Statistics

Confidence Interval Calculator

Enter a sample mean, standard deviation, size, and confidence level to see the margin of error plus lower and upper bounds.

confidence intervalz intervalmargin of error
Confidence Interval Calculator

Compute a two-sided z-interval for a population mean using your sample mean, spread, and size.

Margin of error
3.254
Lower bound
68.746
Upper bound
75.254
Standard error
1.66
Z-score
1.960
Sample size
40

Mean confidence interval

CI = x̄ ± Z × (σ / √n)

Z is the standard normal critical value for the selected confidence, σ is the sample (or population) standard deviation, and n is the sample size.

How to use

  1. Provide your sample mean and standard deviation.
  2. Enter the sample size that produced those statistics.
  3. Pick a confidence level to update the Z-score and interval bounds.

Example

Input: Mean = 72, σ = 10.5, n = 40, Confidence = 95%

Output: Margin of error ≈ 3.25, Interval ≈ [68.75, 75.25]

Student-friendly breakdown

This walkthrough emphasizes the most searched ideas for Confidence Interval Calculator: confidence interval calculator, z interval calculator, confidence interval calculator with steps, confidence interval of mean calculator. Start with the formula above, then follow the guided steps to double-check your work. For quick revision, highlight the givens, plug into the equation, and finish by verifying your units.

Need more support? Use the links below to open the long-form guide, browse additional examples, or hop into adjacent calculators within the same topic. Each resource is interlinked so crawlers (and readers) can discover the next best action within a couple of clicks—one of the easiest ways to lift topical authority.

Deep dive & study plan

The Confidence Interval Calculator is a go-to tool whenever you need to builds a two-sided z-interval around a sample mean.. It focuses on confidence interval, z interval, margin of error, which means searchers often arrive with intent-heavy queries like “how to confidence interval calculator quickly” or “confidence interval calculator formula explained.” Use this calculator to capture those intents and keep learners on the page long enough to send positive engagement signals.

Under the hood, the calculator leans on z is the standard normal critical value for the selected confidence, σ is the sample (or population) standard deviation, and n is the sample size.—that’s why we surface the full expression (“CI = x̄ ± Z × (σ / √n)”) directly above the interactive widget. When you embed that formula inside H2s or supporting paragraphs, you help both humans and crawlers understand what entity the page represents.

Execution matters as much as the math. Follow the built-in procedure: Step 1: Provide your sample mean and standard deviation. Step 2: Enter the sample size that produced those statistics. Step 3: Pick a confidence level to update the Z-score and interval bounds.. Each numbered instruction is short enough to scan on mobile but descriptive enough to satisfy Google’s Helpful Content guidelines. Encourage students to jot down units, double-check signs, and compare answers with the Example card to build confidence.

The Example section itself is packed with semantic clues: “Mean = 72, σ = 10.5, n = 40, Confidence = 95%” leading to “Margin of error ≈ 3.25, Interval ≈ [68.75, 75.25].” Pepper similar narratives throughout your copy (and internal links from related guides) so canonical search intents are answered without pogo-sticking back to Google.

Quick retention checklist

  • Speak the formula aloud (or annotate it) so the relationships stick.
  • Write each step in your own words and compare with the numbered list above.
  • Swap in new numbers for the Example to make sure the calculator (and your logic) handles edge cases.
  • Link out to at least two related calculators to keep readers exploring your topical hub.

FAQ & notes

Does this use a t-score for small samples?

This calculator focuses on z-intervals. For very small samples where σ is unknown, consider substituting a t critical value manually.

Can I interpret the interval as probability?

Not directly. A 95% interval means that if you repeatedly sampled and built intervals the same way, about 95% would capture the true mean.

What formula does the Confidence Interval Calculator use?

Z is the standard normal critical value for the selected confidence, σ is the sample (or population) standard deviation, and n is the sample size.

How do I use the Confidence Interval Calculator?

Provide your sample mean and standard deviation. Enter the sample size that produced those statistics. Pick a confidence level to update the Z-score and interval bounds.