## Introduction to Newton's Method Calculator:

Newton's method calculator is an amazing online that helps you to **find the approximate value** of a given function. Our tool evaluates the real root values from the given function and its differentiation of the function.

The newton raphson method calculator is a very convenient tool that can keep you away from doing tiresome efforts to calculate the estimated value especially when you are dealing with complex function evaluation and do not get the desired result.

## What is Newton Raphson's Method?

Newton Rapson Method is a **numerical analysis process** in which you use the iteration method to solve the estimated value of a given real-valued root function. This method gives information about whether the given function is coverage or not.

Newton's Raphson method is sometimes called Newton's method only in linear algebra. This is a complex method because sometimes iterations become too lengthy that you cannot find the approximation value or get a solution after doing so many iterations. This flaw makes it a less accurate solution than the regular falsi method or scant method.

## Formula of Newton Raphson Method:

The **formula of Newton raphson** has a function f(x), the function differentiation f’(x) in n number of times, and xn+1 is the root value of that given function. The formula behind the newton method calculator is given,

$$ f(x_{n+1}) \;=\; x_n - \frac{f(x_n)}{f’(x_n)} $$

- f′(x): the first-order of differentiation
- x0: the initial root value of the given function
- n: the number of root in which it is vary as n = 0,1,2, 3, …

## How to Find the Newton-Raphson Method?

For the **calculation** of the Newton-Raphson method, newton raphson calculator uses the iterative steps to get the approximate root value of a real value function. You need to perform some simple steps in order to calculate it which are:

**Step 1**:

Identify the function f(x) on which you want to find the estimated root value.

**Step 2**:

Evaluate the derivative f′(x) of the given function.

**Step 3**:

Choose an initial approximation x1 by taking two random numbers and putting it into the given function if it gives an opposite value then the root ly between both numbers. The root you select can affect the convergence and the accuracy of the result.

**Step 4**:

The Newton raphson formula for the approximation value of a function f(x) is,

$$ f(x_{n+1}) \;=\; x_n - \frac{f(x_n)}{f’(x_n)} $$

**Step 5**:

For successive iteration put the function value and differential value and n=0,1,2,3… and x1=m root value which you choose in the Newton Raphson formula.

**Step 6**:

Repeat the step 4 process until you do not get the solution has converged during successive iterations method.

## Solved Example of Newton Raphson Method:

An **example of newton raphson** method is given below to let you understand the working process of the newton's method calculator.

### Example: Find the Newton-Raphson method of the given function

$$ f(x) \;=\; x^2 - 2 \;=\; 0 $$

**Solution**:

The given function is,

$$ f(x) \;=\; x^2 - 2 \;=\; 0 $$

Differentiate the given function with respect to x

$$ f’(x) \;=\; 2x $$

The Newton raphson method formula is,

$$ f(x_{n+1}) \;=\; x_n - \frac{f(x_n)}{f’(x_n)} $$

Add the given function value in the Newton raphson method formula,

$$ x_{n+1} \;=\; x_n - \frac{f(x_n)}{f’(x_n)} \;=\; x_n - \frac{x_n^2 - 2}{2x_n} \;=\; \frac{x_n}{2} + \frac{1}{x_n} $$

To find the initial root value let's suppose x = 1,2 and put the given function f(x).

$$ f(1) \;=\; (1)^2 - 2 \;=\; -1 < 0 $$

$$ f(2) \;=\; (2)^2 - 2 \;=\; 2 > 0 $$

So root between 1 and 2. Let's take a root x1 = 1.5. For successive iteration put n=0,1,2,3,.... or x2, Put n=0 and x1 = 1.5

$$ x_2 \;=\; \frac{1}{2}x_1 + \frac{1}{x_1} \;=\; \frac{1}{2}(1.5) + \frac{1}{1.5} $$

$$ =\; 1.416666667 $$

For x3, Put n = 1 and x1 = 1.4166,

$$ x_3 \;=\; \frac{1}{2} x_2 + \frac{1}{x_2} \;=\; \frac{1}{2}(1.416666667) + \frac{1}{1.416666667} $$

$$ =\; 1.414215686 $$

For x4, Put n=2 and x1 = 1.41421,

$$ x_4 \;=\; \frac{1}{2}x_3 + \frac{1}{x_3} \;=\; \frac{1}{2}(1.414215686) + \frac{1}{1.414215686} $$

$$ =\; 1.414213562 $$

For x5, Put n = 3 and x4 = 1.414213,

$$ x_5 \;=\; \frac{1}{2}x_4 + \frac{1}{x_4} \;=\; \frac{1}{2}(1.414213562) + \frac{1}{1.414213562} $$

$$ =\; 1.414213562 $$

## How to Use Newton's Method Calculator?

The newton raphson method calculator has a simple design that helps you to solve the given real root function to find the estimated value immediately. You just need to put your given function in this tool only by following some simple steps. These steps are:

- Enter the real value function to find the real root value in the input box of Newton Raphson calculator.
- Choose the variable of differentiation for the given function for the Newton method in the input field.
- Check your given function value to get the exact solution of the Newton-Repson method question.
- Click on the
**Calculate**button to get the result of the given Newton raphson method for a given function. - If you want to check the working procedure of newton method calculator then you can use the given example to get a solution.
- The “Recalculate” button for the calculation of more examples of real value functions with the solution using the Newton method.

## Final Result of Newton Raphson Method Calculator:

The newtons method calculator provides you with a **solution** as per your input problem when you click on the calculate button. It may include as:

**In the Result Box:**

Click on the result button so you get the solution of your Newton raphson method question.

**Steps Box:**

When you click on the steps option, Newton's method calculator gives you the results of the given Newton raphson method question in a step-by-step process.

## Benefits of Using Newton Raphson Calculator:

The newton's method approximation calculator has many **benefits** when you use it to find the solution of a given real value root function. Our tool only takes the input value and provides a solution of the root value without taking any external assistance. These benefits are:

- Newton's method of approximation calculator is an efficient tool that provides solutions to the given Newton raphson method problems in a few seconds.
- It is a trustworthy tool as it always provides you with accurate solutions to given function problems using Newton's raphson method.
- Newton's formula calculator is a learning tool that provides you with in-depth knowledge about the concept of real-valued root functions very easily on an online platform.
- It is a handy tool that evaluates various types of functions for Newton-Repson method problems quickly without manual calculation.
- Newtons method calculator is a free tool that allows you to use it for the calculation of real value function questions without paying.
- Newton's method calculator is an easy-to-use tool, anyone or even a beginner can easily use it for the solution of Newton raphson method problems.