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Confidence Interval Calculator

A Confidence Interval Calculator is a free online tool that solves 95% confidence interval using 95% confidence interval, margin of error, statistical significance. Students, teachers, and engineers use it to check homework, prep for exams, and verify hand calculations.

Last updated: June 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

Quick reference

Common z-scores by confidence level:

Confidencez-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:

TermMeaning
Point estimateSample mean or proportion
Margin of errorz x standard error
Confidence levelHow often the method captures the true value
WidthNarrower 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

What does a 95% confidence interval mean?
If you repeated the sampling many times, about 95% of the resulting intervals would contain the true population value.
How do I calculate margin of error?
Multiply the critical value (z or t) by the standard error. For a mean that's z x s/sqrt(n).
When do I use t instead of z?
Use the t-distribution for small samples (n < 30) or when the population standard deviation is unknown.
How does sample size affect the interval?
Larger samples reduce the standard error, producing a narrower, more precise interval.
Does higher confidence make the interval wider?
Yes. A 99% interval is wider than a 95% one because it must capture the true value more often.

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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.

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