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Confidence Interval Calculator

Intervals for a mean or a proportion, with the margin of error.

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At every confidence level

LevelIntervalMargin

What "95% confident" actually means

It does not mean there is a 95 percent chance the true value lies inside this particular interval. The true value is fixed; this interval either contains it or does not. It means that if you repeated the whole sampling procedure many times and built an interval each time, about 95 percent of those intervals would contain the true value. The confidence is in the method, not in this one result.

Confidence interval

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Details

Margin of error—
Standard error—
Critical value—
Distribution used—

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Total width of the interval

The t distribution is used whenever the population standard deviation is unknown, which is nearly always; the difference from z matters most below about 30 observations. To narrow an interval, collect a larger sample — width scales with the square root of n.

Quick Tool Overview

The Confidence Interval Calculator builds an interval around a sample mean or proportion at any confidence level, choosing the t distribution automatically for small samples where the population standard deviation is unknown.

What it does
Calculates confidence intervals for means and proportions
You give it
A sample statistic, sample size and confidence level
You get back
Lower and upper bounds plus the margin of error
Best for
Reporting survey results and coursework
Calculators Free, unlimited use No sign-up Runs in your browser

About the Confidence Interval Calculator

Build a confidence interval around a sample mean or a sample proportion at whatever confidence level you need. The t distribution is used automatically for small samples where the population standard deviation is unknown, and the z distribution otherwise.

The interpretation is the part worth getting right, because the intuitive reading is wrong. A 95 percent confidence interval does not mean there is a 95 percent chance the true value lies inside this particular interval — the true value is fixed, and this interval either contains it or does not. It means that if you repeated the sampling procedure many times, 95 percent of the intervals you built would contain it. The distinction matters, and the page states it plainly.

Key features of the Confidence Interval Calculator

Means and proportions

Both interval types, with the right standard error formula applied to each.

Automatic t or z

The t distribution is used when the population standard deviation is unknown, which is nearly always.

The correct interpretation

The page states plainly that 95 percent describes the method across repeated samples, not this one interval.

Any confidence level

90, 95 and 99 percent presets, or a level you set yourself.

Says which distribution it used

So the result can be reproduced and checked rather than taken on trust.

How to use the Confidence Interval Calculator

  1. 1

    Choose mean or proportion

    Means need a standard deviation; proportions need a count or a percentage.

  2. 2

    Enter your sample

    The sample statistic, the sample size, and the spread where relevant.

  3. 3

    Pick a confidence level

    90, 95 or 99 percent, or any level you enter yourself.

  4. 4

    Read the interval

    The lower and upper bounds, the margin of error, and which distribution was used.

Frequently asked questions

That if you repeated the sampling many times and built an interval each time, about 95 percent of those intervals would contain the true population value. It is a statement about the method, not about this one interval.

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