Newton Raphson Method in Excel

The Newton-Raphson method is a numerical method used to find the roots of an equation, i.e., the values of x that make the equation equal to zero. It is a powerful tool for solving complex non-linear equations, and it can be implemented in Excel using a combination of the “Goal Seek” function and a user-defined function.

The Newton-Raphson method is based on the idea of iteratively improving an estimate of the root, based on the tangent line to the curve of the equation at the current estimate. The method starts with an initial guess for the root, and then calculates a new estimate.

Follow the steps below to learn how to use Newton Raphson Method in Excel.

Newton Raphson Method to solve the equation

We are going to use the Newton Method to solve the equation x^2=5

First, you need to label the column like this.

first Newton's method

Note: Argument (x) is required for a column for function evaluations (f(x)), and a column for slope (f\’(x)).

Preparing Newton’s method calculator

Fill in the value in (x).

In column B write the formula =A2^2-5 and in column C write the formula 2*A2

second Newton's method

In column A cell A3 enter the formula =A2-B2/C2. Select cell B2, move the cursor to the bottom right, a black plus sign will appear. Drag the black plus sign to cell B7.

third Newton's method

Repeat with cell C2.

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Repeat with cell A1. That’s it. You have now learned how to use the Newton Method in Excel.

fifth Newton's method

Note that once the value of x no longer varies from row to row and f(x) is small (close to zero), you have the solution (assuming the process has converged).

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sixth Newton's method

Note: Answer is shaded in yellow.