Interpolate Between Two Values In Excel Made Easy

In various fields such as finance, engineering, and science, it's common to need to interpolate between two values in Excel. Interpolation is a process of finding a value between two known values in a dataset. Excel provides several methods to perform interpolation, and in this article, we'll explore the most commonly used techniques.

Why Interpolate Between Two Values in Excel?

Interpolation is useful when you need to estimate a value that falls within a range of known values. For example, if you have a dataset of temperatures measured at specific times of the day, you can use interpolation to estimate the temperature at a time that wasn't measured. Interpolation can also be used to fill in missing data points in a dataset.

Methods for Interpolating Between Two Values in Excel

There are several methods for interpolating between two values in Excel, including:

Linear Interpolation

Linear interpolation is a simple method that assumes a linear relationship between the two known values. This method is suitable when the relationship between the variables is linear.

To perform linear interpolation in Excel, you can use the following formula:

y = y1 + (x - x1) * (y2 - y1) / (x2 - x1)

Where:

• y is the interpolated value
• y1 and y2 are the known values
• x is the value at which you want to interpolate
• x1 and x2 are the corresponding x-values for y1 and y2

For example, suppose you want to interpolate the value of y at x = 5, given the points (x1, y1) = (2, 3) and (x2, y2) = (7, 8). The formula would be:

=3 + (5 - 2) * (8 - 3) / (7 - 2)

Using the FORECAST Function

Alternatively, you can use the FORECAST function in Excel to perform linear interpolation. The FORECAST function takes the following syntax:

FORECAST(x, known_y's, known_x's)

Where:

• x is the value at which you want to interpolate
• known_y's is the range of known y-values
• known_x's is the range of corresponding x-values

For example, using the same data as above, the FORECAST function would be:

=FORECAST(5, {3, 8}, {2, 7})

Polynomial Interpolation

Polynomial interpolation is a more complex method that assumes a polynomial relationship between the variables. This method is suitable when the relationship between the variables is non-linear.

To perform polynomial interpolation in Excel, you can use the TREND function. The TREND function takes the following syntax:

TREND(known_y's, known_x's, [const])

Where:

• known_y's is the range of known y-values
• known_x's is the range of corresponding x-values
• [const] is an optional argument that specifies whether the polynomial should be forced to pass through the origin (i.e., (0,0))

For example, suppose you want to interpolate the value of y at x = 5, given the points (x1, y1) = (2, 3), (x2, y2) = (7, 8), and (x3, y3) = (10, 12). The TREND function would be:

=TREND({3, 8, 12}, {2, 7, 10}, 5)

Using the INDEX and MATCH Functions

Alternatively, you can use the INDEX and MATCH functions to perform polynomial interpolation. The INDEX and MATCH functions take the following syntax:

INDEX(array, MATCH(x, known_x's, [match_type]))

Where:

• array is the range of known y-values
• x is the value at which you want to interpolate
• known_x's is the range of corresponding x-values
• [match_type] is an optional argument that specifies the type of match to perform (e.g., exact, approximate)

For example, using the same data as above, the INDEX and MATCH functions would be:

=INDEX({3, 8, 12}, MATCH(5, {2, 7, 10}, 0))

Gallery of Interpolation Examples

Interpolation Examples

Conclusion

Interpolating between two values in Excel is a common task that can be performed using various methods, including linear interpolation, polynomial interpolation, and others. By understanding the different methods and techniques available, you can choose the best approach for your specific problem and improve your data analysis and visualization skills.

We hope this article has been informative and helpful! If you have any questions or need further clarification on any of the topics discussed, please don't hesitate to ask. Share your thoughts and experiences with interpolation in the comments below!