Sample Size Calculator
Calculate the sample size needed for statistically valid research
How to Use This Sample Size Calculator
- Select your goal: Find Sample Size or Find Margin of Error
- Choose your confidence level (95% is standard for most research)
- Enter the margin of error you want (typically 3-5% for surveys)
- Set population proportion (use 50% if unknown - most conservative)
- Optionally enter population size for finite population correction
Example: Planning a customer satisfaction survey with 95% confidence and +/-5% margin of error: Using 50% proportion (unknown), you need 385 responses. If your customer base is only 2,000 people, the finite correction reduces this to 323 responses.
Tip: Always plan for non-response by targeting 10-20% more than your calculated sample size.
Why Use a Sample Size Calculator?
Proper sample sizing ensures your research conclusions are statistically valid and worth the investment.
- Plan customer surveys with reliable results
- Design market research studies with adequate statistical power
- Determine minimum subjects needed for academic research
- Calculate whether your existing data has enough responses to draw conclusions
- Balance research precision against time and cost constraints
- Satisfy grant requirements for statistically valid methodology
Understanding Your Results
Larger samples reduce margin of error but cost more. Find the balance for your needs.
| Result | Meaning | Action |
|---|---|---|
| Sample < 100 | Small sample | May have wide margins - consider increasing if feasible |
| Sample 100-500 | Typical survey range | Adequate for most market research and internal surveys |
| Sample 500-1500 | Large survey | Provides narrow margins - common for national polls |
| Sample > 1500 | Very large sample | Diminishing returns - only needed for very precise estimates |
Meaning: Small sample
Action: May have wide margins - consider increasing if feasible
Meaning: Typical survey range
Action: Adequate for most market research and internal surveys
Meaning: Large survey
Action: Provides narrow margins - common for national polls
Meaning: Very large sample
Action: Diminishing returns - only needed for very precise estimates
Note: The +/- percentage in poll results is the margin of error. If 52% +/- 3%, the true value is likely between 49% and 55%.
About Sample Size Calculator
Formula
n = (Z^2 x p x (1-p)) / E^2 Where Z is the z-score for your confidence level (1.96 for 95%), p is population proportion (0.5 if unknown), and E is margin of error as decimal (0.05 for 5%). For finite populations: n' = n / (1 + (n-1)/N).
Current Standards: Z-scores: 90% = 1.645, 95% = 1.960, 99% = 2.576, 99.9% = 3.291. Most research uses 95% confidence with 5% margin of error.
Frequently Asked Questions
Why use 50% for population proportion if I don't know it?
The formula p x (1-p) is maximized when p = 0.5, giving 0.25. Any other proportion gives a smaller product (e.g., 0.3 x 0.7 = 0.21). Using 50% guarantees your sample is large enough regardless of the actual proportion - it's the most conservative choice.
How does confidence level affect sample size?
Higher confidence requires larger samples. Going from 95% to 99% confidence increases sample size by about 70%. Going to 99.9% more than doubles it. Most research uses 95% as a balance between confidence and practicality.
What's the finite population correction?
When your sample is a significant fraction of the population (>5%), you need fewer responses. If 1,000 people exist total and you survey 500, you've already sampled half - the formula adjusts for this. For very large populations, the correction is negligible.
Why don't national polls survey millions of people?
Sample size needed for a given precision is surprisingly small. A sample of 1,000 gives +/-3% margin at 95% confidence whether the population is 1 million or 300 million. Beyond about 1,500, additional responses barely improve precision. The key is random selection, not sheer volume.
How do I account for expected non-response?
Divide your target sample by expected response rate. If you need 400 responses and expect 20% response rate, send to 400/0.20 = 2,000 people. For email surveys, 10-30% is common; phone surveys may be lower. Always plan for more outreach than the minimum calculation shows.