Confidence Interval Calculator

Eliminate Statistical Uncertainty

Stop guessing your population parameters. This Confidence Interval Calculator allows you to statistically estimate the range in which your true mean lies. Whether you are analyzing survey results, conducting A/B testing, or performing academic research, you need to know how reliable your sample data represents the whole.

This tool automatically handles the complex math behind the Z-distribution (for large samples n ≥ 30) and the T-distribution (for smaller samples). By calculating the Margin of Error and defining the Upper and Lower bounds, it provides a comprehensive statistical summary instantly.

How to Use the Confidence Interval Calculator

1. Enter Data: Input your Sample Mean, Sample Size (n), and Standard Deviation.
2. Select Level: Choose a standard Confidence Level (90%, 95%, 99%) or input a custom percentage.
3. Choose Method: Select Z-Interval if your sample size is large or you know the population standard deviation. Select T-Interval for smaller samples.
4. Calculate: Click the button to view your interval bounds, standard error, and critical values.

Frequently Asked Questions

How to calculate a 95% confidence interval?

Use the formula: Mean ± (Critical Value × Standard Error). For a 95% level, the Z-score is 1.96. Multiply 1.96 by the standard deviation divided by the square root of the sample size, then add and subtract this margin from the mean to find your range.

What is the z-score for 95% confidence interval?

The Z-score for 95% confidence is 1.96. This critical value indicates that 95% of the area under a normal distribution curve lies within 1.96 standard deviations from the center mean.

How to find 95% confidence interval on TI-84?

Press STAT, scroll to TESTS, and select 7:ZInterval (or 8:TInterval). Enter your statistics (mean, Sx, n) and set the C-Level to 0.95. Press Calculate to display the lower and upper bounds.

How to calculate confidence interval in Excel?

For Z-tests, use =CONFIDENCE.NORM(alpha, standard_dev, size). For T-tests, use =CONFIDENCE.T(alpha, standard_dev, size). This returns the margin of error; add and subtract it from your mean to get the interval.

When to use z interval vs t interval?

Use a Z-Interval when your sample size is large (n ≥ 30) or the population standard deviation is known. Use a T-Interval when working with small samples (n < 30) where the population standard deviation is unknown.