Confidence Interval Calculator
Last updated: June 2026 · Free · No sign-up required
Enter values above and click Calculate to see your result instantly.
Quick reference
Common z-scores by confidence level:
| Confidence | z-score |
|---|---|
| 90% | 1.645 |
| 95% | 1.960 |
| 99% | 2.576 |
functions Shows the working, not just the answer
For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.
calculate Accurate to the spec
Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.
school Free for classroom use
Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.
tips_and_updates Pair with the spoke articles
Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.
Interpretation guide
Confidence interval terms:
| Term | Meaning |
|---|---|
| Point estimate | Sample mean or proportion |
| Margin of error | z x standard error |
| Confidence level | How often the method captures the true value |
| Width | Narrower with larger samples |
Formula & methodology
Formula: CI = x-bar +/- z x (s / sqrt(n)); for a proportion, +/- z x sqrt(p(1-p)/n)
A confidence interval gives a range that likely contains the true population mean or proportion. The calculator multiplies the standard error by the z (or t) value for your confidence level to get the margin of error, then adds and subtracts it from the sample estimate. Larger samples shrink the standard error and narrow the interval; higher confidence widens it. A 95% interval means that about 95% of such intervals from repeated samples would contain the true value.
Frequently asked questions
Explore the full statistics toolkit
Every CalcaTools statistics calculator — descriptive measures, probability distributions, hypothesis tests, confidence intervals, and Six Sigma process metrics — with step-by-step workings on each result.