Formula Explanation
CI = mean +/- z x sd / sqrt(n)
This calculator applies the formula CI = mean +/- z x sd / sqrt(n). Enter each value with the matching unit, and AZCalculate updates the result instantly.
Mathematics
Confidence Interval Calculator
Use this confidence interval calculator to calculate estimate confidence interval from mean, standard deviation, sample size, and z value.
confidence intervalstatisticsmargin of error
Calculator
Calculate instantly
Calculator Inputs
Choose what you want to calculate, enter realistic values, adjust units where shown, and use the scenario section for repeated-use planning.
Input and Formula Breakdown
This calculator applies the formula CI = mean +/- z x sd / sqrt(n). Enter each value with the matching unit, and AZCalculate updates the result instantly.
Sample mean
72
Standard deviation
12
Sample size
100
Z value
1.96
Margin of error
2.35
Lower bound
69.65
Upper bound
74.35
Scenario and Comparison
Current
2.35
Projected
28.22
Adjusted
2.59
Visual Comparison
Current result2.35
Projected usage28.22
Comparison scenario2.59
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Use Cases
- Estimate interval
- Report survey range
- Study statistics
Step-by-Step Explanation
- Step 1Enter the known values in the calculator fields.
- Step 2Keep the units consistent with the labels shown beside each input.
- Step 3Apply the formula: CI = mean +/- z x sd / sqrt(n).
- Step 4Review the primary result and supporting values.
Example calculation
Example confidence interval calculator
Given
- Sample mean: 72
- Standard deviation: 12
- Sample size: 100
- Z value: 1.96
Steps
- Use the values shown above.
- Apply CI = mean +/- z x sd / sqrt(n).
Result
The calculator above shows the computed answer instantly from these example values.
Calculator guide
About this Confidence Interval Calculator
Estimate confidence interval from mean, standard deviation, sample size, and z value. This page includes an interactive calculator, concise formula notes, worked examples, FAQs, related calculators, and practical guidance you can revisit whenever needed.
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Calculator usage
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Most active date
2026-06-05
FAQ
Confidence Interval Calculator FAQs
How does the confidence interval calculator work?+
It uses CI = mean +/- z x sd / sqrt(n) and calculates the result from the values you enter.
Can I copy or print the result?+
Yes. AZCalculate calculator pages include copy, share, and print actions.
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