*20*

**Interpolation** is the process of estimating an unknown value of a function between two known values.

Given two known values (x_{1}, y_{1}) and (x_{2}, y_{2}), we can estimate the y-value for some point x by using the following formula:

y = y_{1} + (x-x_{1})(y_{2}-y_{1})/(x_{2}-x_{1})

This tutorial explains how to use linear interpolation to find some unknown y-value based on an x-value in Excel.

**Example: Linear Interpolation in Excel**

Suppose we have the following dataset in Excel:

If we create a quick plot of the data, hereâ€™s what it would look like:

Now suppose that weâ€™d like to find the y-value associated withÂ a new x-value ofÂ **13**. We can see that we haveÂ *measured* y-values for x-values of 12 and 14, but not for an x-value of 13.

We can use the following formula to perform linear interpolation in Excel to find the estimated y-value:

=FORECAST(NewX,OFFSET(KnownY,MATCH(NewX,KnownX,1)-1,0,2), OFFSET(KnownX,MATCH(NewX,KnownX,1)-1,0,2))

Hereâ€™s how to use this function to estimate the y-values associated with an x-value of 13:

The estimated y-value turns out to be **33.5**.

If we add the point (13, 33.5) to our plot, it appears to match the function quite well:

We can use this formula to estimate the y-value of any x-value by simply replacing theÂ **NewX** in the formula with any new x-value.

Note that in order for this function to work, the new x-value should fall within the range of the existing x-values.

*You can find more Excel tutorials here.*