Confidence Interval Calculator
Confidence interval and margin of error for a sample mean.
95% confidence interval
47.5208 — 52.4792
Margin of error
± 2.4792
Standard error
1.2649
Critical z
1.96
ShowHide the working
- 1Standard error = 8 ÷ √40 = 1.2649
- 2Critical z for 95% = 1.96
- 3Margin = z × SE = 2.4792
Formula
CI = x̄ ± z × (σ ÷ √n)How it works
The range likely to contain the true population mean, using the normal (z) approximation for the given confidence level.
Example
A mean of 50, SD 8, n = 40 gives a 95% interval of roughly 47.5 to 52.5.
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About the Confidence Interval Calculator
Confidence interval and margin of error for a sample mean. 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 Confidence Interval 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 Confidence Interval Calculator runs entirely in your browser using JavaScript. Nothing you type is uploaded, logged or stored on a server.
- Can I use the Confidence Interval 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.