Confidence Interval Calculator

Your details

Use z when the population standard deviation is known; use t when you only have a sample standard deviation. Use Proportion for a fraction or percentage from a sample.
Enter any value between 1 and 99.99, such as 90, 95 or 99.
%
Two-sided is the standard choice. One-sided gives a lower or upper bound only.
The average of your sample (x-bar).
The known population standard deviation (sigma).
The number of observations in your sample (n). Must be at least 2 for t-intervals.
observations
Enter a target margin of error to calculate the minimum sample size needed.
Lower bound
94.6324
Upper bound105.3676
Margin of error5.3676
Standard error2.7386
Critical value1.96
Interval width10.7352
Lower bound94.6324
Upper bound105.3676
Margin of error5.3676

We are 95% confident the true mean lies between 94.6324 and 105.3676.

  • The margin of error is +/-5.3676, so the interval spans 10.7352 units in total.
  • "95% confident" means that if you drew many random samples and built an interval each time, about 95% of those intervals would contain the true parameter. Any single interval either contains it or does not.
  • To shrink the margin of error, increase the sample size (it falls with the square root of n) or lower the confidence level.

Next stepToggle "Find required sample size" to see how many observations you need for a target margin of error.

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