What's the difference between VAR.P and VAR.S?

VAR.P calculates variance for an entire population (dividing by n), while VAR.S calculates sample variance (dividing by n-1). Use VAR.P when your data represents all observations you're studying. Use VAR.S when your data is a sample from a larger population. The VAR.S result will always be slightly larger than VAR.P for the same data.

Can VAR.P handle negative numbers?

Yes, absolutely. VAR.P processes negative numbers normally since it squares deviations from the mean. A dataset containing -5, 0, and 5 will calculate variance correctly. The squaring operation ensures negative values contribute positively to variance measurement, which is mathematically correct.

How does VAR.P handle empty cells?

VAR.P automatically ignores empty cells within ranges. If your range A1:A10 contains 7 numbers and 3 empty cells, VAR.P calculates variance using only the 7 numeric values. This automatic handling makes VAR.P robust for real-world datasets with occasional missing values.

What happens if all values in my range are identical?

VAR.P returns 0 when all values are the same, which is mathematically correct. Zero variance indicates no dispersion—every observation equals the mean. This is expected behavior and not an error; it simply reflects perfect uniformity in your data.

Is VAR.P available in Google Sheets and LibreOffice?

Yes, VAR.P is available in Google Sheets with identical syntax. LibreOffice Calc also supports VAR.P. However, always verify compatibility when working across different platforms, as some advanced statistical functions may have minor syntax variations or availability differences.

Master the VAR.P Function: Calculate Population Variance in Excel

Intermediate

=VAR.P(number1, [number2], ...)

The VAR.P function is a fundamental statistical tool in Excel that calculates the variance of an entire population dataset. Unlike VAR.S, which estimates variance from a sample, VAR.P assumes your data represents the complete population and provides an exact variance measurement. This distinction is crucial in statistical analysis, as population variance divides by the total number of observations (n), while sample variance divides by n-1 to account for sampling bias. Understanding when and how to use VAR.P is essential for data analysts, financial professionals, and researchers who need accurate population-level statistical measures. Whether you're analyzing quality control metrics across all production units, evaluating investment portfolio risk for an entire fund, or conducting comprehensive demographic studies, VAR.P delivers precise variance calculations. This function has been available since Excel 2010 and works seamlessly across all modern Excel versions including 365, making it a reliable choice for professional statistical analysis.

Syntax & Parameters

The VAR.P function follows a straightforward syntax: =VAR.P(number1, [number2], ...). The first parameter, number1, is mandatory and represents your primary data range or individual values comprising the population. This can be a single cell range like A1:A100 or multiple non-contiguous ranges. The optional number2 parameter and subsequent parameters allow you to include additional data ranges or individual values, enabling flexibility in data organization. Each parameter accepts numeric values, cell references, ranges, or arrays. Excel automatically ignores logical values (TRUE/FALSE) and text entries within ranges, processing only numeric data. When using multiple ranges, ensure they're separated by commas in most Excel versions. The function calculates variance by determining how far each data point deviates from the mean, squaring those deviations, and averaging them. This mathematical approach provides insight into data dispersion and volatility. Important tip: verify all your data is truly population data, not a sample, before using VAR.P. If analyzing sample data, use VAR.S instead to get statistically valid estimates.

number1

First number or range (population)

number2

Additional numbers or ranges

Optional

Practical Examples

Manufacturing Quality Control Analysis

=VAR.P(B2:B501)

This formula calculates the exact variance of all 500 widget weights in the population. The range B2:B501 contains weight measurements for every single unit produced, representing the complete population rather than a sample.

Investment Portfolio Risk Assessment

=VAR.P(D2:D25)

The manager uses VAR.P instead of VAR.S because they're analyzing the fund's complete 24-month history—the entire population of available data. This provides the true variance for this specific fund period.

Student Test Score Distribution

=VAR.P(E2:E151)

Since this includes every student in the grade level, it represents the complete population. VAR.P calculates how dispersed scores are around the mean score for this entire population.

Key Takeaways

VAR.P calculates exact population variance by dividing the sum of squared deviations by n (total count), making it ideal for complete datasets.
Choose VAR.P for population data and VAR.S for sample data; using the wrong function leads to incorrect statistical conclusions.
VAR.P automatically ignores text, logical values, and empty cells, processing only numeric data within specified ranges.
Population variance is always less than or equal to sample variance for identical data, reflecting the mathematical difference in their denominators.
Combine VAR.P with other functions like AVERAGE, STDEV.P, and IF statements to build comprehensive statistical analysis models.

Pro Tips

Always verify your data represents a true population before using VAR.P. If you're unsure whether data is population or sample, document your assumption clearly for stakeholder communication and audit trails.

Impact : Prevents statistical errors and ensures correct interpretation of variance results, maintaining analytical credibility and decision-making accuracy.

Compare VAR.P results with VAR.S on the same dataset to understand the sampling adjustment. The ratio between them (typically n/(n-1)) reveals how sample size affects variance estimates.

Impact : Deepens statistical understanding and helps identify when sample size is sufficient for reliable statistical inference.

Use named ranges with VAR.P for complex models: =VAR.P(ProductionWeights) instead of =VAR.P(Sheet1!B2:B501). This improves formula readability, reduces errors, and makes maintenance easier.

Impact : Enhances spreadsheet professionalism, reduces formula-related errors, and facilitates collaboration by making intentions explicit.

Combine VAR.P with conditional formatting to highlight when variance exceeds acceptable thresholds. Create visual alerts that flag quality control issues or portfolio risk levels automatically.

Impact : Enables proactive monitoring and faster response to statistical anomalies, improving operational efficiency and risk management.

Useful Combinations

Variance with Conditional Logic

=VAR.P(IF(C2:C101>50,B2:B101))

This array formula calculates population variance only for rows where column C values exceed 50. Enter with Ctrl+Shift+Enter in older Excel versions. Useful for analyzing variance within specific data segments without creating helper columns.

Variance Coefficient of Variation

=SQRT(VAR.P(A1:A100))/AVERAGE(A1:A100)*100

Combines VAR.P with SQRT and AVERAGE to calculate the coefficient of variation—variance expressed as a percentage of the mean. This normalized metric allows comparison of variance across datasets with different scales.

Variance with Data Validation

=IF(COUNT(A1:A50)<2,"Insufficient Data",VAR.P(A1:A50))

Wraps VAR.P in an IF statement that checks for minimum data requirements before calculating. Returns a meaningful message if fewer than 2 numeric values exist, improving error handling and user experience.

Common Errors

#VALUE!

Cause: The range contains text values, dates formatted as text, or logical operators that Excel cannot convert to numbers. For example: =VAR.P(A1:A10) where A5 contains 'N/A' or a formula error.

Solution: Clean your data by removing or replacing text entries. Use IFERROR to handle problematic cells: =VAR.P(IFERROR(A1:A10,NA())). Alternatively, manually exclude non-numeric cells or use helper columns to convert text numbers to actual numbers.

#DIV/0!

Cause: This error typically occurs when VAR.P receives fewer than 2 data points or when all values in the range are identical, though VAR.P usually returns 0 in the latter case rather than #DIV/0!.

Solution: Verify your range contains at least 2 numeric values. Check for empty cells or hidden rows that might reduce your effective data count. Use COUNTA to verify data presence: =IF(COUNTA(A1:A10)<2,'Insufficient data',VAR.P(A1:A10)).

#REF!

Cause: The formula references a deleted range or uses incorrect range syntax. For example: =VAR.P(A1:A10 B1:B10) with missing comma, or referencing a deleted sheet.

Solution: Verify all ranges are separated by commas: =VAR.P(A1:A10,B1:B10). Check that referenced sheets still exist. Use the Name Manager to verify named ranges are valid. Re-enter the formula carefully, using the mouse to select ranges.

Troubleshooting Checklist

1.Verify all data is numeric by checking cell formats (should be Number, not Text) and using ISNUMBER() to test individual cells
2.Confirm your data represents the complete population, not a sample; if uncertain, use VAR.S instead and document your choice
3.Check for hidden rows or columns that might affect your range; unhide all data and recalculate to verify results
4.Ensure range references use correct syntax with commas separating multiple ranges: =VAR.P(A1:A10,C1:C10) not =VAR.P(A1:A10 C1:C10)
5.Verify minimum data requirement of at least 2 numeric values; use COUNT() to confirm: =COUNT(A1:A100) should return ≥2
6.Test with a small known dataset to validate formula logic; manually calculate variance for 3-4 values and compare with VAR.P result

Edge Cases

Range contains a single numeric value

Behavior: VAR.P returns #DIV/0! error or 0 depending on Excel version, as variance requires at least 2 data points

Solution: Add validation to check COUNT before calculating: =IF(COUNT(range)<2,"Error: Need 2+ values",VAR.P(range))

This is mathematically correct since variance is undefined with only one observation

Range contains only zeros

Behavior: VAR.P correctly returns 0, indicating no variance from the mean (which is also 0)

This is expected behavior; zero variance with zero mean is mathematically valid and represents perfect uniformity

Range contains extremely large numbers (scientific notation)

Behavior: VAR.P may experience precision loss or return results in scientific notation; calculation remains mathematically valid but display may be unclear

Solution: Format cells as Number with appropriate decimal places, or use scientific notation formatting if displaying results

Excel maintains internal precision even when display shows scientific notation; actual calculations remain accurate

Limitations

•VAR.P requires truly population data; misidentifying sample data as population leads to underestimated variance and incorrect statistical conclusions about variability
•The function ignores text and logical values automatically, which can silently reduce your effective sample size if data cleaning is incomplete; always verify COUNT of numeric values matches expectations
•VAR.P cannot handle non-numeric data types like dates stored as text; dates must be formatted as actual date values for inclusion in calculations
•The function provides variance in squared units of the original data, which can be difficult to interpret; consider using STDEV.P or calculating coefficient of variation for more intuitive results

Alternatives

VAR.S Function

Calculates sample variance using n-1 denominator, providing unbiased estimates for sample data with automatic degrees-of-freedom adjustment.

When: When analyzing a representative sample from a larger population or when you want to estimate population parameters from sample data.

STDEV.P Function

Calculates population standard deviation (square root of population variance), providing results in original data units rather than squared units.

When: When you need variance expressed as standard deviation for easier interpretation and comparison with data measured in original units.

Manual Calculation with SUMPRODUCT

Offers maximum flexibility and transparency by calculating variance step-by-step, allowing custom handling of outliers or conditional variance.

When: When you need to exclude specific values, apply conditional logic, or require complete visibility into the calculation process for audit purposes.

Compatibility

✓ Excel

Since 2010

=VAR.P(number1,[number2],...) - Available in Excel 2010, 2013, 2016, 2019, and 365 with identical syntax

✓Google Sheets

=VAR.P(value1,[value2],...) - Fully compatible with Google Sheets using same syntax

Google Sheets treats VAR.P identically to Excel; array formulas use standard Ctrl+Shift+Enter or ARRAYFORMULA() function

✓LibreOffice

=VAR.P(number1,[number2],...) - LibreOffice Calc supports VAR.P with full compatibility to Excel syntax

Frequently Asked Questions

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