Confidence Interval Calculator

Calculate the confidence interval and margin of error for sample means or proportions with custom confidence levels (90%, 95%, 99%, or custom).

Confidence Interval for Mean (Known/Unknown SD)

Enter the sample mean, sample size, standard deviation, and select confidence level to compute margin of error and interval bounds.

Sample Mean ($\bar{x}$):

Standard Deviation ($s$ or $\sigma$):

Sample Size ($n$):

Confidence Level:

Standard Deviation Type:

Sample SD ($s$) — Uses Student's t-distribution Population SD ($\sigma$) — Uses Z-distribution

Confidence Interval for Proportion

Enter the number of events (successes) or sample proportion along with sample size to estimate population proportion confidence intervals.

Number of Events ($x$):

Sample Size ($n$):

Sample Proportion ($\hat{p}$ or %):

Confidence Level:

How To Use the Confidence Interval Calculator

A Confidence Interval (CI) provides a range of plausible values for an unknown population parameter based on sample data.

Mean Interval Formula: $CI = \bar{x} \pm t^* \left(\frac{s}{\sqrt{n}}\right)$ or $\bar{x} \pm Z^* \left(\frac{\sigma}{\sqrt{n}}\right)$
Proportion Interval Formula: $CI = \hat{p} \pm Z^* \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$
Margin of Error (MoE): The distance added and subtracted from the sample statistic.

Frequently Asked Questions (FAQs)

A confidence interval gives an estimated range of values which is likely to include an unknown population parameter, calculated from a given set of sample data.

Use the t-score when the population standard deviation is unknown and estimated using the sample standard deviation ($s$). Use the Z-score when the population standard deviation ($\sigma$) is known.

Increasing the sample size ($n$) decreases the standard error and narrows the margin of error, making the estimate more precise.

It means that if you draw repeated independent random samples and compute a 95% confidence interval for each, approximately 95% of those intervals will contain the true population mean or proportion.

Increasing the confidence level (for example, from 95% to 99%) increases the critical value (Z* or t*), which makes the margin of error larger and results in a wider confidence interval.