Micro Tools
Advertisement

Confidence Interval Calculator

Build a confidence interval for a population mean from the sample mean, SD, and size.

Confidence Interval

Enter sample statistics and pick a confidence level.

Result
-

Enter numbers to see the result.

Lower bound
-
Upper bound
-
Margin of error
-
Formula: CI = x-bar +/- z x (s / sqrt(n)). z is 1.645 for 90%, 1.96 for 95%, 2.576 for 99%.
Advertisement

Mean plus or minus error

A confidence interval takes the sample mean and extends it by the margin of error: z times the standard error s/sqrt(n). With mean 50, SD 8, and n = 64 at 95% confidence, the interval is 50 +/- 1.96, or [48.04, 51.96].

What 95% really means

It does not mean a 95% chance this specific interval contains the truth. It means the procedure captures the true mean in 95% of repeated samples. Bigger samples shrink the interval; higher confidence widens it.

Related tools

Mortgage calculatorMonthly cost with taxes, insurance, PMI and payoff schedule. Loan calculatorMonthly payment and interest for auto and personal loans. Compound interestSee how savings grow with compound interest.

Confidence Interval FAQs

What is the 95% CI for mean 50, SD 8, n = 64?
[48.04, 51.96]. The margin of error is 1.96 x 8/8 = 1.96. Defaults are preloaded.
What is the confidence interval formula?
x-bar +/- z x (s / sqrt(n)), where z depends on the confidence level: 1.645 for 90%, 1.96 for 95%, 2.576 for 99%.
How do I make the interval narrower?
Increase the sample size n: the margin of error shrinks with 1/sqrt(n), so quadrupling n halves the width.
Why is the 99% interval wider?
Higher confidence needs a larger z multiplier (2.576 vs 1.96) to be safer, which stretches the interval.
Is my data uploaded?
No. The interval is computed locally in your browser.
Advertisement