Sample Size Calculator – Calculate Survey Sample Size
Estimate the sample size needed for a survey or experiment.
About the Sample Size Calculator
What is the Sample Size Calculator?
A sample size calculator estimates how many responses you need so a survey or test reaches a chosen precision.
Why use this calculator?
Too few responses and your results are noise; too many and you waste budget. The maths gives the smallest defensible number.
How to use it
- Pick the confidence level and margin of error.
- Enter the population size if it is small and known.
- Read the required sample size and the worst-case estimate.
Formula
n = (z²·p·(1−p)) ÷ e², with finite-population correction when N is given.
Assumes simple random sampling. Real-world designs with clusters need larger samples.
Frequently Asked Questions
Why does 50% give the biggest sample?
p·(1−p) is largest at p = 0.5, so planning for a 50/50 split is the safest when you do not know the true proportion.
Does response rate matter?
Yes — this gives the number of completed responses, so if you expect a 20% response rate you must invite ~5× as many.
What order of operations does this use?
It follows standard PEMDAS/BODMAS rules: parentheses, exponents, multiplication and division, then addition and subtraction.
How precise are the answers?
The calculator uses double-precision floating-point math (about 15 significant digits) and rounds the display. For exact symbolic results use dedicated algebra software.
Can I enter negative numbers or decimals?
Yes. Negative values, decimals and very large or small numbers are all supported unless a field says otherwise.
What does it mean if I get an error?
Errors usually mean an invalid input, such as division by zero or a negative value where only positives make sense. Check your entries and try again.
What is the difference between population and sample?
A population includes every member of a group; a sample is a subset. Sample statistics use n−1 in the denominator to correct for bias.
When should I use median instead of mean?
Use the median when data contains outliers or is skewed, because it is less affected by extreme values than the mean.
What does standard deviation tell me?
It measures how spread out the values are around the mean. A small standard deviation means the data clusters tightly; a large one means it is more scattered.
Is this calculator free to use?
Yes. Every calculator on this site is completely free, with no hidden fees, no subscriptions and no limits on how many times you can use it.