Confidence Interval Calculator

Calculate the confidence interval for a sample mean, based on sample size, standard deviation, and confidence level.

Margin of Error-
Lower Bound-
Upper Bound-
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About the Confidence Interval Calculator

The Confidence Interval Calculator estimates a range around a sample mean that is likely to contain the true population mean, at a chosen confidence level.

It uses the standard normal (z-score) method, which works well when the sample size is reasonably large (typically n ≥ 30).

How to Use This Calculator

Formula

Margin of Error = z × (σ ÷ √n). Confidence Interval = Mean ± Margin of Error, where z is the z-value for the chosen confidence level.

Example

A sample mean of 50 with a standard deviation of 10 and a sample size of 40, at 95% confidence, gives a margin of error of about 3.10 — an interval of roughly 46.90 to 53.10.

Frequently Asked Questions

What is a confidence interval?

It's a range of values, calculated from sample data, that's likely to contain the true population parameter (like a mean) at a stated confidence level, commonly 95%.

How is a 95% confidence interval calculated?

It typically uses the sample mean plus and minus a margin of error, where the margin depends on the standard error and a critical value (like 1.96 for a 95% interval with a normal distribution).

Does a 95% confidence interval mean there's a 95% chance the true value is in that range?

Not exactly — the more precise interpretation is that if you repeated the sampling many times, about 95% of the calculated intervals would contain the true population value.

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