How to Use Linear Interpolation in Excel
Linear interpolation is a method used to estimate a value between two known data points. In Excel, this can be achieved by using a simple formula. Follow these steps to perform linear interpolation in Excel:
- Organize your data: Arrange your data in two columns, with the independent variable (e.g., x-values) in the first column and the dependent variable (e.g., y-values) in the second column. Ensure that the data points are sorted in ascending order.
- Identify the interval: Determine the interval in which the x-value you want to interpolate lies. In other words, find the two data points that surround the desired x-value.
- Calculate the slope: The slope is the rate at which the dependent variable (y) changes with respect to the independent variable (x). To calculate the slope, use the following formula:Slope = (y2 - y1) / (x2 - x1)Here, (x1, y1) and (x2, y2) are the coordinates of the two data points surrounding the desired x-value.
- Calculate the interpolated y-value: Use the following formula to estimate the y-value corresponding to the desired x-value:y = y1 + slope * (desired x-value - x1)
- Enter the formula in Excel: Type the formula into a cell in Excel to calculate the interpolated y-value.
Example
Let's say we have the following data points:
| x | y |
|---|---|
| 1 | 2 |
| 3 | 4 |
| 5 | 6 |
| 7 | 8 |
We want to interpolate the y-value for x = 4.
- Organize your data: The data is already organized in two columns.
- Identify the interval: The desired x-value (4) lies between the data points (3, 4) and (5, 6).
- Calculate the slope: Use the formula to find the slope:Slope = (6 - 4) / (5 - 3) = 2 / 2 = 1
- Calculate the interpolated y-value: Use the formula to find the interpolated y-value:y = 4 + 1 * (4 - 3) = 4 + 1 = 5
- Enter the formula in Excel: In a cell, type the following formula:
=4 + (1 * (4 - 3))Press Enter, and Excel will calculate the interpolated y-value, which is 5 in this case.
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