Confidence interval calculator
Interval that contains the true value with a given probability
Confidence interval — range that contains the true parameter (e.g. proportion, mean) with a given confidence level (e.g. 95%).
Parameters
Percentage in the sample with the characteristic of interest
Number of respondents surveyed
Assumptions and limitations
- Formula is for proportion, not mean
- Simple random sample assumed
- n × p and n × (1−p) should be > 5
Confidence interval
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Confidence interval examples
1 Proportion in sample
p = 60%, n = 400, 95% confidence
95% CI ≈ [55%, 65%] — with 95% probability the true proportion in the population lies in this range.
2 Narrowing the interval
Increase sample size
Quadrupling n roughly halves the CI width. Plan a larger n for a more precise estimate.
3 NPS promoter proportion
"9–10" proportion = 50%, n = 200, 95% CI
CI for promoter proportion ≈ [43%, 57%]. NPS is computed from proportion difference; for full NPS build CI separately or via bootstrap.
4 Small proportion (rare event)
p = 5%, n = 400. CI is asymmetric due to 0 boundary
95% CI ≈ [3%, 7%]. For small p, Wilson score or exact binomial interval is better.
5 99% confidence level
p = 50%, n = 500. Wider interval at 99%
99% CI is wider than 95% (Z = 2.576 instead of 1.96). Used when minimizing the risk of missing the true value is more important.
6 Comparing two proportions
Group A: 60% (n=300). Group B: 45% (n=300). Build CI for each proportion
CI A: [54%, 66%], CI B: [39%, 51%]. Intervals do not overlap — difference is statistically significant at α = 0.05.
Frequently asked questions
What is a confidence interval?
How does CI differ from margin of error?
Why is 95% the standard confidence level?
How to narrow the confidence interval?
Can CI be used for comparison?
What does "with 95% probability" mean?
What formula is used for the confidence interval?
When to use CI in a report?
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