About Confidence Interval Calculator

Calculate confidence intervals for population parameters. Part of the DevTools Surf developer suite. Browse more tools in the Statistics collection.

Use Cases

• Calculate margins of error for survey results before publishing
• Determine precision of an A/B test metric before declaring a winner
• Report results of user research with appropriate statistical uncertainty
• Validate that a sample-based estimate is within acceptable error bounds

Tips

• Choose the correct distribution: use z-score for large samples (n>30) or known population variance; use t-distribution for small samples (n<30) or unknown variance
• The margin of error output directly answers how precise your estimate is — it equals half the confidence interval width
• For proportions (like conversion rates), use the Wilson interval option instead of the normal approximation — it is more accurate near 0% and 100%

Fun Facts

• The concept of confidence intervals was developed by Jerzy Neyman in 1937, who invented them as an alternative to the p-value approach of significance testing. Neyman and Karl Pearson's son Egon collaborated on much of classical statistics during this period.
• A 95% confidence interval does not mean there is a 95% probability the true value is in the interval. It means that if you repeated the experiment 100 times, approximately 95 of those intervals would contain the true value — a subtle but important distinction.
• In physics, 'five sigma' (99.99997% confidence) is the standard for claiming a new particle discovery — the level used when announcing the Higgs boson in 2012. The threshold is far stricter than social science's 95% because the implications of a false positive are vastly different.

FAQ

What is the difference between confidence level and confidence interval?

Confidence level (e.g., 95%) is the probability that the procedure produces an interval containing the true value. The confidence interval is the specific numeric range calculated from that procedure and your data. The level is a setting; the interval is the result.

Why use 95% and not 99%?

95% is the convention established in early 20th-century statistics. 99% gives a wider interval (more certain but less precise). The choice should match the consequences of error: medical trials often use 99%, while marketing tests commonly use 90% for faster decisions.

Does a wider confidence interval mean the data is bad?

A wide CI means the estimate is imprecise, usually because of a small sample size or high variance in the data. Collecting more data narrows the interval. 'Bad data' means biased or invalid data — that is a different problem than imprecision.