Sample Size Calculator
How many responses you need for a given confidence and margin.
%
%
Required sample size
383
for 95% confidence, ±5%
Before correction
385
Critical z
1.96
Population
100,000
ShowHide the working
- 1n₀ = z²·p(1−p) ÷ e² = 1.96² × 0.5×0.5 ÷ 0.05² = 384.1
- 2Finite-population correction for N = 100,000 → 383
Formula
n = z²·p(1−p) ÷ e² (with finite-population correction)How it works
How many survey responses you need for a target confidence and margin of error. A 50% proportion gives the most conservative (largest) size.
Example
For 95% confidence and ±5% from a large population, you need about 385 responses.
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About the Sample Size Calculator
How many responses you need for a given confidence and margin. It sits in the Statistics section of NWS Calc, a free collection of calculators that run entirely in your browser. There is no signup, no paywall and no tracking — open the page, enter your numbers, get an answer.
Frequently asked questions
- Is the Sample Size Calculator free to use?
- Yes. Every calculator on NWS Calc is completely free, with no signup, no usage limits and no ads.
- Does my data leave my device?
- No. The Sample Size Calculator runs entirely in your browser using JavaScript. Nothing you type is uploaded, logged or stored on a server.
- Can I use the Sample Size Calculator on my phone?
- Yes. The page is fully responsive and works in any modern mobile or desktop browser — there is nothing to install.
- What else is in Statistics?
- Mean, deviation, regression, probability and distributions. You can browse the full Statistics category for related calculators.