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MATH

Confidence Interval Calculator

Estimate margin of error from sample mean, confidence level, standard deviation with the Confidence Interval Calculator.

Choose an interval workflowBuild an interval from sample statistics or inspect an interval you already have.
2 options
MARGIN OF ERROR2.93994598

Build confidence interval: Builds a normal confidence interval at the selected confidence level, optionally corrects for a finite population, and reports the lower and upper bounds.

Confidence level
95%
Critical Z
1.95996399
Standard error
1.5
Finite-population factor
1
Margin of error
2.93994598
Lower bound
97.06005402
Upper bound
102.93994598
Estimate based on the values shown
MethodBuilds a normal confidence interval at the selected confidence level, optionally corrects for a finite population, and reports the lower and upper bounds.

Before you use the result

The result depends on the entered values, selected mode, and displayed mathematical assumptions.

Sources

CALCULATOR GUIDE

How to use the Confidence Interval Calculator

Estimate margin of error from sample mean, confidence level, standard deviation with the Confidence Interval Calculator. It includes Build confidence interval, Analyze interval bounds workflows, so choose the one that matches the values you actually know. Use it to check the arithmetic while keeping the displayed method and entered values with your work.

Step by step

  1. For the Confidence Interval, enter sample mean, confidence level, standard deviation, sample size, population size. Keep each value in the unit displayed beside its field.
  2. Review the selected Confidence Interval workflow and inputs, then read margin of error in the result panel.
  3. Change one Confidence Interval assumption at a time to compare scenarios. Use Reset to restore this tool's worked example values.

How the calculation works

Builds a normal confidence interval at the selected confidence level, optionally corrects for a finite population, and reports the lower and upper bounds.

Worked example

In the Confidence Interval worked example, sample mean 100, confidence level 95 %, standard deviation 15, sample size 100 produces margin of error of 2.93994598. Build confidence interval: Builds a normal confidence interval at the selected confidence level, optionally corrects for a finite population, and reports the lower and upper bounds. Review the displayed units before comparing the result.

Understanding the result

The Confidence Interval reports margin of error. Use it to check the arithmetic while keeping the displayed method and entered values with your work. The result depends on the entered values, selected mode, and displayed mathematical assumptions.

How to check the answer

Check the Confidence Interval answer by substituting margin of error back into the stated relationship. Test a simple value such as zero, one, or an equal pair, then confirm that sign, scale, units, and rounding match Builds a normal confidence interval at the selected confidence level, optionally corrects for a finite population, and reports the lower and upper bounds.

Common questions

What does the Confidence Interval calculate?

Estimate margin of error from sample mean, confidence level, standard deviation with the Confidence Interval Calculator.

Which Confidence Interval inputs have the biggest effect?

margin of error responds directly to sample mean, confidence level, standard deviation, sample size, population size. Change one input while holding the others constant to see its effect.

Is the Confidence Interval result exact?

The result depends on the entered values, selected mode, and displayed mathematical assumptions. Recheck sample mean, confidence level, standard deviation and use margin of error only for a decision where that level of precision is appropriate.

Formula tests, limits, sources, and guide registry updated September 1, 2026.
INTERPRET THE RESULTRead the math guideCheck assumptions, limitations and comparison methods →