Math July 13, 2026 · 8 Min Read

Sample Size Calculator – Guide & Formulas

Calculate the minimum sample size required for survey research or statistical experiments. Supports margin of error, confidence level, and population values.

Identify the ideal number of respondents or subjects required to achieve target statistical bounds. Balance margin of error, confidence levels, and population size.

Key Takeaway

Use the free Sample Size Calculator to calculate the minimum sample size required for survey research or statistical experiments. supports margin of error, confidence level, and population values. Get instant results with step-by-step explanations.

How to Use the Sample Size Calculator

  1. Enter the known total population size (leave blank or use very large numbers if unknown).
  2. Select your desired Confidence Level (e.g., 90%, 95%, or 99%).
  3. Input the target Margin of Error (standard is 5%).
  4. Input the estimated population proportion (50% is standard for maximum safety).

The Formula

n = (Z^2 * p * (1-p)) / E^2 adjusted by population N

Variable Definitions

  • n: Required minimum sample size
  • Z: Z-score corresponding to selected confidence level
  • p: Estimated sample proportion
  • E: Margin of error (expressed as decimal)
  • N: Total population size

Determining Survey Respondents for a Large Town

Find the minimum sample size needed to survey a town of 100,000 residents with 95% confidence and a 5% margin of error.

  1. Step 1: Set Population N = 100,000.
  2. Step 2: Set Confidence Level = 95% (Z ≈ 1.96).
  3. Step 3: Set Margin of Error = 5% (E = 0.05) and proportion p = 50% (0.50).
  4. Step 4: Compute: (1.96^2 * 0.25) / 0.0025 = 384.16.
  5. Step 5: Adjusted for N, the final target sample size is 383 respondents.

Frequently Asked Questions

Why is 50% used as the default population proportion?

A proportion of 50% (0.5) maximizes the product p * (1 - p), resulting in the most conservative (largest) sample size estimate to guarantee representation.

How does margin of error affect sample size?

The margin of error has an inverse-square relationship with sample size. Halving the margin of error (e.g., from 10% to 5%) quadruples the required sample size.

What is the confidence level?

It indicates the percentage of times the true population parameter would fall within the calculated confidence interval if you took repeated random samples.