Statistics
Confidence Interval Calculator
Enter a sample mean, standard deviation, size, and confidence level to see the margin of error plus lower and upper bounds.
Compute a two-sided z-interval for a population mean using your sample mean, spread, and size.
Mean confidence interval
CI = x̄ ± Z × (σ / √n)
Z is the standard normal critical value for the selected confidence, σ is the sample (or population) standard deviation, and n is the sample size.
How to use
- Provide your sample mean and standard deviation.
- Enter the sample size that produced those statistics.
- Pick a confidence level to update the Z-score and interval bounds.
Example
Input: Mean = 72, σ = 10.5, n = 40, Confidence = 95%
Output: Margin of error ≈ 3.25, Interval ≈ [68.75, 75.25]
Student-friendly breakdown
This walkthrough emphasizes the most searched ideas for Confidence Interval Calculator: confidence interval calculator, z interval calculator, confidence interval calculator with steps, confidence interval of mean 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
Confidence Interval Calculator: Builds a two-sided z-interval around a sample mean. It's built around confidence interval, z interval, margin of error, so you can go from a raw question to a checked answer without switching tools.
The math behind it: Z is the standard normal critical value for the selected confidence, σ is the sample (or population) standard deviation, and n is the sample size. The core relationship is CI = x̄ ± Z × (σ / √n), shown above the calculator so you can see exactly how your inputs turn into the result.
To use it well: (1) Provide your sample mean and standard deviation. (2) Enter the sample size that produced those statistics. (3) Pick a confidence level to update the Z-score and interval bounds. 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 Mean = 72, σ = 10.5, n = 40, Confidence = 95% returns Margin of error ≈ 3.25, Interval ≈ [68.75, 75.25]. 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
Does this use a t-score for small samples?
This calculator focuses on z-intervals. For very small samples where σ is unknown, consider substituting a t critical value manually.
Can I interpret the interval as probability?
Not directly. A 95% interval means that if you repeatedly sampled and built intervals the same way, about 95% would capture the true mean.
What formula does the Confidence Interval Calculator use?
Z is the standard normal critical value for the selected confidence, σ is the sample (or population) standard deviation, and n is the sample size.
How do I use the Confidence Interval Calculator?
Provide your sample mean and standard deviation. Enter the sample size that produced those statistics. Pick a confidence level to update the Z-score and interval bounds.