Sample Size Calculator
Calculate the minimum sample size needed for statistically valid survey results. Determine respondents required for customer surveys, QA inspection, A/B testing, and market research at your desired confidence level and margin of error.
Calculate the minimum sample size needed for statistically valid survey results. Enter your confidence level, acceptable margin of error, and expected response proportion. Optionally provide population size for finite population correction.
Expected % of respondents with characteristic (50% if unknown)
For finite population correction
Formula
n = (z² × p × (1-p)) / e² | With FPC: n' = (n × N) / (n + N - 1)
The first formula calculates the required sample size where z is the z-score for your confidence level, p is the expected proportion (0.5 if unknown), and e is the margin of error as a decimal. The second formula applies finite population correction (FPC) when you know your population size (N), resulting in a smaller required sample size. Use this when your population is finite and relatively small compared to your sample.
Worked Examples
Example 1: Customer Satisfaction Survey (Unknown Response Rate)
Confidence Level: 95% (z=1.96)
Margin of Error: ±5%
Expected Proportion: 50% (unknown response characteristic)
Calculation: (1.96² × 0.5 × 0.5) / 0.05² = 384 respondents
A sample of 384 customers will give you 95% confidence that your satisfaction score is accurate to within ±5 percentage points.
Example 2: QA Inspection with Finite Population
Population Size: 5,000 units
Confidence Level: 95% (z=1.96)
Margin of Error: ±3%
Expected Defect Rate: 10%
Base Formula: (1.96² × 0.1 × 0.9) / 0.03² = 384.16
With FPC: (384.16 × 5000) / (384.16 + 4999) = 378 units
Finite population correction saves 6 units. For very large populations, the correction approaches zero.
Example 3: A/B Test with High Confidence
Confidence Level: 99% (z=2.576)
Margin of Error: ±2%
Expected Conversion: 50%
Calculation: (2.576² × 0.5 × 0.5) / 0.02² = 4,148 visitors
Higher confidence and tighter margins require larger samples. This test needs 4,148 visitors per variant for statistical reliability.
Common Mistakes
- 1.Using 100% confidence level. There is no such thing as 100% confidence in statistics. Use 99% for mission-critical decisions (most conservative), 95% for standard business decisions, or 90% for exploratory research. Higher confidence requires larger samples.
- 2.Confusing margin of error with confidence level. Margin of error is how close your result is to the true population value (±5% means answer is within 5 points). Confidence level is how certain you are that the true value falls within that margin (95% means 95 out of 100 similar surveys would capture the true value).
- 3.Forgetting response rate when distributing surveys. If you need 384 completed surveys but expect only 50% response rate, you must send 768 survey invitations. Sample size calculators give you responses needed, not invitations to send.
- 4.Using wrong expected proportion. The 50% default (most conservative) maximizes required sample size. If you know your population has specific characteristics (e.g., you know 20% typically respond "yes"), use 20% to get a smaller sample. Unknown = use 50%.
- 5.Ignoring finite population correction for small populations. If your population is small (e.g., 100 customers, 1,000 employees), always enter the population size. FPC can significantly reduce required sample size for small, finite populations.
Frequently Asked Questions
How to use this calculator
Enter your confidence level (90%, 95%, or 99%), acceptable margin of error (typically 3-5% for business surveys), and expected response proportion (use 50% if unknown). Optionally provide your population size for finite population correction, which reduces required sample when surveying defined populations. The calculator determines the minimum respondents needed for statistically valid results. Remember to account for expected response rates when determining how many people to contact.
When to use this calculator
- →Planning customer satisfaction, NPS, or feedback surveys to determine how many responses you need
- →QA and quality inspection to decide how many units to inspect for statistical confidence
- →A/B testing and conversion rate optimization to calculate required traffic per variant
- →Market research and focus groups to determine interview or participant requirements
- →Scientific studies and healthcare research requiring minimum respondent numbers for validity
Key Statistics in Sample Size Planning
Understanding these terms helps you choose appropriate settings.
Confidence Level
The probability your sample result reflects the true population value. 95% confidence is standard business practice (95 out of 100 similar surveys would capture the true value). 90% is used for exploratory research (smaller sample, less certainty). 99% for mission-critical decisions (larger sample, maximum certainty).
Margin of Error
How close your result is to the true population value. ±5% is standard for business surveys (±3% more precise but requires larger sample, ±10% less precise but needs fewer respondents). Always report both: "73% approval ±5% confidence" means true value is between 68-78%. Smaller margin = larger sample required.
Expected Proportion
The expected percentage of respondents with your characteristic of interest (e.g., "% who will buy", "% satisfied", "% defective units"). Use 50% if unknown (most conservative, maximizes sample size). If you know 30% typically respond "yes", use 30% to reduce sample size requirements.
Finite Population Correction
Applied when surveying a defined, finite population (e.g., your 5,000 employees, 10,000 customers). Reduces required sample size compared to infinite population assumption. Most valuable for small populations or when sample exceeds 5% of population size. Negligible for large populations (national surveys).
Business use cases
Customer Surveys
Determine respondents needed for satisfaction surveys. For 10,000 customers, 95% confidence, ±5% margin: ~370 responses (after FPC) validates your results and drives improvements.
QA & Inspection
Calculate inspection samples for manufacturing or inventory control. Inspecting 370 of 10,000 units (after FPC) at 95% confidence gives you statistically valid defect rate estimates.
A/B Testing
Determine traffic per variant needed for conversion rate tests. Testing a 10% conversion with ±2% margin at 95% confidence requires ~2,000 visitors per variant.
Market Research
Plan focus groups or interview studies. Need confidence in market demand estimates? 95% confidence with ±5% margin requires ~384 respondents, ensuring research validity.
Employee Surveys
For 500 employees, 95% confidence, ±5% margin: ~218 responses. Ensures representative feedback and statistically valid engagement metrics.
Compliance & Audit
Regulatory requirements often specify confidence and error margins. Use this calculator to justify sample sizes for audits, inspections, or compliance verification.
Survey Planning Tips
Best practices for converting sample size to actual responses.
Calculate sample size first
Use this calculator to determine exact respondents needed for your confidence and accuracy requirements.
Factor in response rate
If you need 384 responses and expect 50% response rate, send 768 invitations. Account for opt-out, non-completion, and attrition.
Apply stratification if needed
For diverse populations (age groups, regions, departments), allocate samples proportionally or apply stratified sampling for better representation.
Use finite population correction
Always enter population size if you know it. Even for moderately sized populations (1,000-10,000), this reduces required sample meaningfully.
Collect a bit more if possible
Build in 10-20% buffer for incomplete responses, data quality issues, or analysis needs. 422 responses instead of 384 provides extra confidence.