Statistics
Sample Size Calculator
Use your desired confidence, margin of error, and response distribution to size surveys with or without a finite population.
Estimate how many responses you need for surveys or polls with margin of error and confidence tuning.
Sample size with finite correction
n₀ = (Z² × p(1 − p)) / E² n = n₀ / [1 + (n₀ − 1)/N]
Z is the critical value for the confidence level, p is the assumed response proportion, E is the margin of error, and N is the population (optional).
How to use
- Pick a confidence level to set the Z-score.
- Enter the acceptable margin of error and expected response distribution.
- Optionally add a population size to apply the finite population correction.
Example
Input: Confidence = 95%, Margin of error = 5%, Distribution = 50%, Population = 10,000
Output: Sample size ≈ 385 without population, ≈ 370 with finite correction
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Sample Size Calculator: sample size calculator, survey sample size calculator, sample size margin of error, finite population sample size calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.
Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic — each one is a quick way to double-check your work or handle a related question without starting from scratch.
Deep dive & study plan
Sample Size Calculator: Estimates the responses needed to hit a target margin of error and confidence level. It's built around sample size, margin of error, confidence level, so you can go from a raw question to a checked answer without switching tools.
The math behind it: Z is the critical value for the confidence level, p is the assumed response proportion, E is the margin of error, and N is the population (optional). The core relationship is n₀ = (Z² × p(1 − p)) / E² n = n₀ / [1 + (n₀ − 1)/N], shown above the calculator so you can see exactly how your inputs turn into the result.
To use it well: (1) Pick a confidence level to set the Z-score. (2) Enter the acceptable margin of error and expected response distribution. (3) Optionally add a population size to apply the finite population correction. Keep your units consistent as you go, and re-run a case you already know the answer to — it's the fastest way to catch a typo before it throws off a result you're relying on.
Worked example: entering Confidence = 95%, Margin of error = 5%, Distribution = 50%, Population = 10,000 returns Sample size ≈ 385 without population, ≈ 370 with finite correction. Try swapping in your own numbers next, especially a case you're unsure about, before you use this for something that matters.
Quick retention checklist
- Speak the formula aloud (or annotate it) so the relationships stick.
- Write each step in your own words and compare with the numbered list above.
- Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
- Check at least one related calculator below — it's the fastest way to confirm your numbers still line up from a different angle.
FAQ & notes
What response distribution should I use?
If you do not know the true proportion, use 50%. It produces the largest (safest) sample size requirement.
Can I model different confidence levels?
Yes—switch between 80%, 85%, 90%, 95%, or 99% confidence to see how the Z-score scales the required sample.
What formula does the Sample Size Calculator use?
Z is the critical value for the confidence level, p is the assumed response proportion, E is the margin of error, and N is the population (optional).
How do I use the Sample Size Calculator?
Pick a confidence level to set the Z-score. Enter the acceptable margin of error and expected response distribution. Optionally add a population size to apply the finite population correction.