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Confidence Interval Calculator

Calculate the confidence interval for a population mean given sample mean, standard deviation, sample size, and confidence level.

What is Confidence Interval Calculator?

The confidence interval calculator computes the range of values within which the true population mean is likely to fall, based on sample data. It uses the Z-distribution for known population standard deviations and large samples.

How to use

  1. 1 Enter the sample mean (the average of your data).
  2. 2 Enter the standard deviation of your sample.
  3. 3 Enter the sample size (number of observations).
  4. 4 Select your desired confidence level (90%, 95%, or 99%).
  5. 5 Click Calculate to get the confidence interval, margin of error, and standard error.

Formula

CI = x̄ ± Z × (σ/√n). Standard error = σ/√n. Margin of error = Z × SE. Z-values: 90%→1.645, 95%→1.96, 99%→2.576.

Example calculation

Sample mean = 50, SD = 10, n = 100, 95% confidence: SE = 10/√100 = 1.0. Margin = 1.96 × 1.0 = 1.96. CI = (48.04, 51.96).

Frequently asked questions

What does a 95% confidence interval mean?

If you repeated the study many times, 95% of the calculated confidence intervals would contain the true population mean. It does not mean there is a 95% chance the true mean is in this specific interval.

When should I use a Z vs T distribution?

Use Z when your sample size is large (n > 30) or when population SD is known. Use T for small samples with unknown population SD. This calculator uses Z-distribution.

How does sample size affect the interval?

Larger sample sizes produce narrower confidence intervals because the standard error (σ/√n) decreases. Doubling precision requires quadrupling the sample size.

What is standard error?

Standard error is the standard deviation of the sampling distribution of the mean. It measures how much the sample mean is expected to vary from the true population mean.

Can I use this for proportions?

This calculator is designed for means. For proportions, use the sample size calculator or a proportion-specific confidence interval formula: p ± Z×√(p(1−p)/n).