Sample Size Calculator

Determine optimal sample sizes for surveys and research

A sample size calculator helps researchers determine how many participants are needed in a survey or experiment to obtain statistically significant results. Our calculator considers confidence level, margin of error, population size, and response distribution to provide accurate sample size recommendations for your study.

Calculate Sample Size

Use 50% for maximum variability (recommended)

Calculate Margin of Error

Use 50% for maximum variability (recommended)

Sample Size Formulas

For Infinite Population (Unknown Population Size):

n = (Z² × p × (1-p)) / e²

  • n = sample size
  • Z = Z-score (based on confidence level)
  • p = response distribution (0.5 for maximum variability)
  • e = margin of error (as decimal, e.g., 0.05 for 5%)

For Finite Population (Known Population Size):

n = [ (Z² × p × (1-p)) / e² ] / [ 1 + ( (Z² × p × (1-p)) / (e² × N) ) ]

or the adjusted formula:

nₐ = n / (1 + (n - 1)/N)

  • N = population size
  • n = sample size from infinite formula
  • nₐ = adjusted sample size

Margin of Error Formula:

e = Z × √( p × (1-p) / n )

Common Z-Scores:

Confidence Level Z-Score
99% 2.576
95% 1.96
90% 1.645
80% 1.28

How to Determine Sample Size

Key Factors in Sample Size Calculation:

  • Confidence Level: How confident you need to be that the results reflect the views of the population (typically 90%, 95%, or 99%)
  • Margin of Error: The acceptable amount of error in your results (typically 3%, 5%, or 10%)
  • Population Size: The total number of people in the group you're studying (often unknown)
  • Response Distribution: The expected distribution of responses (50% gives the most conservative estimate)

Recommended Sample Sizes:

Population Size Margin of Error 5% Margin of Error 3% Margin of Error 1%
100 80 92 99
500 217 341 475
1,000 278 516 906
10,000 370 964 4,900
100,000+ 384 1,056 9,513

Practical Considerations:

  • For national surveys with large populations, sample sizes between 1,000-1,500 are often sufficient
  • For specialized populations or rare characteristics, larger samples may be needed
  • Consider response rates - if you expect a 30% response rate, you'll need to invite more participants
  • Balance statistical requirements with practical constraints like budget and time

Common Applications:

  • Market Research: Determining how many customers to survey
  • Academic Research: Planning study participant numbers
  • Political Polling: Calculating representative sample sizes
  • Quality Control: Determining inspection sample sizes
  • Healthcare Studies: Planning clinical trial participant numbers