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MATH

Sample Size Calculator

Estimate required sample size from confidence level, expected proportion, target margin of error with the Sample Size Calculator.

What do you want to plan?Use 0 for population size when the population is very large or unknown.
2 options
REQUIRED SAMPLE SIZE385

Required sample size: Plans a proportion sample from confidence and precision, applies finite-population correction when a population is supplied, and can reverse the formula to show achieved margin.

Confidence level
95%
Critical Z
1.95996399
Expected proportion
0.5
Population
Unlimited
Unlimited-population estimate
384.14588269
Required sample size
385
Target margin of error
0.05
Estimate based on the values shown
MethodPlans a proportion sample from confidence and precision, applies finite-population correction when a population is supplied, and can reverse the formula to show achieved margin.

Before you use the result

The result depends on the entered values, selected mode, and displayed mathematical assumptions.

Sources

CALCULATOR GUIDE

How to use the Sample Size Calculator

Estimate required sample size from confidence level, expected proportion, target margin of error with the Sample Size Calculator. It includes Required sample size, Achieved precision workflows, so choose the one that matches the values you actually know. Use it to check the arithmetic while keeping the displayed method and entered values with your work.

Step by step

  1. For the Sample Size, enter confidence level, expected proportion, target margin of error, population size, chosen sample size. Keep each value in the unit displayed beside its field.
  2. Review the selected Sample Size workflow and inputs, then read required sample size in the result panel.
  3. Change one Sample Size assumption at a time to compare scenarios. Use Reset to restore this tool's worked example values.

How the calculation works

Plans a proportion sample from confidence and precision, applies finite-population correction when a population is supplied, and can reverse the formula to show achieved margin.

Worked example

In the Sample Size worked example, confidence level 95 %, expected proportion 0.5, target margin of error 0.05, population size 0 produces required sample size of 385. Required sample size: Plans a proportion sample from confidence and precision, applies finite-population correction when a population is supplied, and can reverse the formula to show achieved margin. Review the displayed units before comparing the result.

Understanding the result

The Sample Size reports required sample size. Use it to check the arithmetic while keeping the displayed method and entered values with your work. The result depends on the entered values, selected mode, and displayed mathematical assumptions.

How to check the answer

Check the Sample Size answer by substituting required sample size back into the stated relationship. Test a simple value such as zero, one, or an equal pair, then confirm that sign, scale, units, and rounding match Plans a proportion sample from confidence and precision, applies finite-population correction when a population is supplied, and can reverse the formula to show achieved margin.

Common questions

What does the Sample Size calculate?

Estimate required sample size from confidence level, expected proportion, target margin of error with the Sample Size Calculator.

Which Sample Size inputs have the biggest effect?

required sample size responds directly to confidence level, expected proportion, target margin of error, population size, chosen sample size. Change one input while holding the others constant to see its effect.

Is the Sample Size result exact?

The result depends on the entered values, selected mode, and displayed mathematical assumptions. Recheck confidence level, expected proportion, target margin of error and use required sample size only for a decision where that level of precision is appropriate.

Formula tests, limits, sources, and guide registry updated September 1, 2026.
INTERPRET THE RESULTRead the math guideCheck assumptions, limitations and comparison methods →