Confidence Interval Calculator

Margin of error = z × (standard deviation ÷ √sample size), where z is 1.645 for 90% confidence, 1.96 for 95%, or 2.576 for 99%. The interval is then [mean − margin, mean + margin].

If you repeated your sampling many times, about {confidence}% of the calculated intervals would contain the true population mean. A narrower interval (from a larger sample or lower confidence level) reflects a more precise estimate.

Increase your sample size (margin shrinks with the square root of n) or accept a lower confidence level — both narrow the interval, but only a larger sample improves precision without sacrificing confidence.

They use the same z-value lookup table (1.645/1.96/2.576) but solve for different things — this tool computes an interval around a mean you already measured, while Sample Size Calculator works backward to tell you how many observations you'd need before measuring.