BINOM.DIST.RANGE Function
Calculate binomial distribution probabilities over a range with BINOM.DIST.RANGE. Learn syntax, examples, and statistical applications.
=BINOM.DIST.RANGE(trials, probability_s, number_s, [number_s2])Quick Answer
BINOM.DIST.RANGE function BINOM.DIST.RANGE function calculates the probability of achieving a specific range of successes in a fixed number of independent trials with constant success probability. Essential for quality control, marketing analysis, and risk assessment.
=BINOM.DIST.RANGE(trials, probability_s, number_s, [number_s2])Practical BINOM.DIST.RANGE Examples
Quality Control: Defect Rate Analysis
Manufacturing quality control checking acceptable defect range in product batch
Marketing: Email Campaign Success Rate
Predicting email open rate range for campaign planning
Clinical Trials: Treatment Success Range
Evaluating probability of treatment success within acceptable range
Finance: Loan Default Probability Range
Risk assessment for loan portfolio default rate forecasting
Exact Probability: Single Outcome Analysis
Calculate probability for specific number of successes (omitting number_s2)
Common BINOM.DIST.RANGE Errors and Solutions
BINOM.DIST.RANGE returns #NUM! error
Most commonly occurs when: (1) probability_s is not between 0 and 1, (2) trials is negative, (3) number_s or number_s2 are negative or greater than trials, or (4) number_s2 is less than number_s. This error indicates that one or more parameters violate the mathematical constraints of the binomial distribution.
1. Verify probability_s is between 0 and 1 inclusive (use MIN/MAX functions to constrain if needed) 2. Ensure trials is a non-negative integer (use ROUND or INT if working with calculated values) 3. Check that 0 <= number_s <= number_s2 <= trials 4. Use ISNUMBER() to validate inputs before calculation 5. For percentage inputs, divide by 100 (e.g., 5% should be 0.05, not 5) 6. Add input validation: =IF(OR(B2<0, B2>1), "Invalid Probability", BINOM.DIST.RANGE(A2,B2,C2,D2))
Create data validation rules for input cells: probability between 0 and 1, trials as positive integers, and logical ordering of success counts. Use dropdown lists for common probability values.
Example:
BINOM.DIST.RANGE returns #VALUE! error
Arguments contain non-numeric values, text strings, or cell references to text. Excel cannot perform calculations on text data even if it looks like a number. This often occurs with imported data where numbers are stored as text, cells containing formulas that return text, or cells with hidden formatting characters.
1. Check all referenced cells contain numbers, not text (look for left-aligned numbers, which indicate text) 2. Use VALUE() function to convert text numbers to numeric values: =BINOM.DIST.RANGE(VALUE(A2), VALUE(B2), VALUE(C2), VALUE(D2)) 3. Verify no hidden characters or spaces in cells using CLEAN() or TRIM() functions 4. Use ISNUMBER() to test if inputs are numeric: =IF(AND(ISNUMBER(A2), ISNUMBER(B2), ISNUMBER(C2)), BINOM.DIST.RANGE(...), "Invalid type") 5. Check for dates or times formatted as numbers—these may cause unexpected results 6. Re-type values directly into cells if import formatting is problematic
Format input cells as Number before entering data. When importing data, use Text to Columns feature to convert text numbers to actual numbers. Build validation formulas that test data types before performing calculations.
Example:
Function returns unexpected probability value or counterintuitive results
Logic error in parameter order or misunderstanding of range boundaries. Common mistakes include: (1) swapping trials and probability_s positions, (2) using number_s2 as exclusive upper bound instead of inclusive (thinking 3 to 7 means 3 to 6), (3) expecting cumulative probability from 0 instead of from number_s, (4) entering probability as percentage (30) instead of decimal (0.3), or (5) confusion about whether endpoints are included in the range.
1. Double-check parameter order: trials first, then probability, then lower bound, then upper bound 2. Remember number_s2 is INCLUSIVE (range 3 to 7 includes both 3 and 7, giving 5 values total) 3. Verify probability_s is decimal (0.3) not percentage (30) 4. For cumulative probability from 0 to X, use: =BINOM.DIST.RANGE(trials, prob, 0, X) 5. Validate expected value: trials × probability should equal approximate midpoint of range 6. Test with known scenarios: =BINOM.DIST.RANGE(100, 0.5, 50, 50) should give ~0.08 (probability of exactly 50 heads in 100 coin flips) 7. Cross-check results using BINOM.DIST for verification
Use named ranges or clearly labeled cell references to avoid parameter confusion. Create a helper column showing expected value (trials × probability) to validate that your range makes sense. Document what each parameter represents in adjacent cells for complex models.
Example:
BINOM.DIST.RANGE Best Practices and Advanced Tips
Efficient Range Probability Calculation
BINOM.DIST.RANGE is significantly more efficient than summing multiple BINOM.DIST calculations. For a range of 10 values, you save 10 formula cells and improve calculation speed by approximately 5x. This efficiency gain becomes critical in large financial models or Monte Carlo simulations with thousands of probability calculations.
Dynamic Confidence Intervals
Combine BINOM.DIST.RANGE with standard deviation calculations to create dynamic confidence intervals for binomial distributions. Calculate the expected value as trials × probability_s, then calculate standard deviation as SQRT(trials × probability_s × (1-probability_s)). For approximately 95% confidence, use expected value ± 2 standard deviations.
Large Sample Size Considerations
For very large trials (n > 1000) with moderate probability values (0.1 < p < 0.9), consider using normal approximation methods instead of BINOM.DIST.RANGE. The function becomes computationally expensive for large samples and may experience precision limitations.
Complement Probability Shortcut
To find the probability OUTSIDE a range (fewer than X or greater than Y), calculate 1 minus the probability INSIDE the range. This is more intuitive and less error-prone than calculating two separate tail probabilities and adding them together.
Wrap in IFERROR for Production Spreadsheets
Always wrap BINOM.DIST.RANGE in IFERROR when building templates or shared workbooks. This prevents #NUM! and #VALUE! errors from disrupting calculations when users enter invalid parameters. Provide user-friendly error messages to guide corrections.
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Example Excel formula:
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