Confidence Interval Calculator

What Is a Confidence Interval Calculator?

Why Use Our Confidence Interval Calculator?

How to Use It in 3 Steps

Confidence Interval Calculator FAQ

How to calculate confidence interval?

Take the estimate and add and subtract the margin of error, which is the critical value times the standard error. For a mean that is x̄ ± t* × s/√n. Enter your figures above and the confidence interval calculator does the arithmetic.

What is a confidence interval?

A range of values, worked out from a sample, that is likely to contain the true population value. Its width shows how precise the estimate is: narrow means precise, wide means uncertain.

How to interpret confidence intervals?

A 95% interval comes from a method that captures the true value in 95% of repeated samples. It does not mean a 95% chance that this particular interval holds it. Report it next to the estimate.

How to calculate 95 confidence interval?

Multiply the standard error by 1.96 for large samples and proportions, or by the t value for n − 1 degrees of freedom for small-sample means, then add and subtract the result from the estimate. In the confidence interval calculator, pick 95% and the right critical value is used for you.

How to find 90 confidence interval?

Use the same steps with a smaller critical value: 1.645 for z, or the t value for a 90% two-sided interval. The result is narrower than the 95% interval because you accept more risk of missing the true value.

How to report confidence intervals?

Give the level, the estimate and both bounds, as in M = 100, 95% CI [93.8, 106.2], which follows APA style. Use the same number of decimals as the estimate.

How to find sample size from confidence interval?

For a mean, n = (critical value × s / margin)². For a proportion, n = z² × p(1 − p) / margin². The sample size calculator works this out for surveys and two-group studies.

How to find margin of error from confidence interval?

Subtract the lower bound from the upper bound and halve it. For 93.8 to 106.2 the margin of error is 6.2, and the point estimate is the midpoint, 100.

When to use confidence interval vs hypothesis test?

Use an interval to show how large and how precise an effect is, and a test when you need a yes-or-no decision. A 95% interval that excludes the null value matches a significant two-sided test at 0.05.

How to find confidence interval for slope of regression line?

Use b ± t* × SE(b), with t* from n − 2 degrees of freedom; regression output usually lists SE(b). This tool covers means and proportions, so take the slope interval from your statistics software.

How to calculate confidence interval for a proportion?

Choose Proportion above and enter the successes and the sample size. The Wilson score interval used here behaves better than the simple p̂ ± z√(p̂(1 − p̂)/n) formula for small samples or proportions near 0 or 1.

How many standard deviations is 95 confidence interval?

About 1.96 standard errors either side of the estimate for a normal distribution, often rounded to 2. Note that these are standard errors of the estimate, not standard deviations of the data.

Can I calculate a confidence interval from raw data?

Work out the mean, standard deviation and count first, then enter them here. A spreadsheet gives all three in seconds with its average, standard deviation and count functions. The confidence interval calculator then gives the bounds at once.

Can I calculate a confidence interval without the standard deviation?

A mean needs some measure of spread; if you only have the standard error, multiply it by √n to get the standard deviation. Proportions need no standard deviation, only the successes and the sample size.

When should I use t instead of z for a confidence interval?

Use t for means whenever the population standard deviation is unknown; it widens the interval for small samples. With large samples, t and z give almost the same result. Proportions use z. Large here means about 30 or more observations.

Which method does the calculator use for proportions?

The Wilson score interval. It stays inside 0 and 1 and keeps close to the stated coverage even with small samples, unlike the plain Wald interval taught in many introductions.

How do I write a confidence interval in LaTeX?

In math mode, for example $95\%~\mathrm{CI}~[93.8, 106.2]$; the calculator writes a ready line for you. Use \bar{x} for a sample mean and \hat{p} for a sample proportion.

What are the lower and upper bounds of a confidence interval?

They are the two ends of the interval: the estimate minus and plus the margin of error. Both appear above, next to the margin and the critical value used.

Is my data sent anywhere?

No. The confidence interval calculator runs entirely in your browser; nothing you type is sent or stored.