Free Confidence Interval Calculator Online
This free online confidence interval calculator computes the CI and margin of error from your sample mean, sample size, standard deviation, and chosen confidence level.
Sample Parameters
Confidence Interval
Enter parameters above
How the Confidence Interval Calculator Works
The confidence interval calculator uses the formula: CI = x̄ ± Z × (σ / √n), where x̄ is the sample mean, Z is the z-score for the confidence level, σ is the standard deviation, and n is the sample size. This gives the range in which the true population mean likely falls.
For example, with a sample mean of 50, standard deviation of 10, sample size of 100, and 95% confidence: the margin of error is 1.96 × (10/10) = 1.96. The confidence interval calculator gives CI = [48.04, 51.96]. There is a 95% probability this interval contains the true mean.
The confidence interval calculator supports 90% (Z=1.645), 95% (Z=1.96), and 99% (Z=2.576) confidence levels. Higher confidence means a wider interval but greater certainty.
When You Need a Confidence Interval
Surveys report results like "42% approve, margin of error ±3%" — that is a confidence interval. The confidence interval calculator helps you compute these ranges for your own data.
Clinical trials use confidence intervals to report treatment effects. "The drug reduced symptoms by 15 points (95% CI: 12–18)" means the true effect is likely between 12 and 18 points. The confidence interval calculator quantifies this uncertainty.
Quality control uses confidence intervals to determine if a manufacturing process meets specifications. The confidence interval calculator helps engineers verify that the true mean measurement falls within tolerance.
Tips for Using the Confidence Interval Calculator
Larger n = Narrower CI
Increasing sample size reduces the margin of error. The confidence interval calculator shows how n affects precision.
95% Is Standard
Most research uses 95%. Use 99% only when errors are costly. The confidence interval calculator supports all levels.
Use Sample Std Dev
If you do not know the population standard deviation, use the sample standard deviation. The confidence interval calculator works with either.
Interpret Correctly
A 95% CI does not mean 95% of data falls in the range. It means 95% of similarly constructed intervals would contain the true mean.
Frequently Asked Questions
More Math Calculators
Percentage Calculator
Calculate percentages, percent change, and percent of a number.
Percent Change Calculator
Calculate the percentage change between two values — increase or decrease.
Percentage Increase Calculator
Calculate the percentage increase from one value to another.
Fraction Calculator
Add, subtract, multiply, and divide fractions instantly.