Confidence Interval Calculator
Calculate confidence interval using your data.
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What this tool does
Calculate confidence interval using your data. Z interval assumes known population SD or adequate large-sample approximation; small samples with unknown SD require a t interval.
How to use the Confidence Interval Calculator
- Enter or select sample mean.
- Enter or select known population sd / large-sample sd.
- Enter or select sample size.
- Enter or select confidence level.
- Read the calculated result; change any measurement to compare alternatives.
Formula
CI=mean±z×SD/sqrt(n)
- mean
- Sample mean
- sd
- Known population SD / large-sample SD
- sample
- Sample size
- confidence
- Confidence level
Z interval assumes known population SD or adequate large-sample approximation; small samples with unknown SD require a t interval.
Worked example
For confidence interval calculator, the following measurements illustrate the exact method: Sample mean: 50; Known population SD / large-sample SD: 10; Sample size: 100; Confidence level: 95.
Inputs
- Sample mean50
- Known population SD / large-sample SD10
- Sample size100
- Confidence level95%
Result
- Lower confidence bound48.04
- Upper confidence bound51.96
- Margin of error1.96
Results explained
- Lower confidence bound
- Lower confidence bound from the formula above. Z interval assumes known population SD or adequate large-sample approximation; small samples with unknown SD require a t interval.
- Upper confidence bound
- Upper confidence bound from the formula above. Z interval assumes known population SD or adequate large-sample approximation; small samples with unknown SD require a t interval.
- Margin of error
- Margin of error from the formula above. Z interval assumes known population SD or adequate large-sample approximation; small samples with unknown SD require a t interval.
Frequently asked questions
CI=mean±z×SD/sqrt(n)
Z interval assumes known population SD or adequate large-sample approximation; small samples with unknown SD require a t interval.
Enter numbers only, separated as described in the labels. Check sample units and remove missing values rather than substituting zero.
No. Statistical inference depends on sampling design, independence, model fit and interpretation; a p-value is not the probability that a hypothesis is true.
No. Calculations and numerical distribution algorithms run entirely in the browser.