Confidence Interval Calculator
Build confidence intervals for proportions and means with step-by-step solutions, margin of error, and critical values.
- Proportion — CI for a population proportion using z*
- Mean (σ known) — z-interval when the population standard deviation is known
- Mean (σ unknown) — t-interval when using the sample standard deviation
CI for a population proportion using z*
Formulas Used
CI for proportion
CI for mean (σ known)
CI for mean (σ unknown)
How to Use This Calculator
- Select a mode — proportion, mean with known σ, or mean with unknown σ
- Choose a confidence level — 90%, 95%, or 99%
- Enter your values — sample statistic, spread measure, and sample size
- See the result with the full interval, margin of error, and step-by-step work
When to Use Each Mode
- Proportion — you have a sample percentage (e.g., “42% of 500 surveyed voters support the policy”) and want to estimate the true population proportion
- Mean (σ known) — you know the population standard deviation from prior research and want to estimate the population mean from a sample
- Mean (σ unknown) — you only have the sample standard deviation (the most common real-world scenario) and want to estimate the population mean
Common Confidence Levels
| Level | z* | Use |
|---|---|---|
| 90% | 1.645 | Screening, preliminary analysis |
| 95% | 1.960 | Standard for most research |
| 99% | 2.576 | High-stakes decisions, medical research |
Related
- Confidence Intervals for Proportions — theory, conditions, and worked examples
- Confidence Intervals for Means — z-intervals vs t-intervals explained
- Normal Distribution Calculator — find probabilities and z-scores