Confidence Interval Calculator

Calculate the confidence interval for a population mean.

Margin of Error
5.37
Lower Bound
94.63
Upper Bound
105.37

Formula

CI = x̄ ± z·σ/√n

Share results:

What is Confidence Interval Calculator?

Calculate the confidence interval for a population mean. The Confidence Interval Calculator gives you the answer in seconds without manual math.

Getting the numbers right matters — whether you are planning a budget, checking a homework answer, or making a health decision. This calculator applies the standard formula every time, so you can trust the result and focus on what to do with it.

This guide explains how the calculation works, shows a worked example with real numbers, and answers the most common questions about this topic.

How does the Confidence Interval Calculator work?

CI = x̄ ± z·σ/√n

The calculator applies the standard formula for confidence interval using the values you enter. Each result is computed instantly and updated as you change the inputs.

The formula is the same one used in textbooks and professional practice, so the output matches what you would get from a careful manual calculation.

How to use the Confidence Interval Calculator?

  1. Enter the sample Mean.
  2. Enter the std Dev.
  3. Enter the sample Size.
  4. Enter the z-Score (1.96 for 95%).
  5. The margin of error, lower bound, upper bound are displayed instantly and update as you change the inputs.

Example

Example calculation

  1. Enter 100 as the sample Mean.
  2. Enter 15 as the std Dev.
  3. Enter 30 as the sample Size.
  4. Enter 1.96 as the z-Score (1.96 for 95%).
  5. The results update instantly.
Margin of Error: 5.37 • Lower Bound: 94.63 • Upper Bound: 105.37

Benefits of using the Confidence Interval Calculator

  • Get accurate results in seconds without manual calculations.
  • Free to use, no registration needed.
  • Works on any device with a browser.
  • Helps you understand how your inputs affect the result.

Who should use the Confidence Interval Calculator?

  • Students practising problems and verifying homework answers.
  • Teachers preparing examples and checking student work.
  • Engineers and analysts who need quick, reliable calculations.
  • Anyone who wants to double-check manual arithmetic.

Tips for getting the most out of the Confidence Interval Calculator

  • Check your inputs for typos — a single wrong digit changes the result completely.
  • Use the result to verify your manual working, not to replace understanding.
  • Try a simple case first (like 0 or 1) to make sure the output makes sense.

Frequently Asked Questions

What is the Confidence Interval Calculator?

Calculate the confidence interval for a population mean.

How accurate is the Confidence Interval Calculator?

The calculator uses standard formulas and rounds results to a sensible number of decimal places, so the output is accurate for practical purposes.

What inputs do I need for the Confidence Interval Calculator?

You need sample mean, std dev, sample size, z-score (1.96 for 95%). Enter them and the result appears instantly.

Is the Confidence Interval Calculator free to use?

Yes, it is completely free with no limits on usage.

The Confidence Interval Calculator turns a tedious calculation into an instant answer, so you can focus on understanding the concept instead of the arithmetic.

Related Calculators