Confidence Interval Calculator

This calculator builds a confidence interval around Sample Mean using the z-based formula Margin of Error = z × (Standard Deviation / √Sample Size) (lines 9, 15), where the z-value comes from inverting the standard normal CDF at the chosen Confidence Level (line 13). Margin of Error, Standard Error, Z-Value, and Interval Width are all completely unaffected by Sample Mean — none of their formulas ever reference it (lines 9-18); Sample Mean only shifts where the interval is centered, via Lower Bound and Upper Bound, which it dominates. Confidence Level, similarly, has zero effect on Standard Error, since Standard Error depends only on Standard Deviation and Sample Size — but it's the single input driving Z-Value, and by extension Margin of Error and Interval Width.

Interval Width is always exactly twice Margin of Error, since Upper Bound minus Lower Bound algebraically cancels Sample Mean and leaves 2 × Margin of Error (line 18) — a fixed relationship, not a separate calculation. This calculator does not switch to a t-distribution for small samples: it always uses the z-approximation regardless of Sample Size, even down to the field's allowed minimum of 2, where a t-based interval would normally be noticeably wider than what this calculator reports.