Sample Size Calculator

Calculate the required sample size for surveys, experiments, and research studies. Determine statistical power and confidence intervals for reliable results.

Sample Size Parameters

Study Type

Expected Proportion (%)

Margin of Error (%)

Confidence Level

Population Size (Optional)

Quick Examples

Sample Size Guidelines

Descriptive Studies:

30-100 participants for basic descriptive statistics

Correlational Studies:

30+ for small correlations, fewer for large correlations

Experimental Studies:

15-30 per group for medium to large effects

Survey Research:

384+ for large populations with 95% confidence

Required Sample Size

Minimum Sample Size

385

Proportion/Percentage Study

Confidence Level:

95%

Margin of Error:

±5%

Sample Size Analysis

Recommended Sample Size:

385

With 10% Buffer:

424

Accounts for potential dropouts

With 20% Buffer:

462

Conservative estimate for high dropout risk

Calculation Details

Formula Used:

n = (Z²×p×(1-p)) / E²

Z-Score:

1.960 (95% confidence)

How to Use This Calculator

This sample size calculator helps you determine the minimum number of participants needed for your research study to achieve reliable and statistically significant results.

Select your study type from the dropdown menu
Enter the required parameters based on your study design
Choose your desired confidence level (typically 95%)
For experimental studies, specify the expected effect size and desired power
Review the calculated sample size and consider adding a buffer for dropouts

Understanding Sample Size Calculation

Key Concepts

Confidence Level: The probability that your sample accurately represents the population (typically 95%)
Margin of Error: The range of values above and below the sample statistic in a confidence interval
Statistical Power: The probability of detecting an effect if it truly exists (typically 80% or higher)
Effect Size: The magnitude of the difference you expect to find between groups

Factors Affecting Sample Size

Confidence Level: Higher confidence requires larger samples
Margin of Error: Smaller margins require larger samples
Population Variability: More variable populations require larger samples
Effect Size: Smaller effects require larger samples to detect
Statistical Power: Higher power requires larger samples

Study Types

Proportion Studies: Estimate percentages or proportions in a population
Mean Studies: Estimate average values with known population standard deviation
Comparison Studies: Compare means between two groups
Correlation Studies: Detect relationships between variables

Example Calculations

Example 1: Survey Research

You want to estimate the proportion of people who support a policy with 95% confidence and 5% margin of error, expecting about 50% support.

Sample size needed: 384 participants

Example 2: Experimental Study

You're testing a new treatment and expect a medium effect size (Cohen's d = 0.5) with 80% power and 95% confidence.

Sample size needed: 64 participants per group (128 total)

Example 3: Correlation Study

You want to detect a correlation of r = 0.3 with 80% power and 95% confidence.

Sample size needed: 84 participants

Example 4: Mean Estimation

You want to estimate a population mean with a known standard deviation of 10, margin of error of 2, and 95% confidence.

Sample size needed: 97 participants

Frequently Asked Questions

What if I don't know the expected proportion or effect size?

For proportions, use 50% as it gives the largest (most conservative) sample size. For effect sizes, use previous research, pilot studies, or assume a medium effect (0.5) as a starting point.

Should I add extra participants for dropouts?

Yes, it's recommended to add 10-20% extra participants to account for dropouts, non-responses, or data quality issues. The exact percentage depends on your study design and population.

What's the difference between confidence level and statistical power?

Confidence level relates to the precision of your estimate (how confident you are in your results), while statistical power relates to your ability to detect an effect if it exists (avoiding false negatives).