Confidence Interval Calculator
Calculate statistical confidence intervals quickly and accurately for your research and data analysis needs 📊
Master confidence interval calculations for your statistical analysis, research studies, and data-driven decision making with this comprehensive calculator.
Table of Contents
How to Use This Calculator
For Population Mean Estimation:
- Enter your sample mean, sample size, and standard deviation
- Choose 95% confidence level for standard research
- Select auto-detect for distribution (uses t-distribution for small samples)
- Click calculate to get your confidence interval
For Proportion Analysis:
- Select “Population Proportion” from calculation type
- Enter your sample proportion (as decimal: 0.65 for 65%)
- Provide your sample size
- Get confidence intervals for survey data and categorical outcomes
For Sample Size Planning:
- Choose “Required Sample Size” calculation type
- Enter your desired margin of error
- Specify expected standard deviation
- Calculate how many observations you need for your study
Key Formulas
Population Mean (Normal Distribution):
CI = x̄ ± z(α/2) × (σ/√n)
Population Mean (t-Distribution):
CI = x̄ ± t(α/2,df) × (s/√n)
Population Proportion:
CI = p̂ ± z(α/2) × √[p̂(1-p̂)/n]
Critical Values Reference
| Confidence Level | Z-Value | Common Use Case |
|---|---|---|
| 90% | 1.645 | Exploratory analysis |
| 95% | 1.960 | Standard research |
| 99% | 2.576 | High-stakes decisions |
Frequently Asked Questions
When should I use t-distribution vs normal distribution?
Use t-distribution for small samples (n < 30) or when the population standard deviation is unknown. Use normal distribution for large samples (n ≥ 30) with known population standard deviation.
How do I interpret a 95% confidence interval?
A 95% confidence interval means that if we repeated the sampling process many times, 95% of the calculated intervals would contain the true population parameter.
What sample size do I need for a specific margin of error?
Use the sample size calculator option. Enter your desired margin of error, expected standard deviation, and confidence level to determine the required sample size.
Start Your Statistical Analysis
Use our confidence interval calculator to make data-driven decisions with statistical precision. Perfect for researchers, analysts, students, and professionals who need reliable interval estimates.