Statistics
Sample Size Calculator
Use this sample size calculator to plan surveys and proportion estimates before collecting data.
Try an example
Result
Required sample size
—
- Z critical value
- —
Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the sample size calculator solves
Use this A smaller group taken from a population, used to estimate facts about the whole group. size calculator to plan surveys and proportion estimates before collecting data.
Formula
How to use it
- Choose confidence level.
- Enter margin of error.
- Use 50% expected proportion if unsure.
How to read the answer
Smaller margins of error and higher confidence require larger samples. The result is a planning estimate for proportions, not a guarantee that the final survey will be unbiased.
Common mistakes and edge cases
- This is for proportions, not means.
- Biased sampling cannot be fixed by larger sample size.
- Finite Every member of the group you actually care about, not just the ones measured. correction is not included.
Worked examples
Common survey setup
Required sample size
385
Tighter margin
Required sample size
1,068
Frequently asked questions
Why does 50% give the largest sample?+
p(1-p) is largest at p = 0.5, so it is conservative.
Does population size matter?+
For very small populations, a finite population correction can reduce the required sample. For large populations, confidence level and margin of error usually matter much more.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- May 8, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
Related calculators
Confidence Interval Calculator
Calculate confidence intervals for a mean or proportion with margin of error and z critical value.
Probability Calculator
Calculate event probability, complement probability, odds, and repeated independent event probabilities.
Standard Deviation Calculator
Calculate sample or population standard deviation, variance, mean, and z-score-ready summary statistics from a data list.
Average Calculator
Calculate arithmetic, weighted, geometric, or harmonic averages from a list of numbers with steps and summary statistics.
Mean Median Mode Range Calculator
Find mean, median, mode, range, count, sum, minimum, and maximum for a list of numbers with sorted values and steps.
Normal Distribution Calculator
Find P(X < x), P(X > x), P(a < X < b), z-scores, and percentiles for any normal distribution, or work backward from a probability to x. Includes a shaded bell curve and full steps.
Last updated: May 8, 2026