✓ Effortless Math · Free Tool

Confidence Interval Calculator — for a Mean (Z)

Enter the sample mean x̄, the sample standard deviation s, and the sample size n, pick a confidence level — get the z-based interval x̄ ± z*·s/√n with the critical value, standard error, margin of error, and step-by-step working.

Interval:  x̄ ± z*·(s / √n)
sample mean x̄ , std dev s , size n Confidence: custom % %

Sample size n must be a whole number ≥ 1, the standard deviation s ≥ 0, and the confidence level strictly between 0 and 100. Decimals are fine.

Results

Confidence interval
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Critical value z*
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Standard error — s/√n
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Margin of error — z*·SE
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Lower bound
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Upper bound
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Step-by-step (z-interval for a mean)

    Note: This is a z-interval, which assumes a known/large-sample standard error. For a small sample (roughly n < 30) with an unknown population σ, a t-interval is more appropriate.