Sample Size Calculator for Population Proportion

Calculate the required sample size for estimating a population proportion based on confidence level, estimated proportion, and margin of error.

Calculate the required sample size for estimating a population proportion based on confidence level, estimated proportion, and margin of error. Enter your Z-score (Z), Estimated Proportion (p), Margin of Error (E) to get an instant required sample size (n). Formula: round((z * z * p * (1 - p)) / (e * e), 0).

Z value corresponding to desired confidence level (e.g., 1.96 for 95%)
Expected population proportion as a decimal (e.g., 0.5)
Desired margin of error as a decimal (e.g., 0.05)

Required Sample Size (n)

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Required Sample Size (n)

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How It Works

How It Works

This calculator estimates how many respondents you need to accurately measure a population proportion. It uses your chosen confidence level (Z-score), expected proportion (p), and desired margin of error (E) to determine the minimum sample size required.

  • The Z-score reflects your confidence level (e.g., 1.96 for 95% confidence).
  • The estimated proportion (p) is your best guess of the population percentage.
  • The margin of error (E) shows how precise you want your results to be.
  • The formula calculates the minimum number of respondents needed.
  • The result is rounded to the nearest whole number.

Understanding the Results

The result shows the minimum number of respondents required to achieve your desired confidence level and precision. A larger sample size increases accuracy but may require more time and resources.

  • Higher confidence levels increase the required sample size.
  • Smaller margins of error require larger samples.
  • If you are unsure about p, using 0.5 gives a conservative (larger) estimate.
  • The output is the number of respondents you should survey.

Disclaimer

This calculator provides estimates for informational purposes only. It is not professional advice. Verify results with a qualified professional. Disclaimer.

Created by CalcLearn Team Reviewed for accuracy Last updated: Apr 19, 2026

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