Confidence Interval Calculator

Calculate Z- or t-based confidence intervals from sample mean, standard deviation, and sample size.

Category: Calculators

When to use?

Use it to estimate a population mean from survey data, calculate a margin of error, or compare uncertainty in small and large samples.

How to use

  • Enter sample mean, standard deviation, and sample size.
  • Choose the confidence level.
  • Select Z or t distribution and review the interval.

Input Explanation

Mean is the sample average, standard deviation is the population or sample standard deviation depending on method, and n is the sample size. Use n of at least 2 for t-based intervals.

Calculation Basis

The interval is x̄ ± z*(σ/√n) for Z or x̄ ± t*(s/√n) for t. Critical values come from the selected confidence level.

Usage Examples

  • Survey analysis - Estimate the range where a population mean is likely to fall.
  • A/B test review - Compare uncertainty before interpreting experiment results.

Examples

  • n=30, mean=50, sd=10, 95% Z CI → [46.42, 53.58]
  • n=10, mean=5.2, sd=0.8, 95% t CI → approximately [4.63, 5.77]
  • Survey average 4.1, sd 0.7, n=50 → estimate the likely population-mean range

Cautions

  • t critical values are approximated. Use specialized statistics software for publication-grade analysis.

FAQ

Should I use Z or t?

Use Z when the population standard deviation is known or the sample is large. Use t when the sample is small or only sample standard deviation is available.

Does a higher confidence level mean better?

Higher confidence creates a wider interval. It reduces risk of missing the true mean but gives a less precise range.

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