Confidence Interval Calculator

Calculate CI for means and proportions

Confidence Interval Calculator

Calculate how confident you can be about your sample data. Get the range where the true value likely falls.

Enter Your Data Recommended

💡 Tip: Paste directly from Excel or any spreadsheet

Enter Summary Statistics

Proportion / Percentage Data

95% Confidence
27.12 to 32.88
The true mean is likely within this range

Visualized on a Distribution

27.12
30.00
32.88
⬇️
Lower Bound
27.12
📍
Point Estimate
30.00
⬆️
Upper Bound
32.88

💡 What This Means

We are 95% confident that the true population mean falls between 27.12 and 32.88. The margin of error is ±2.88.

📐 Statistical Details & Calculation Steps

▼
Margin of Error
±2.88
Standard Error
1.27
Critical Value
t = 2.26
Degrees of Freedom
9
Sample Size
10
Std Deviation
4.03
Step-by-Step Calculation

Understanding Confidence Intervals

What is a Confidence Interval?

A confidence interval gives you a range of values that likely contains the true population value. Instead of saying "the average is 30," you can say "we're 95% confident the true average is between 27 and 33."

The Key Formula

For a sample mean (when population σ is unknown):

CI = x̄ ± t × (s / √n)

Where x̄ is sample mean, t is the critical value, s is standard deviation, and n is sample size.

Quick Reference: Z-Values

Confidence Level α (Alpha) z* Value Common Use
90% 0.10 1.645 Exploratory research, quick estimates
95% 0.05 1.960 Most common — standard for research
99% 0.01 2.576 High-stakes decisions, medical trials

Common Misconception

⚠️ Important: A 95% CI does NOT mean "95% probability the true value is in this interval." It means if we repeated this sampling many times, about 95% of the intervals we calculate would contain the true value.

Tips for Narrower Intervals

  • Increase sample size — Most effective way to reduce uncertainty
  • Accept lower confidence — 90% instead of 95% gives a tighter range
  • Reduce variability — More consistent data means smaller intervals

Privacy & Limitations

  • All calculations run entirely in your browser -- nothing is sent to any server.
  • Results are computed using standard formulas and should be verified for critical applications.

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Confidence Interval Calculator FAQ

What is Confidence Interval Calculator?

Confidence Interval Calculator is a free math tool that helps you Calculate confidence intervals for sample means and proportions.

How do I use Confidence Interval Calculator?

Enter your input values, review the calculated output, and adjust inputs until you reach the result you need. The result updates in your browser.

Is Confidence Interval Calculator private?

Yes. Calculations run locally in your browser. Inputs are not uploaded to a server by default, and refreshing the page clears session data.

Does Confidence Interval Calculator require an account or installation?

No. You can use this tool directly in your browser without sign-up or software installation.

How accurate are results from Confidence Interval Calculator?

This tool applies standard formulas or deterministic processing logic for estimates. For medical, legal, tax, or investment decisions, verify with a qualified professional.

Can I save or share outputs from Confidence Interval Calculator?

You can bookmark this page and copy outputs manually. Results are not persisted in your account and are typically not embedded in the URL.

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