Math

Confidence Interval Calculator

Use OmniCalc's confidence interval calculator to estimate a plausible range around a sample mean using a chosen confidence level.

Confidence interval calculator

Estimate the likely range around a sample mean.

Enter a sample mean, standard deviation, sample size, and confidence level to calculate a quick z-based confidence interval.

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Why this result matters

What this calculator helps you answer

A distinct follow-on stats page for estimating uncertainty around sample means, bridging descriptive stats into inference. Use the tool above to enter a few clear inputs and get a practical answer you can use right away.

This confidence interval calculator helps students, analysts, and everyday users estimate a range around a sample mean without doing the margin-of-error formula by hand. Enter the sample mean, standard deviation, sample size, and confidence level to see the interval instantly.

Formula and method

How the calculation works

The calculator uses a z-based confidence interval for a mean: sample mean ± critical value × (standard deviation / square root of sample size).

Example

Example confidence interval

If the sample mean is 72, the standard deviation is 12, the sample size is 36, and the confidence level is 95%, the interval is about 68.08 to 75.92.

FAQ

Common questions about this calculator.

Short answers to the questions people often ask before or after using the tool.

Question

What does a confidence interval show?

It shows a range of plausible values for the population mean based on the sample statistics you entered.

Question

Why does the interval get narrower with a larger sample?

A larger sample reduces the standard error, which usually shrinks the margin of error and tightens the interval.

Question

Why does a higher confidence level create a wider interval?

Higher confidence levels use a larger critical value, so the margin of error increases and the interval becomes wider.

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