Confidence Interval Calculator for Proportions and Means
Get the confidence interval for a proportion or a mean. Compares Wald, Wilson, Agresti-Coull, Clopper-Pearson and Jeffreys, and accepts raw data. Free.
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How to use the confidence interval calculator
- Choose A proportion for yes/no or "percentage who" results, A mean for averages, or Raw data to paste your values.
- Enter the counts or summary figures.
- Pick a confidence level and, for small populations, the population size.
For proportions you get five methods side by side, with the recommended one highlighted, so you can see when the choice matters.
Which confidence interval method should I use?
| Method | When to use it |
|---|---|
| Wald (normal) | Large samples with results well away from 0% and 100%. Taught in textbooks but unreliable for small bases. |
| Wilson score | The best general default. Accurate for small samples and extreme results, and stays inside 0–100%. |
| Agresti–Coull | A simple "add two successes and two failures" fix to Wald. Close to Wilson. |
| Clopper–Pearson | "Exact" and conservative. The interval is usually wider than needed, but it never undercovers. |
| Jeffreys | A Bayesian interval with excellent average coverage. Good for small samples. |
Brown, Cai and DasGupta's 2001 review in Statistical Science showed that the Wald interval can have far less than its stated coverage even with large samples, and recommended Wilson or Jeffreys instead. That is why Wilson is highlighted here.
Worked example: a small B2B base
Three of 40 IT directors say they plan to switch supplier. That is 7.5%.
- Wald gives 7.5% ± 8.2 points: a lower bound below zero, which is impossible (the calculator shows it as 0%).
- Wilson gives 2.6% to 19.9%.
- Clopper–Pearson gives 1.6% to 20.4%.
The honest message for a client is "somewhere between about 3% and 20%", not "7.5% ± 8". Press Example to load it.
Intervals for means
For an average, the calculator uses the t-distribution with n − 1 degrees of freedom. It gives a slightly wider interval than the z-based formula for small samples and converges to it as the sample grows. Paste raw values to get the mean, standard deviation and median as well.
Frequently asked questions
What is the difference between a confidence interval and the margin of error?
The margin of error is half the width of a symmetric confidence interval. Wilson, Clopper–Pearson and Jeffreys intervals are not symmetric around the result, so it is clearer to report the lower and upper bounds.
What does 95% confidence actually mean?
If you repeated the survey many times and built an interval each time, about 95% of those intervals would contain the true population value. It is a statement about the method, not a 95% probability for one interval.
Why is the interval not centred on my result?
Near 0% or 100% the uncertainty is lopsided: a result cannot fall below zero. Good methods reflect that, so the interval stretches further towards 50%.
Can I use this for weighted data?
Divide your sample size by the design effect and enter that effective sample instead. The weighting efficiency calculator gives you the design effect.
Need the respondents, not just the numbers?
Global Vox Populi runs quantitative and qualitative fieldwork in 170+ countries through its own proprietary panels of consumers, B2B and IT decision-makers, physicians, nurses, patients, caregivers and payers. ISO 9001, ISO 20252 and ISO/IEC 27001 certified and HIPAA compliant, following ESOMAR and Insights Association guidelines.
Check feasibilityLink to this tool
Free to use in proposals, courses and articles. If it helped, a link back is appreciated:
<a href="https://globalvoxpopuli.com/tools/confidence-interval-calculator/">Confidence Interval Calculator</a> by Global Vox Populi