Distance Formula Calculator


 

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This Online Distance Formula Calculator is a great way to put your skills to the test in a fun environment. By practicing, you’ll be able to use the distance formula efficiently.
 




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Distance Formula Calculator
The distance formula is used to find the distance between two points on the coordinate plane. It is a direct application of the Pythagorean theorem and is used to calculate the length of the line segment connecting these two points. Scroll down the page for a more detailed explanation.
 
This interactive application explains the distance formula, allows you to calculate the distance for any two points, and show you the step-by step solution. The initial values are pre-filled with an example. Just enter new coordinates and click “Calculate” to see it update.
 

    Distance Formula Calculator

    A tool to calculate the distance between two points.

    What is the Distance Formula?

    The distance formula is used to find the distance, d, between two points (x1, y1) and (x2, y2) in a coordinate system. It is derived directly from the Pythagorean theorem.

    \(d=\sqrt{ \left( x_2-x_1 \right)^{2} + \left( y_2-y_1 \right)^{2} }\)

    Interactive Calculator

    Enter the coordinates of two points below to calculate the distance between them. A step-by-step solution will be provided below.

    Enter Endpoint Coordinates

    Calculated Distance (d)

    5.00

    Step-by-Step Solution


 

Distance Formula
Distance Formula Lesson
The distance formula is \(d=\sqrt{ \left( x_2-x_1 \right)^{2} + \left( y_2-y_1 \right)^{2} }\), which calculates the straight-line distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) on a coordinate plane. This formula is an application of the Pythagorean theorem and involves finding the differences in the x and y coordinates, squaring them, adding them, and then taking the square root of the sum.

 

How to Use the Distance Formula

  1. Identify the Coordinates: Given two points, label them \((x_1, y_1)\) and \((x_2, y_2)\).
  2. Substitute into the Formula: Plug the values of the coordinates into the distance formula: \(d=\sqrt{\left( x_2-x_1 \right)^{2} + \left( y_2-y_1 \right)^{2}}\).
  3. Calculate the Differences: Subtract the x-coordinates \((x_2 - x_1)\) and the y-coordinates \((y_2 - y_1)\).
  4. Square the Differences: Square the results from the previous step.
  5. Add the Squares: Add the squared differences together.
  6. Take the Square Root: Find the square root of the total sum to get the distance, d.
     

The video gives a clear, step-by-step approach to walk through the process of using the distance formula.


 

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