Confidence Interval Calculator

This calculator builds a confidence interval around Sample Mean using Margin of Error = z × (Standard Deviation ÷ √Sample Size) (line 67-68), where z comes from a fixed lookup table for 90%, 95%, or 99% confidence (lines 10-14) rather than a t-distribution — it uses the same normal (z-based) approximation regardless of how small Sample Size is set. Sample Mean is completely inert for Margin of Error, Standard Error, and Interval Width: none of those three formulas reference it at all (lines 67-71), so it only shifts where the interval is centered, through Lower Bound and Upper Bound — and Sample Mean dominates Lower Bound's sensitivity, since nudging it up or down by 10% moves Lower Bound over twenty times more than the same-sized nudge to Standard Deviation, and over fifty times more than the same nudge to Sample Size. Interval Width is always exactly double Margin of Error, because Upper Bound minus Lower Bound algebraically cancels Sample Mean and leaves 2 × Margin of Error (lines 69-71).

Unlike this site's other confidence-interval calculator (statistics/confidence-interval.ts), whose line 5 combines a boolean-OR fallback with a `Math.max` floor, clamps both a genuinely negative Standard Deviation and a tiny positive one (like 0.0001) up to 0.001 — a Standard Deviation of exactly 0 is falsy, so the boolean-OR fallback substitutes a hardcoded 1 (not the field's own default of 10) before that floor ever runs, never reaching the 0.001 floor for that particular case — this engine leaves Standard Deviation unclamped entirely and instead checks Sample Size directly: a Sample Size of 0 or less (line 18) returns an explicit "Sample size must be greater than 0" result rather than dividing by zero or silently substituting a different value. This calculator does not switch to a t-distribution for small samples and does not validate that Standard Deviation is a population parameter rather than a sample estimate.