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Sample Size Calculator

Use this sample size calculator to summarize a data set for sample size. The page returns required sample size plus supporting values for adjusted sample size, unadjusted sample size, and z critical value; check.

Primary answer
Required sample size
Inputs to verify
Confidence level, Margin of error, and Estimated proportion
Use type
Use as an estimate that depends on assumptions.
Keyword intent
sample size calculator

Calculator

Sample Size Calculator

Calculates required sample size from confidence level, margin of error, estimated proportion. Defaults are filled in so you can review a working example before changing inputs.

Choose the two-sided confidence level for the proportion estimate.

%

Enter the desired half-width in percentage points; 5 means 5%, not 0.05.

%

Use 50% when there is no prior estimate; it gives the most conservative sample size.

Enter an integer population size for finite population correction, or 0 to ignore it.

Result

Result reflects the current submitted inputs.

  • Risk B
  • Reviewed 2026-05-26
  • 2 sources
Required sample size385 observations
Adjusted sample size384.1459 observations
Unadjusted sample size384.1459 observations
z critical value1.959964
Margin of error5%
Estimated proportion50%

Breakdown

Confidence level
95%
Estimated proportion
0.5
Margin of error
0.05
Population size
not applied
  • This calculator estimates sample size for one population proportion.
  • Percent inputs are entered as percent values; 5 means 5%, not 0.05.
  • The normal approximation is used for planning the confidence interval margin of error.
  • Population size 0 means the finite population correction is ignored.
  • Design effects, clustering, nonresponse, and power analysis are out of scope.

Accuracy notes

Risk level
B
Reviewed
2026-05-26
Sources
2
Primary result
Required sample size

Formula logic is kept in a pure calculator module with fixtures, source notes, and page-visible assumptions.

Categories

What the result means

Required sample size answers the page's main sample size question. Ceiling-rounded sample size to plan for. Read the center or spread metric first, then compare count, minimum, maximum, and sample/population notes. Use adjusted sample size, unadjusted sample size, and z critical value to explain why required sample size moved when an input changed. Review the raw values and decide whether outliers or missing data should be handled before reporting the result.

Required sample sizeCeiling-rounded sample size to plan for.
Adjusted sample sizeSample size after optional finite population correction.
Unadjusted sample sizeNormal-approximation sample size before finite population correction.
z critical valueTwo-sided standard normal critical value for the selected confidence level.

Use the result this way

  1. Start with Required sample size, then use supporting outputs only to explain the primary answer.
  2. Verify confidence level, margin of error, and estimated proportion before copying the result.
  3. Choose the mode or method first because it can change which formula is applied, keep units consistent with the labels shown in the form, and stay within the documented minimum and maximum ranges.
  4. Review the raw values and decide whether outliers or missing data should be handled before reporting the result.

User job

How to use this calculator

Use Sample Size Calculator when you need required sample size, then use adjusted sample size and unadjusted sample size to check the context for data review, classwork, quality checks, and quick descriptive summaries.

Best for

  • Summarizing a list of values
  • Checking spread, center, or sample assumptions
  • Reviewing a default example before entering your own confidence level and margin of error.

Check before relying

  • Confirm whether the data is a sample or population and whether outliers should stay in the list.
  • This calculator estimates sample size for one population proportion.
  • Percent inputs are entered as percent values; 5 means 5%, not 0.05.
  • Source context: Penn State Eberly College of Science, reviewed 2026-05-26.

Next useful step

  • Confidence Interval CalculatorUse next when you need lower bound from sample mean and population standard deviation after checking required sample size.
  • Median CalculatorUse next when the data-summary task needs median instead of required sample size.
  • P-Value CalculatorUse next when you need p-value from sample mean and hypothesized mean after checking required sample size.

Formula

For one population proportion, n0 = z^2 p(1-p) / e^2. Optional finite population correction uses n = n0 / (1 + (n0 - 1) / N). Key assumptions: This calculator estimates sample size for one population proportion. Percent inputs are entered as percent values; 5 means 5%, not 0.05. The normal approximation is used for planning the confidence interval margin of error.

  • For one population proportion, n0 = z^2 p(1-p) / e^2. Optional finite population correction uses n = n0 / (1 + (n0 - 1) / N).
  • This calculator estimates sample size for one population proportion.
  • Percent inputs are entered as percent values; 5 means 5%, not 0.05.
  • Primary source context: Penn State Eberly College of Science.

Inputs

Enter confidence level, margin of error, estimated proportion, and population size for data review, summaries, quality checks, and classwork. Before calculating, choose the mode or method first because it can change which formula is applied, keep units consistent with the labels shown in the form, and stay within the documented minimum and maximum ranges. Confidence level: Choose the two-sided confidence level for the proportion estimate. Margin of error: Enter the desired half-width in percentage points; 5 means 5%, not 0.05. Estimated proportion: Use 50% when there is no prior estimate; it gives the most conservative sample size.

Confidence levelChoose the two-sided confidence level for the proportion estimate.
Margin of errorEnter the desired half-width in percentage points; 5 means 5%, not 0.05.
Estimated proportionUse 50% when there is no prior estimate; it gives the most conservative sample size.
Population sizeEnter an integer population size for finite population correction, or 0 to ignore it.

Example

Using the default inputs, Sample Size Calculator returns required sample size of 385. Adjust confidence level, margin of error, estimated proportion, and population size to match your own scenario.

FAQ

How is required sample size calculated here?

For one population proportion, n0 = z^2 p(1-p) / e^2. Optional finite population correction uses n = n0 / (1 + (n0 - 1) / N). The first assumption to check is: This calculator estimates sample size for one population proportion.

What does Required sample size mean for sample size?

Read the center or spread metric first, then compare count, minimum, maximum, and sample/population notes. Secondary values such as adjusted sample size, unadjusted sample size, and z critical value are there to explain the primary answer, not to replace it.

What should I enter for Confidence level?

Choose the two-sided confidence level for the proportion estimate. Choose the mode or method first because it can change which formula is applied, keep units consistent with the labels shown in the form, and stay within the documented minimum and maximum ranges.

How does Margin of error change required sample size?

Enter the desired half-width in percentage points; 5 means 5%, not 0.05. Changing it can alter required sample size because the formula uses the submitted inputs together. Also compare sample versus population mode, separators, missing values, outliers, and rounding precision.

Why does the sample size example show 385 for required sample size?

The default inputs produce 385 for required sample size. Treat that as a format and scale check, then replace every default value with your own inputs.

What should I check before reporting required sample size?

Confirm how the values were parsed, whether the data is a sample or population, and whether outliers or missing values should stay in the set.

Sources

Last reviewed: 2026-05-26

  • Reviewed 2026-05-26 · Source n.d.
    STAT 506: 2.3 Sample Size Needed for Estimating ProportionPenn State Eberly College of Science. One-proportion sample size formula with and without finite population correction, and the conservative p = 0.50 rationale.
    Scope
    Sampling theory lesson for confidence intervals and sample size for estimating one population proportion.
    Supports
    One-proportion sample size formula with and without finite population correction, and the conservative p = 0.50 rationale.
  • Reviewed 2026-05-26 · Source n.d.
    NIST/SEMATECH e-Handbook: Cumulative Distribution Function of the Standard Normal DistributionNational Institute of Standards and Technology. Critical z values used for 90%, 95%, and 99% two-sided confidence levels.
    Scope
    Standard normal cumulative probability table and common critical values.
    Supports
    Critical z values used for 90%, 95%, and 99% two-sided confidence levels.

Disclaimer

This calculator is an educational estimate based on the inputs and assumptions shown on the page.