Reference definitions and notation for mathematical functions.
Math
Confidence interval
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Your result
Margin of error: 1.568
Formulamean ± z × s/√n
- Select the z critical value.
- Calculate standard error.
- Add and subtract the margin.
Worked example: Mean 50, SD 8, n=100 gives approximately 48.43–51.57 at 95%.
Accuracy notice: The arithmetic follows the displayed formula. Its practical accuracy still depends on valid inputs, appropriate units, and display rounding.
Understand the result before using it
Confidence interval uses sample mean, sample standard deviation, sample size, and confidence level to calculate its result. It applies a defined mathematical relationship to the values you enter and reports the resulting quantity.
Formula, assumptions, and example
Formula
mean ± z × s/√n
Assumptions
- The entered sample mean, sample standard deviation, sample size, and confidence level are complete, valid, and use the units or format shown beside each field.
- Inputs represent ordinary real numbers unless the tool explicitly accepts another format.
- The displayed operation and order of operations match the formula shown on the page.
Worked example
Mean 50, SD 8, n=100 gives approximately 48.43–51.57 at 95%.
When to use it
Good uses
- Check homework or a hand calculation.
- Explore how changing an input changes the result.
- Create a quick numerical reference without setting up a spreadsheet.
Limitations
Common mistakes to avoid
- An undefined operation, such as division by zero, cannot produce a valid finite result.
- Rounded display values can differ slightly from the full internal result.
- Check the formula, source data, units, and displayed precision before relying on the result.
Sources and further reading
These references explain the underlying standards or provide authoritative context. Your own contract, institution, clinician, product documentation, local code, or governing standard may be the controlling source.
Measurement and numerical-reference guidance from NIST.
Questions about this calculation
What does the Confidence interval calculate?
Confidence interval uses sample mean, sample standard deviation, sample size, and confidence level to calculate its result. It applies a defined mathematical relationship to the values you enter and reports the resulting quantity. The formula used is: mean ± z × s/√n
Which inputs affect the Confidence interval result?
The result uses sample mean, sample standard deviation, sample size, and confidence level. Changing any of these values can change the output, so enter them using the labels and units shown.
Is the Confidence interval result exact?
The arithmetic follows the displayed formula. Its practical accuracy still depends on valid inputs, appropriate units, and display rounding.
When should I verify a Confidence interval result?
Verify it whenever the source measurement, unit convention, rounding, or consequences make small differences important.
Clear answers, without the guesswork
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