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