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Confidence Interval Calculator

Confidence Interval
Margin of Error
Standard Error
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What Your Result Means

How This Calculator Works

You enter a sample mean, standard deviation, and sample size. The tool divides the standard deviation by the square root of the sample size to get the standard error, multiplies by the z-critical value for your confidence level, and adds/subtracts that margin from the mean. It uses z-scores (normal distribution), which is appropriate for large samples or known population standard deviation.

Quick Questions

When should I use a t-distribution instead?

Use a t-distribution when your sample size is small (typically under 30) and the population standard deviation is unknown. The t-distribution produces wider intervals to account for the extra uncertainty.

Does a 95% CI mean there's a 95% chance the true mean is inside it?

Not exactly. The true mean is a fixed value. A 95% CI means that 95% of intervals constructed this way from repeated samples would contain the true mean. Any single interval either does or doesn't contain it.

How can I make my confidence interval narrower?

Increase your sample size (which reduces the standard error), accept a lower confidence level, or reduce measurement variability. Quadrupling the sample size roughly halves the margin of error.

What if my data is not normally distributed?

For large samples (typically n > 30), the Central Limit Theorem says the sampling distribution of the mean is approximately normal regardless of the underlying distribution, so the z-based CI is still reasonable.

Can I use this for proportions (like survey percentages)?

This calculator is designed for means. For proportions, the standard error formula differs: SE = √(p(1−p)/n). Use a proportion-specific CI calculator for survey percentages.

Sources

Method & review

MethodologyHow we calculate this Reviewed & Updated2026-04 Next review2027-04

Estimate only. Results reflect your inputs and standard formulas. Double-check important decisions independently.