When should I use t-distribution vs z-distribution for confidence intervals?

Use t-distribution when your sample size is less than 30 or when the population standard deviation is unknown (which is most cases). Use z-distribution for large samples (n ≥ 30) when the population standard deviation is known. Our calculator automatically selects the appropriate distribution based on your sample size.

What confidence level should I choose?

95% is the standard confidence level used in most research and publications. Use 99% when you need higher certainty and can accept a wider interval (e.g., critical medical decisions). Use 90% when you need more precision with a slightly higher risk of error.

What is the difference between Wilson and Wald methods for proportion confidence intervals?

The Wilson score method is generally more accurate, especially for small sample sizes or extreme proportions (near 0 or 1). The Wald method is simpler but can produce intervals outside the valid 0-1 range for proportions. Our calculator uses the Wilson method by default for better accuracy.

How do I interpret a confidence interval?

A 95% confidence interval means that if you repeated your study many times, approximately 95% of the calculated intervals would contain the true population parameter. It represents the range of plausible values for the population parameter based on your sample data.

Confidence Interval Calculator - Free Statistical CI Tool

1) Choose what to estimate

Selected

Mean

One-sample (t/z), by group

• t-distribution (n < 30)
• z-distribution (n ≥ 30)
• By group comparison

Click "Select →" below to configure

Proportion

Wilson (default), Wald, Exact

• Wilson score (recommended)
• Wald method
• Exact binomial

Variance

Chi-square CI for σ²

• Chi-square distribution
• Confidence interval for σ²
• Standard deviation CI

Difference

Two-sample / Paired (mean or proportion)

• Two-sample mean difference
• Paired mean difference
• Two-proportion difference