Sample Size Calculator

Statistical Tool

Determine Your Ideal Sample Size

Calculate statistically valid sample sizes for your research study. Our calculator uses standard formulas to ensure your results are reliable and publication-ready.

Cochran
Formula
±5%
Margin
95%
Confidence
Cochran's Formula
n₀ = (Z² × p × q) / e²
n = required sample size
Z = Z-score for confidence level
p = expected proportion (0.5 default)
q = 1 − p
e = margin of error
Recommended Sample Size
385
participants / respondents
10,000
Population
95%
Confidence Level
±5%
Margin of Error
Confidence Level Z-Score Typical Usage
80% 1.282 Pilot / exploratory studies
85% 1.440 Market research
90% 1.645 Social science surveys
95% 1.960 Standard academic research
99% 2.576 Clinical / medical trials
Calculator Inputs
Total number in your target population. Leave blank or enter a large number (100,000+) for unknown populations.
90% 95% 99%
Probability that your sample accurately reflects the population. Standard research uses 95%.
5%
Acceptable deviation in your results. Most research uses ±5%.
Use 50% if unknown - this gives the most conservative (largest) sample size estimate.
Why It Matters

Understanding Sample Size

Proper sample size calculation ensures statistical validity and prevents wasted research resources

Statistical Power

A correctly sized sample ensures your study has enough power to detect true effects and avoid false negatives (Type II errors).

Reduced Sampling Bias

Adequate sample sizes increase the likelihood that your sample represents the broader population accurately.

Cost & Time Efficiency

Avoid costly over-sampling by calculating the minimum valid sample size needed for reliable results.

Journal Compliance

Peer-reviewed journals require documented sample size justification based on established statistical formulas.