Confidence Interval Calculator

Calculate confidence intervals for population means using sample statistics. Choose between known or unknown population standard deviation.

Confidence Level *

Population Standard Deviation *

Sample Mean (x̄) *

mean

Sample Size (n) *

Population Standard Deviation (σ) *

Known population standard deviation

Decimal Precision

Show Steps

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Confidence Interval

Lower Bound

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± Margin

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Upper Bound

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Interval Visualization

Graphical representation of the confidence interval

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Calculation Breakdown

Step-by-step confidence interval calculation

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Interval

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CI range

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Margin of Error

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± E

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Critical Value

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z* or t*

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Sample Size

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Confidence Interval Formulas

Key statistical concepts

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Confidence Interval Tips

Understanding confidence intervals

📊 Statistical Disclaimer: This confidence interval calculator uses the z-distribution for known population standard deviation and t-distribution for unknown. Results assume random sampling and normally distributed data (or n ≥ 30 for CLT).