Confidence Interval Calculator
Calculate the confidence interval from sample mean, standard deviation, and size.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Enter your sample mean, sample standard deviation, and sample size. Choose your confidence level (90%, 95%, or 99%). The calculator computes the confidence interval, margin of error, and standard error using the t-distribution for small samples.
About This Calculator
A confidence interval gives a range of plausible values for a population parameter based on sample data. A 95% confidence interval means that if you repeated the study many times, about 95% of the intervals would contain the true population parameter. The width depends on the confidence level, sample size, and variability.
Frequently Asked Questions
Why use the t-distribution instead of z?
The t-distribution accounts for the extra uncertainty when estimating the population standard deviation from a sample. For large samples (n > 30), the t and z values are nearly identical.
How do I make a confidence interval narrower?
Increase the sample size, lower the confidence level (e.g., 90% instead of 99%), or reduce variability in your measurements.
Does a 95% CI mean 95% probability the true value is inside?
Not exactly. The true value is fixed. The 95% refers to the long-run proportion of intervals that would capture the true value if you repeated the sampling.