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Confidence Interval Calculator | Get mean & proportion CIs

Builds a confidence interval for a mean or a proportion from your data. Enter the sample mean, sample size, standard deviation, and the confidence level — 90%, 95%, or 99% — and the tool computes the margin of error and the lower and upper bounds of the interval using the correct z-score or t-score.

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

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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.

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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

lightbulb Worked example

Let's say you are using the Confidence Interval Calculator. Builds a confidence interval for a mean or a proportion from your data. Enter the sample mean, sample size, standard deviation, and the confidence level — 90%, 95%, or 99% — and the tool computes the Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula CI = x-bar +/- z x (s / sqrt(n)); for a proportion, +/- z x sqrt(p(1-p)/n) and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

Formula & methodology

Formula: CI = x-bar +/- z x (s / sqrt(n)); for a proportion, +/- z x sqrt(p(1-p)/n)

The Confidence Interval Calculator is built on a well-established calculation method. It uses the formula CI = x-bar +/- z x (s / sqrt(n)); for a proportion, +/- z x sqrt(p(1-p)/n) to turn your inputs into a reliable result. Builds a confidence interval for a mean or a proportion from your data. Enter the sample mean, sample size, standard deviation, and the confidence level — 90%, 95%, or 99% — and the tool computes the margin of error and The steps are shown on the page so you can follow the reasoning from input to output.

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.

What is the Confidence Interval Calculator?

The Confidence Interval Calculator is a free, browser-based math calculator tool that helps you Builds a confidence interval for a mean or a proportion from your data. Enter the sample mean, sample size, standard deviation, and the confidence level — 90%, . Instead of working through the math by hand or in a spreadsheet, you enter your values and the calculator returns an accurate result instantly — while still showing the formula and the steps so you can verify the reasoning. It is designed for quick everyday use: no sign-up, no installation, and everything runs locally in your browser for complete privacy.

How to use the Confidence Interval Calculator

  1. Enter the required values into the input fields.
  2. Press the calculate button — the result appears immediately, updated live as you change any value.
  3. Read the step-by-step breakdown below the result to see exactly how the calculation was performed.
  4. Use the interpretation guide to understand what the result means for your situation, and try different inputs to see how they change the outcome.

How to use the Confidence Interval Calculator

Enter the sample mean, the sample standard deviation, the sample size, and the confidence level you want — typically 95%. For a proportion, enter the number of successes and the sample size instead. The tool computes the margin of error and the interval with CI = x̄ ± z × (s ÷ √n) for a mean, or ± z × √(p(1−p) ÷ n) for a proportion, where z is the critical value for your chosen level.

Interpreting your result

The interval means that if you repeated the study many times, about 95% of the computed intervals would contain the true population value — it is a statement about the method, not a 95% probability that this specific interval contains the true value. A wider interval means more uncertainty, which comes from a smaller sample, more variable data, or a higher confidence level. The margin of error shrinks with the square root of the sample size: quadrupling n halves the margin.

Common mistakes to avoid

The most common error is using the population standard deviation σ when you only have the sample s — with small samples you should use the t-distribution, which the calculator accounts for. Second, misreading the interval as a range that must contain the sample mean — it always does; the interval is about the unknown population mean. Third, ignoring the sample size: intervals from tiny samples are very wide and often useless. Finally, don't confuse confidence level with statistical power or p-values — they answer different questions.

Tips for best results

Use the standard 95% level for most reporting, and 99% when the stakes are high and you can tolerate a wider interval. To narrow an interval, increase the sample size — the square-root rule makes this the most effective lever. For proportions, the interval is only reliable when you have at least 10 successes and 10 failures; the calculator flags borderline cases. When comparing two groups, check whether their confidence intervals overlap before drawing conclusions about differences.

Authoritative source: Wolfram MathWorld

Frequently asked questions

What does a 95% confidence interval mean?
The Confidence Interval Calculator is a free online tool that builds a confidence interval for a mean or a proportion from your data. enter the sample mean, sample size, standard deviation, and the confidence level — 90%, 95%, or 99% — and the tool computes the margin of error and the lower and upper bounds of the. You enter a few values, and it returns an accurate result together with a step-by-step explanation, so it works as both a calculator and a quick reference for the underlying concept.
How do I calculate margin of error?
Enter the required values into the input fields and press the calculate button. The tool applies the formula CI = x-bar +/- z x (s / sqrt(n)); for a proportion, +/- z x sqrt(p(1-p)/n) and returns the result with a short explanation of each step, so you can check the working yourself.
When do I use t instead of z?
The Confidence Interval Calculator is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Builds a confidence interval for a mean or a proportion from your data. Enter the sample mean, sample size, standard deviation, and the confidence level — 90%, 95%, or 99% — and the tool computes the margin of error and the lower and upper bounds of the There is no limit on usage, and it works on any device.
How does sample size affect the interval?
The interval narrows as the sample grows because the standard error s ÷ √n shrinks with the square root of n. Quadrupling the sample size halves the margin of error — going from 100 to 400 observations cuts the interval width in half. This is why larger surveys produce tighter estimates, and why tiny samples yield intervals too wide to be useful.
Does higher confidence make the interval wider?
Yes — a 99% confidence interval is wider than a 95% interval for the same data, because the critical z-value grows from about 1.96 to 2.58. You are trading precision for certainty: to be more confident the interval contains the true value, you must accept a larger range. There is no free lunch — narrower intervals require bigger samples or lower confidence.
What does the Confidence Interval Calculator do?
Builds a confidence interval for a mean or a proportion from your data. Enter the sample mean, sample size, standard deviation, and the confidence level — 90%, 95%, or 99% — and the tool computes the margin of error and the lower and upper bounds of the. The calculator takes your inputs, applies the standard calculation, and returns a clear result so you can make an informed decision without doing the math by hand.
What formula does the Confidence Interval Calculator use?
The Confidence Interval Calculator applies the standard formula: CI = x-bar +/- z x (s / sqrt(n)); for a proportion, +/- z x sqrt(p(1-p)/n). The tool walks through each step of the calculation so you can verify the numbers yourself.
Is the Confidence Interval Calculator free and private?
Yes — the Confidence Interval Calculator. There is no sign-up, no paywall, no trial, and no limit on how many calculations you can run. CalcaTools covers its costs with non-intrusive display advertising, so the calculator itself never asks for payment or restricts any feature.
How accurate is the Confidence Interval Calculator?
The Confidence Interval Calculator applies the standard formula: CI = x-bar +/- z x (s / sqrt(n)); for a proportion, +/- z x sqrt(p(1-p)/n). It is tested against published worked examples before launch and uses native double-precision arithmetic, so results are accurate to typical precision for the values you enter — with no intermediate rounding that could distort the answer.

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