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Confidence Interval Calculator

CI for a mean with known standard deviation.

Introduction

Confidence Interval Calculator — CI for a mean with known standard deviation. Enter Sample mean, Std. deviation, Sample size, Confidence level to get an instant, accurate result.

Formula

Margin of error = z × (sd/√n). Interval = mean ± margin of error, where z is the critical value for the chosen confidence level (1.645/1.96/2.576 for 90/95/99%).

Step-by-step

  1. Enter the Sample mean.
  2. Enter the Std. deviation.
  3. Enter the Sample size.
  4. Enter the Confidence level.
  5. Click Calculate to see your result instantly.

Real-world example

Example: With Sample mean = 100, Std. deviation = 15, Sample size = 30, Confidence level = 95, the Confidence Interval Calculator gives Lower: 94.6324, Upper: 105.3676, Margin Error: 5.3676.

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 mean.
Why does a larger sample size narrow the interval?
The margin of error shrinks as sample size increases, since √n grows in the denominator.
What inputs does the Confidence Interval Calculator need?
You'll need to provide: Sample mean, Std. deviation, Sample size, Confidence level. All fields use sensible defaults, so you can see a working example immediately and then adjust the values to match your own numbers.
How accurate is the Confidence Interval Calculator?
The Confidence Interval Calculator applies the formula exactly as calculated — Margin of error = z × (sd/√n). Interval = mean ± margin of error, where z is the critical value for the chosen confidence level (1.645/1.96/2.576 for 90/95/99%). — so results are precise for the inputs you provide. Accuracy depends on entering correct, realistic input values.
Is the Confidence Interval Calculator free to use?
Yes, the Confidence Interval Calculator is completely free, requires no signup, and runs instantly in your browser.

About the Confidence Interval Calculator

The Confidence Interval Calculator uses a real, verifiable formula — Margin of error = z × (sd/√n). Interval = mean ± margin of error, where z is the critical value for the chosen confidence level (1.645/1.96/2.576 for 90/95/99%). — so results are accurate every time, not an approximation.