Confidence Interval Calculator

Calculate the confidence interval for a population mean using sample data. Uses z-based approximation suitable for large samples.

Inputs

Sample Mean (x̄)

Standard Deviation (σ or s)

Sample Size (n)

Confidence Level (%)

Tab to move between fields

Results

Lower Bound

48.04

Upper Bound

51.96

Margin of Error

1.96

Standard Error1

Z-Value1.96

Interval Width3.92

How to Use This Calculator

Enter Sample Mean (x̄), Standard Deviation (σ or s), and Sample Size (n).
Set Confidence Level (%).
Review Lower Bound, Upper Bound, and Margin of Error.
Use Standard Error and Z-Value to inform your decision.
Use the chart to visualize the results and explore different scenarios by adjusting inputs.

How the result changes with Sample Mean (x̄)

Sample Mean (x̄)	Lower Bound	Upper Bound	Margin of Error
-800,000	-800,001.96	-799,998.04	1.96
-300,000	-300,001.96	-299,998.04	1.96
300,000	299,998.04	300,001.96	1.96
800,000	799,998.04	800,001.96	1.96

What each input means

Sample Mean (x̄): The arithmetic mean of your sample data.
Standard Deviation (σ or s): Population or sample standard deviation. Use sample SD if population SD is unknown.
Sample Size (n): Number of observations in the sample. Larger samples yield narrower intervals.
Confidence Level (%): Desired confidence level as a percentage. Common choices: 90%, 95%, 99%.

How this is calculated

Worked example, using the default values

Identify Input Parameters
4 parameters
Sample Mean (x̄) = 50, Standard Deviation (σ or s) = 10, Sample Size (n) = 100, Confidence Level (%) = 95 = 4 input(s) provided
Calculate Lower Bound
Lower Bound
48.0396 = 48.0396
Calculate Upper Bound
Upper Bound
51.9604 = 51.9604
Calculate Margin of Error
Margin of Error
1.9604 = 1.9604
Calculate Standard Error
Standard Error
1 = 1
Calculate Z-Value
Z-Value
1.9604 = 1.9604

Engine last updated July 11, 2026. Checked against 2 independently-derived tests — how we verify calculators.

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