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.

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Put these formulas into practice with our instant, step-by-step Sample Size Calculator.

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Use our free **sample size calculator** to **determine the minimum number of respondents** needed for survey research or statistical experiments. This **sample size calculator** factors in **confidence level**, **margin of error**, and **population size** to give you accurate results. Whether you need to **calculate sample size for a poll**, **plan a research study**, or **set survey parameters**, this tool provides reliable results. 100% free — no signup required!

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).
  5. Review the calculated minimum sample size and the adjustment for finite population.
  6. Compare results across different confidence levels to find your optimal balance.
  7. Copy or save your sample size calculation for your research plan.

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

What is a sample size calculator?

A sample size calculator determines the minimum number of respondents or observations needed for a survey or experiment to achieve a desired margin of error and confidence level.

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.

Is this sample size calculator free to use?

Yes, this sample size calculator is 100% free with no signup required. Use it unlimited times for survey planning and research design.

What is the minimum sample size for a reliable survey?

A minimum of 383 respondents is generally needed for a large population at 95% confidence with a 5% margin of error. For smaller populations, the calculator adjusts downward.

Who should use this sample size calculator?

This calculator is ideal for market researchers, academic researchers, pollsters, business analysts, and students planning surveys or experiments that require statistically valid sample sizes.

What happens if my sample size is too small?

A sample that is too small will have a large margin of error, making results unreliable and potentially misleading. Your findings may not represent the true population characteristics.

How do I account for non-response in my sample size?

Multiply your calculated sample size by (1 / expected response rate). For example, if you expect a 60% response rate, multiply your required sample by 1.67 to ensure enough completed responses.

How does confidence level affect the required sample size?

Higher confidence levels require larger samples. Moving from 95% to 99% confidence increases the sample size by approximately 30%, because you need more data to be more certain of your results.