculates population covariance (dividing by n) rather than sample covariance (n-1), making it less suitable for statistical inference without adjustment. Use COVARIANCE.S for sample data analysis.
- •Covariance values are not standardized and difficult to interpret in isolation. Magnitude depends on data scale, making comparison across different datasets problematic. Convert to correlation coefficient for better interpretability.
- •COVAR requires both arrays to have identical lengths; it cannot handle mismatched dimensions or perform partial correlations. Complex analyses may require data restructuring or alternative functions.
- •The function ignores text and empty cells automatically, which can mask data quality issues. Dirty data with mixed types may produce misleading results without proper validation and cleaning beforehand.
Alternatives
Modern equivalent with clearer naming convention indicating population covariance. Identical functionality to COVAR with better readability and future-proof compatibility.
When: Use in Excel 2010 and later versions when analyzing entire population datasets. Recommended for all new spreadsheets and projects.
Calculates sample covariance using n-1 denominator, providing unbiased estimates for sample data. More appropriate for statistical inference and hypothesis testing.
When: Use when working with sample data from larger populations. Essential for academic research, market surveys, and quality control analysis.
Calculates correlation coefficient, a standardized measure of relationship strength ranging from -1 to 1. More interpretable and comparable across different datasets.
When: Use when you need to compare relationship strengths across multiple variable pairs or when standardized metrics are required for reporting.
Compatibility
✓ Excel
Since 2007
=COVAR(array1, array2) - Available in Excel 2007, 2010. Considered legacy in 2013 and later; COVARIANCE.P recommended as modern replacement.✓Google Sheets
=COVAR(array1, array2) - Fully supported with identical functionality and syntaxGoogle Sheets also supports COVARIANCE.P and COVARIANCE.S. COVAR works seamlessly when importing Excel files to Google Sheets.
✓LibreOffice
=COVAR(array1, array2) - Fully supported in LibreOffice Calc with identical functionality to Excel