Excel Linear Interpolation Formula

Excel Formula for Interpolation

Objective

To interpolate a value ( z_0 ) based on known values ( x_1, y_1, z_1 ) and ( x_2, y_2, z_2 ) using linear interpolation principles.

Formula Structure

The linear interpolation formula can be expressed as:

[ z_0 = z_1 + \frac{(z_2 - z_1)}{(y_2 - y_1)} \times (y_0 - y_1) ]

Excel Formula

In Excel, this can be translated into a formula as follows:

= z1 + ((z2 - z1) / (y2 - y1)) * (y0 - y1)

Explanation of Components

1. z1: The value of z corresponding to the first known point.
2. z2: The value of z corresponding to the second known point.
3. y1: The first known value on the y-axis.
4. y2: The second known value on the y-axis.
5. y0: The known value on the y-axis for which we want to find ( z_0 ).

Practical Example

Known Values

• ( x_1 = 1 ) (not used in interpolation)
• ( y_1 = 10 )
• ( z_1 = 50 )
• ( y_2 = 20 )
• ( z_2 = 100 )
• ( y_0 = 15 ) (the value for which we want to estimate ( z_0 ))

Implementation in Excel

Assuming the following cell references:

• B1 contains y1 (10)
• C1 contains z1 (50)
• B2 contains y2 (20)
• C2 contains z2 (100)
• B3 contains y0 (15)
• In cell C3, to find ( z_0 ), enter:

= C1 + ((C2 - C1) / (B2 - B1)) * (B3 - B1)

Result Calculation

By substituting the values into the formula:

• ( z_0 = 50 + \left(\frac{100 - 50}{20 - 10}\right) \times (15 - 10) )
• ( z_0 = 50 + \left(\frac{50}{10}\right) \times 5 )
• ( z_0 = 50 + 5 \times 5 )
• ( z_0 = 50 + 25 )
• ( z_0 = 75 )

Conclusion

This Excel formula allows for the interpolation of ( z_0 ) based on linear relationships among the specified ( y ) and ( z ) values. Mastering such techniques is crucial for data analysis in Excel, and further training can be pursued through the Enterprise DNA Platform to enhance your data capabilities.