Normal Line Calculator







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Introduction to normal line calculator with steps

Normal line equation calculator is an online tool used to calculate the derivative of the normal line. It uses the normal line equation and the slope formula to calculate the equation. In other words, it is used to calculate the line perpendicular to the tangent line at the given point.

In mathematics, the derivative has many applications such that it can be used to find the tangent line of a function and its slope. So we introduce slope of normal line calculator that can handle any function to calculate its normal line.

Formula used by normal line and tangent line calculator

This equation of the normal line calculator is used to find the normal line equation using tangent at a given point. It uses following step-by-step formulas to calculate the equation:

  • It calculates the value of the function at the given point by putting:
  • $$ x \;=\; x_o $$


    $$ f(x_o) \;=\; y_o $$
  • It calculates the slope M of the normal line at:
  • $$ x \;=\; x_o $$

    by using this formula:

    $$ M(x_o) \;=\; - \frac{1}{f'(x_o)} $$
  • The general form of the equation of tangent passing through:
  • $$ (x_o \;,\; y_o) $$

    And having slope M is:

    $$ (y \;-\; y_o) \;=\; m(x \;-\; x_o) $$

The normal line calculator uses this formula to calculate normal line equation using slope M, given point pf:

$$ x\;=\; x_o $$

And the value of function at the given point of:

$$ y_o $$

How to use slope of normal line calculator?

Normal line equation calculator is simple and easy to use. Follow below steps:

  1. Enter the value of the function in the “Enter Function” box, or you can use the “Load Example” option to try the solution.
  2. Enter the point of x in the “At the point of x” box.
  3. You can review the function to check the values. Then click on the “Calculate” button.

After you enter all inputs, click on "calculate" button. The normal line and tangent line calculator will instantly show you answer step by step.

Why use a normal line equation calculator?

The tangent is the straight line that touches the given curve at a given point. And the normal line is perpendicular to the tangent. So we can say that the normal line is associated with the deviation at a given point. While computing the normal line equation, students may get stuck with this method.

It would be best to use the normal line finder because it provides you with the step-by-step process and the graph as a visual representation of the given curve.

Benefits of using equation of the normal line calculator with steps

In geometry, you can only be an expert in calculations if you practice. The equation of normal line calculator helps you practice with many different curves. Some other benefits of this tool are:

  1. It clarifies the result with the graph by showing where the point x touches the given curve and the tangent to the curve.
  2. It is reliable because it never gives false results.
  3. It can save your time by giving the result with every defined step.
  4. You can practice with unlimited examples for free by using this tool to find the equation of a normal line.
  5. Normal line equation calculator can handle any curve like parabola, ellipse, and hyperbola, making it more beneficial for students.

How to find the equation of a normal line?

Consider a curve given as:

$$ y \;=\; 4x^2 $$

We have to find the normal line at the point of:

$$ x_o \;=\; 1 $$

So, the value of the given function at this point is,

$$ y_o \;=\; 4(1)^2 \;=\; 4 $$

And the slope can be found by,

$$ M(x_o) \;=\; - \frac{1}{f'(x_o)} $$


$$ f'(x_o) \;=\; 8 $$


$$ M(x_o) \;=\; - \frac{1}{8} $$

The point slope form of the equation is,

$$ (y \;-\; y_o) \;=\; M(x \;-\; x_o) $$

So, the equation of normal line at (1, 4) can be calculated as,

$$ (y \;-\; 4) \;=\; -\; \frac{1}{8} (x \;-\; 1) $$ $$ y \;=\; -\; \frac{x}{8} \;+\; \frac{1}{8} \;+\; 4 $$ $$ y \;=\; -\; \frac{x}{8} \;+\; \frac{33}{8} $$

We are sure that you’ll like this normal line calculator at a point.

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Frequently Asked Questions

Is tangent and normal line calculator accurate?

Yes, normal line equation calculator is accurate and efficient. It provides you step by step results instantly.

Can I use normal equation calculator for exam practice?

Yes, you can use this normal line derivative calculator for your exam practice. It makes your learning easier as you can learn and practice online.

How to find the normal line calculator?

You can find this tool on Google by searching "equation of the normal line calculator". You can directly access this tool after typing in your browser.

Alan Walker

Alan Walker

Last Updated June 02, 2022

Studies mathematics sciences, and Technology. Tech geek and a content writer. Wikipedia addict who wants to know everything. Loves traveling, nature, reading. Math and Technology have done their part, and now it's the time for us to get benefits.