How to Use the Confidence Interval Calculator
This calculator takes a sample estimate, a standard error (SE), and your chosen confidence level, then instantly returns the lower and upper bounds of the interval expected to contain the true parameter. The interval is calculated as estimate ± (Z-value × standard error), where the Z-value is 1.645 for 90% confidence, 1.96 for 95%, and 2.576 for 99%.
A 95% confidence level means that if you repeated the sampling process and built the interval 100 times, about 95 of those intervals would contain the true parameter — it does not mean any single interval has a 95% chance of containing it. The interval widens as the standard error grows (from a smaller sample size or more variable data) and as you choose a higher confidence level, reflecting greater uncertainty in the estimate.
This tool applies to any situation where a sample is used to estimate a population value — poll approval ratings, clinical trial effect sizes, or A/B test conversion rate differences. The standard error must be greater than 0 for the calculation to work.
Frequently Asked Questions
A 95% confidence level means that if you repeated the sampling process and built the confidence interval 100 times, about 95 of those intervals would contain the true parameter. It does not mean any single interval has a 95% chance of containing it.
A wide confidence interval means more uncertainty in the estimate. It widens as the standard error increases (smaller sample size or more variable data) or as you choose a higher confidence level.