Sample Size Calculator

All tools

Find how many survey responses you need for a given confidence level and margin of error using Cochran's formula, with an optional finite population correction. Free and instant.

%
%
%
Use 50% for the most conservative (largest) sample.
Applies a finite population correction when provided.
Required sample size – respondents
With population correction –
Z value used –
Uses Cochran's formula n₀ = z²·p·(1−p) ⁄ e². The finite population correction reduces the figure for smaller populations. The result is rounded up to a whole number of respondents.

About Sample Size Calculator

The sample size calculator tells you how many survey responses you need for statistically meaningful results. Set your confidence level, margin of error and expected proportion, and it returns the required number of respondents, rounded up to a whole person.

It uses Cochran’s formula, n₀ = z² × p × (1 − p) ⁄ e², the standard for estimating a proportion. The expected proportion defaults to the conservative 50%, which maximizes the required sample; if you already know the outcome is rarer or more common, adjust it and the requirement drops.

For small audiences, enter the population size and the finite population correction reduces the figure — surveying a 200-person company needs far fewer responses than a national poll at the same precision. Free and instant.

How to use Sample Size Calculator

  1. Pick a confidence level — 95% is the survey-industry standard — or enter a custom one.
  2. Set your acceptable margin of error, such as 5%.
  3. Set the expected proportion; keep 50% for the most conservative (largest) sample.
  4. Optionally enter the population size to apply the finite population correction.
  5. Read the required sample size, the corrected figure and the z value used.

Frequently asked questions

With the conservative 50% proportion, Cochran's formula gives about 385 respondents for a large population. Enter a small population and the finite correction brings that number down.

Because p(1 − p) peaks at p = 0.5, a 50% assumption yields the largest — safest — sample size. If prior data suggests, say, 20%, entering it shrinks the requirement.

An adjustment for small populations: when your sample is a meaningful fraction of the whole group, fewer responses achieve the same precision. Provide the population size and the tool applies it automatically.

No — required sample size plateaus quickly. Polling a country of 10 million needs roughly the same n as one of 100 million; population size only matters much when it is small.

Your real margin of error widens beyond the target. Plan for non-response by inviting more people than the required sample — dividing the target by your expected response rate is a common rule of thumb.
Share this
Related Tools
Percentage Calculator Answer every percentage question — X% of Y, what percent, percentage change, increase/decrease, tips and discounts. Free, in your browser. Free
Scientific Calculator A full scientific calculator with trigonometry, logarithms, powers, roots, factorials, memory and history — in degrees or radians. Free, in your browser. Free
Text to Binary, Octal & Hex Convert text to binary, octal, decimal and hexadecimal — and back again. Every field is live and editable, with delimiter, padding and uppercase options. Free
Fraction Calculator Add, subtract, multiply or divide two fractions and instantly get the simplified result, plus its decimal, mixed-number and percentage forms. Free and instant. Free
Average Calculator Paste a list of numbers to instantly get the mean, median, mode, range, sum, count and more. Robust parsing handles commas, spaces and new lines. Free and instant. Free
Standard Deviation Calculator Enter a data set to compute the sample and population standard deviation, variance and mean. Robust parsing handles commas, spaces and new lines. Free and instant. Free
Need help?
Found an issue with this tool? Let our team know.
Report an issue

Add this free tool to your own website — copy and paste the code below.