**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, here’s what it would look like:

Now suppose that we’d like to find the y-value associated with a new x-value of **13**. We can see that we have *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))

Here’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 the **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.*

Zach, thanks for offering this helpful example. I was wondering if you could offer some assistance with reworking this sample formula for data that is laid out in rows rather than in columns. For example, if you took your data above and placed all X values in row 1 and Y values in row 2, what would the formula be to solve for the same X of 13? Really appreciate your help here.