BINOM.DIST.RANGE Formula: Master Binomial Probability Range Calculations in Excel
=BINOM.DIST.RANGE(trials, probability_s, number_s, [number_s2])The BINOM.DIST.RANGE function is a powerful statistical tool in Excel that calculates the probability of obtaining a specific range of successes in a series of independent trials. This advanced formula is particularly valuable for business analysts, quality control specialists, and data scientists who need to assess the likelihood of multiple outcomes in binomial experiments. Whether you're evaluating product defect rates, analyzing customer conversion probabilities, or conducting hypothesis testing, BINOM.DIST.RANGE provides precise probability calculations without requiring manual computation of individual binomial probabilities. Unlike the standard BINOM.DIST function which calculates probability for a single value, BINOM.DIST.RANGE streamlines the process by computing the cumulative probability across a range of successes in one operation. This efficiency makes it ideal for scenarios where you need to determine the probability of achieving between X and Y successful outcomes. Available in Excel 2013 and later versions, this formula has become essential for professionals working with statistical analysis, risk assessment, and predictive modeling in modern business environments.
Syntax & Parameters
The BINOM.DIST.RANGE function follows a straightforward syntax: =BINOM.DIST.RANGE(trials, probability_s, number_s, [number_s2]). The 'trials' parameter represents the total number of independent experiments or observations you're conducting—this must be a positive integer. 'Probability_s' defines the probability of success in each individual trial, expressed as a decimal between 0 and 1 (for example, 0.25 for a 25% success rate). The 'number_s' parameter specifies the minimum number of successes you want to evaluate, serving as the lower boundary of your probability range. The optional 'number_s2' parameter sets the maximum number of successes; if omitted, the formula calculates probability for exactly 'number_s' successes. All parameters must be non-negative integers except probability_s, which must be between 0 and 1. When number_s2 is provided, the formula returns the cumulative probability of achieving between number_s and number_s2 successes (inclusive). This flexibility allows you to answer questions like 'What's the probability of getting between 5 and 10 defects in a batch of 100 items?' without manually summing individual probabilities.
trialsprobability_snumber_snumber_s2Practical Examples
Quality Control: Manufacturing Defect Analysis
=BINOM.DIST.RANGE(50, 0.02, 0, 2)This formula calculates the cumulative probability of finding 0, 1, or 2 defective units in a sample of 50, where each unit has a 2% chance of being defective. The result helps determine if the production process meets quality standards.
Sales Performance: Customer Conversion Success Rate
=BINOM.DIST.RANGE(20, 0.35, 5, 8)This formula evaluates the probability of achieving between 5 and 8 conversions out of 20 calls with a 35% success rate per call. This helps set realistic performance targets and assess team effectiveness.
Medical Testing: Diagnostic Accuracy Assessment
=BINOM.DIST.RANGE(30, 0.92, 27, 30)This formula determines the probability of achieving high accuracy (27-30 correct results out of 30) when the test accuracy is 92%. This helps validate whether the test maintains acceptable performance standards.
Key Takeaways
- BINOM.DIST.RANGE efficiently calculates cumulative binomial probability for a range of successes in a single formula without manual summation
- The function requires four parameters: trials (positive integer), probability_s (decimal 0-1), number_s (minimum successes), and optional number_s2 (maximum successes)
- Available in Excel 2013 and later versions including Excel 365, but not in Google Sheets or LibreOffice Calc natively
- Common errors (#NUM!, #VALUE!, #REF!) are typically caused by invalid parameter ranges, non-numeric values, or incorrect decimal formatting of probability
- Combine BINOM.DIST.RANGE with IF statements, SUM functions, and data validation to create powerful risk assessment and scenario analysis tools
Pro Tips
Always express probability_s as a decimal (0.25 for 25%, not 25). Excel interprets values above 1 as invalid and returns #NUM! error.
Impact : Prevents common formula errors and ensures accurate probability calculations. This is the most frequent mistake when first using the function.
Use named ranges for frequently used parameters (e.g., name 'DefectRate' for 0.02) to create self-documenting formulas that are easier to audit and modify.
Impact : Improves formula readability, reduces errors during updates, and makes your spreadsheet more professional and maintainable.
Create a sensitivity analysis table by varying number_s and number_s2 values to see how probability changes across different success ranges, helping identify optimal thresholds.
Impact : Enables data-driven decision making by visualizing the probability landscape and identifying the most likely outcome ranges.
Combine with data validation to create dropdown lists for trials and probability_s parameters, allowing non-technical users to perform 'what-if' analysis safely.
Impact : Democratizes statistical analysis within your organization and reduces dependency on specialized analysts for routine probability calculations.
Useful Combinations
Risk Assessment with IF Statement
=IF(BINOM.DIST.RANGE(100, 0.05, 0, 5)>0.9, "Low Risk", "High Risk")Combines BINOM.DIST.RANGE with IF to create a risk classification system. If the probability of 0-5 defects out of 100 units exceeds 90%, it classifies the process as 'Low Risk', otherwise 'High Risk'. Useful for automated quality control decisions.
Multiple Scenario Analysis with SUM
=BINOM.DIST.RANGE(50, 0.3, 10, 15) + BINOM.DIST.RANGE(50, 0.3, 20, 25)Calculates the combined probability of two separate success ranges (10-15 or 20-25 successes). This helps assess multiple acceptable outcome scenarios in a single calculation for complex business decisions.
Dynamic Threshold with ROUND and Percentage
=ROUND(BINOM.DIST.RANGE(A2, B2, C2, D2)*100, 2)&"%"Converts BINOM.DIST.RANGE output to a formatted percentage with two decimal places and appends the % symbol. Useful for creating professional reports and dashboards that display probability as readable percentages.
Common Errors
Cause: The probability_s parameter is outside the valid range (not between 0 and 1), or trials is negative, or number_s/number_s2 exceed the trials value.
Solution: Verify that probability_s is expressed as a decimal between 0 and 1 (use 0.5 for 50%, not 50). Ensure trials is a positive integer and that number_s and number_s2 don't exceed trials. Example: =BINOM.DIST.RANGE(50, 0.25, 5, 10) is valid, but =BINOM.DIST.RANGE(50, 1.5, 5, 10) returns #NUM!
Cause: One or more parameters contain non-numeric values, text strings, or improperly formatted data types.
Solution: Ensure all parameters are numeric values. If referencing cells, verify they contain numbers, not text. Convert text to numbers if necessary using VALUE() function. Example: =BINOM.DIST.RANGE(A1, B1, C1, D1) requires A1, B1, C1, D1 to all contain numeric values.
Cause: Cell references in the formula point to deleted cells or invalid ranges, or the formula references cells that no longer exist.
Solution: Check that all cell references are correct and the referenced cells haven't been deleted. Recreate the formula with valid cell references. Use the Name Manager to verify named ranges if applicable. Example: Update =BINOM.DIST.RANGE(A1, B1, C1, D1) if any referenced cell has been removed.
Troubleshooting Checklist
- 1.Verify that probability_s is between 0 and 1 (express as decimal: 0.5 for 50%, not 50)
- 2.Confirm trials is a positive integer with no decimal places
- 3.Ensure number_s and number_s2 are integers and don't exceed the trials value
- 4.Check that number_s ≤ number_s2 (the minimum should not exceed the maximum)
- 5.Verify all cell references are valid and cells contain numeric values, not text
- 6.Test with simple known values first (e.g., =BINOM.DIST.RANGE(10, 0.5, 2, 5)) before applying to complex data
Edge Cases
number_s equals number_s2
Behavior: The formula calculates probability for exactly that single value, equivalent to BINOM.DIST with cumulative=FALSE
Solution: This is valid behavior; the formula correctly returns the probability of exactly X successes
Useful when you need consistency in formula structure even when calculating single-point probabilities
probability_s equals 0 or 1
Behavior: With probability_s=0, only 0 successes is possible (returns 1 if range includes 0, else 0). With probability_s=1, only maximum trials successes is possible.
Solution: These edge cases are mathematically valid; the function handles them correctly
Represents deterministic scenarios where success is impossible (0) or guaranteed (1)
Very large trials value (e.g., 1,000,000)
Behavior: The function may return 0 or 1 due to floating-point precision limitations in extreme distributions
Solution: For very large trial counts, consider using normal distribution approximation with NORM.DIST as an alternative
Binomial distribution approaches normal distribution as trials increase; use normal approximation for computational efficiency with large datasets
Limitations
- •BINOM.DIST.RANGE is only available in Excel 2013 and later versions; users with Excel 2010 or earlier must use alternative approaches with BINOM.DIST summation
- •The function cannot handle non-integer values for trials or success counts; you must round or truncate decimal values before using them as parameters
- •With extremely large trial counts (>100,000) or extreme probability values very close to 0 or 1, floating-point precision may cause results to round to exactly 0 or 1, losing intermediate probability information
- •BINOM.DIST.RANGE assumes independent trials with constant probability; it cannot model dependent events or scenarios where probability changes between trials
Alternatives
Calculates negative binomial distribution, useful when you're interested in the number of trials needed to achieve a specific number of successes rather than the probability of successes in a fixed number of trials.
When: Use when your question is 'How many trials until we get X successes?' instead of 'What's the probability of X successes in N trials?'
Compatibility
✓ Excel
Since 2013
=BINOM.DIST.RANGE(trials, probability_s, number_s, [number_s2])✗Google Sheets
Not available
✗LibreOffice
Not available