A **tolerance interval** is a range that is likely to contain a specific proportion of a population with a certain level of confidence.

We can use the following formula to calculate the lower and upper limits of a two-sided tolerance interval:

**Tolerance Interval Limits**: x̄ ± z_{(1-p)/2}√(n-1)(1+1/n)/X^{2}_{1-α, n-1}

where:

**x̄**: sample mean**z**: z critical value**p**: proportion of population to be contained in interval**n**: sample size**X**: Chi-Square critical value with 1-α significance level and n-1 degrees of freedom^{2}

The following example shows how to calculate a tolerance interval in Excel for a given sample.

**Example: Calculating a Tolerance Interval in Excel**

Suppose we collect the following sample data:

Suppose we would like to create a tolerance interval that contains 99% of the population values with a 95% level of confidence.

We can use the following formulas in Excel to calculate this tolerance interval:

The tolerance interval turns out to be **[15.102, 73.565]**.

We would interpret this to mean that this interval contains 99% of the population values with a 95% level of confidence.

Note that if we change the values for the confidence level or the proportion of the population in the interval, the lower and upper limits of the tolerance interval will automatically change.

**Note**: You can automatically calculate a tolerance interval for a given sample by using this online Tolerance Interval Calculator.

**Additional Resources**

The following tutorials explain how to calculate other intervals in Excel:

How to Construct a Prediction Interval in Excel

How to Calculate Confidence Intervals in Excel

How to Plot Confidence Intervals in Excel

Hi, in your example I can’t see the cells that the equations are referencing. Could you include what the equations are, particularly for the Z critical Value and the Chi-Square critical value please? thank you

It would be good if the formulas in your sample spreadsheet didn’t reference non-existent spreadsheet cells. See E9 through E13.

What is F2, F3, F5, F6, F7, F8, F9 in the example? column F is not shown

You cropped out column F. Can you please fix?