Why does it warn me about small samples?

Because the normal approximation needs roughly ten observations in each category to behave. Below that the interval it produces is too narrow and too symmetric, and a tool that hides this is doing you harm.

What does 95% confidence actually mean?

That if you repeated the whole survey many times, about 95% of the intervals produced would contain the true value. It says nothing about the probability for this one particular interval.

My interval is clipped at 100%. Is that right?

The clipping is correct — a proportion cannot exceed 100% — but it is a signal that the method is straining. At that point an exact interval is the better tool.

Confidence Interval Calculator

Forty people out of a hundred said yes. The honest way to report that is not 40% — it is somewhere between 30% and 50%, at 95% confidence. This turns a count into that interval, and it tells you when the sample is too small or too lopsided for the standard method to be trustworthy, which most calculators will happily let you past without a word.

How many said yes

The count in the category you are measuring.

How many were asked

The total sample size.

Confidence level

40.2% to 59.8%

Sample proportion: 50.0%
Margin of error: ±9.80 points

50.0% of the sample, with a 95% confidence interval of 40.2% to 59.8%.

A 95% interval means that if you repeated the whole exercise many times, about 95% of the intervals produced would contain the true value. It does not mean there is a 95% chance the true value is in this particular one.

The interval is checked to contain its own sample proportion and to stay inside 0% to 100%.

What this generator does

Calculates the confidence interval for a proportion using the normal approximation, and — unusually — says when that approximation should not be trusted. The standard rule of thumb is at least ten in each category; below that the interval is still shown but flagged, because a calculator that silently produces a confident-looking interval from three responses is worse than no calculator.

How to use this tool

Enter how many people gave the answer you are measuring.
Enter how many were asked in total.
Choose a confidence level.
The interval updates as you type.

Understanding the controls

How many said yes: The count in whichever category you are measuring. It cannot exceed the number asked, and the tool says so rather than producing nonsense.
How many were asked: The total sample. The interval narrows with the square root of this, so quadrupling the sample halves the margin.
Confidence level: Higher confidence means a wider interval, not a better estimate. 95% is the convention; 99% is worth it only when being wrong is expensive.

Common use cases

Reporting a survey result honestly rather than as a bare percentage
Deciding whether two survey results are actually different or just noisy
Checking whether a small pilot tells you anything at all
Explaining to a stakeholder why a 3-point move in a poll is not news
Teaching what a confidence level does and does not mean

How this generator works

The sample proportion is multiplied out through the standard error formula and scaled by the two-sided critical value for the chosen confidence level. The result is clipped at 0% and 100%, since a proportion cannot lie outside them — and clipping is itself reported, because it is a sign the approximation is straining. Before display the interval is checked to contain its own sample proportion and to have a width matching the stated margin.

Randomness and fairness

Nothing here is random. The same counts always give the same interval.

For how randomness is produced across the whole site, see how Generate Random works.

Assumptions this tool makes

Simple random sampling from the population of interest.
The normal approximation is adequate, which the tool checks and warns about.

Limitations and good to know

This is the normal approximation, also called the Wald interval. It is the one taught and the one most reported, and it behaves poorly near 0% and 100%.
For small samples or extreme proportions an exact method such as Clopper-Pearson, or the Wilson interval, is more honest. The tool says when you are in that territory but does not compute them.
It covers a single proportion, not a difference between two.
It assumes simple random sampling; a clustered survey has a wider real interval than this shows.

Common mistakes

Reading it as a 95% chance the true value is in this interval: It is not. The interval either contains the true value or it does not. What is 95% is the long-run rate at which intervals built this way capture it.
Comparing two overlapping intervals and concluding no difference: Overlapping intervals do not imply no significant difference. Testing the difference directly is a separate calculation.
Reporting the point estimate alone: 40% from a sample of 20 and 40% from a sample of 2,000 are very different claims. The interval is what carries that.

Practical tips

Report the interval, not just the percentage. It is the difference between a finding and a number.
If the interval spans a decision boundary, the honest answer is that the survey did not settle the question.
Watch for the small-sample warning on pilot data — it appears more often than people expect.

Privacy and your data

Calculated entirely in your browser. Nothing you enter is sent anywhere or stored between visits.

Frequently asked questions

Why does it warn me about small samples?: Because the normal approximation needs roughly ten observations in each category to behave. Below that the interval it produces is too narrow and too symmetric, and a tool that hides this is doing you harm.
What does 95% confidence actually mean?: That if you repeated the whole survey many times, about 95% of the intervals produced would contain the true value. It says nothing about the probability for this one particular interval.
My interval is clipped at 100%. Is that right?: The clipping is correct — a proportion cannot exceed 100% — but it is a signal that the method is straining. At that point an exact interval is the better tool.