Confidence Interval Calculator for a Mean (Free)

Use this free confidence interval calculator to estimate a population mean. Enter the sample mean, the standard deviation, the sample size and a confidence level, and you’ll get the margin of error and the interval, along with the critical value and standard error.

How to use the calculator

1. Enter the sample mean, the sample standard deviation, and the sample size.
2. Choose a confidence level (90%, 95%, 99%, or custom).
3. Read the interval, the margin of error, and the steps.

How the interval is built

The interval is x̄ ± z*·(s/√n), where s/√n is the standard error and z* is the critical value for your confidence level (about 1.96 for 95%). For small samples a t-interval is more appropriate — the tool notes this.

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Frequently asked questions

What is a 95% confidence interval?

A range that, with a method that’s right 95% of the time, captures the true mean. It uses the critical value z* ≈ 1.96.

What is the margin of error?

Half the width of the interval: z* times the standard error, z*·(s/√n). It’s how far the estimate can plausibly be off.

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When should I use a t-interval instead?

With small samples and an unknown population standard deviation, the t-distribution is more accurate. The tool flags this case.

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Read the full lesson: learn the method step by step.

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