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Calculation Machine

Confidence Interval Calculator

Margin of error and interval around a sample mean.

Reviewed by James Whitfield · How we check our maths

Your values

ⓘ Live results

Results
Confidence interval
66.4636 to 70.3364
Margin of error
± 1.9364
Standard error
0.98796
Relative margin
2.83%

Working

  1. 1SE = 12.1 ÷ √150 = 0.98796
  2. 2MOE = 1.96 × 0.98796 = 1.9364

Quick answer

A confidence interval is the sample mean plus or minus z × the standard error, giving a plausible range for the population mean.

The formula

CI = x̄ ± z·(s ÷ √n)

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Sample mean68.4
  • Standard deviation12.1
  • Sample size150
  • Confidence level95%

Result

  • Confidence interval66.4636 to 70.3364
  • Margin of error± 1.9364
  • Standard error0.98796
  • Relative margin2.83%

How to use the Confidence Interval Calculator

  1. 1Enter your sample mean and standard deviation.
  2. 2Add the sample size.
  3. 3Pick a confidence level.

Frequently asked questions

What does 95% confidence mean?

If you repeated the study many times, about 95% of the intervals produced would contain the true population mean.

How do I halve the margin of error?

Quadruple the sample size — the margin shrinks with the square root of n.

About this calculator