# Distance Calculator

Distance Calculator is an online tool that helps to calculate the distance between two points. Distance can be defined as a measurement that describes how far apart two points or objects are. It is a scalar quantity and has only magnitude.

## What is Distance Calculator?

Distance calculator computes the distance between two points when their x and y coordinates are given. The line segment connecting two points in 2-dimensional space gives the distance between those two points. To use the * distance calculator* enter the values of the x and y coordinates in the input boxes.

### Distance Calculator

**NOTE:** Enter values upto three digits only.

## How to Use Distance Calculator?

Please follow the steps below to find the distance between two points using the online distance calculator:

**Step 1:**Go to Cuemath's online distance calculator.**Step 2:**Enter the coordinates of x and y in the given input box, i.e., (x_{1},y_{1}) and (x_{2},y_{2}).**Step 3:**Click on the**"Calculate"**button to find the distance between two points.**Step 4:**Click on the**"Reset"**button to clear the fields and enter new values.

## How Does Distance Calculator Work?

In coordinate geometry, we can find the distance between two points by calculating the length of the line segment joining both points. There will only be one line that passes through these two points. The steps to calculate the distance between any two points when the x and y coordinates are known are as follows:

- Square the difference of the x coordinates.
- Then square the difference of the y coordinates.
- Add the values obtained in step 1 and step 2.
- Finally, take the square root of the value obtained in step 3. This gives the distance between two points.

The distance formula between two points in 2-dimensional space has been derived using the Pythagoras Theorem. The same method can be extended to calculate the distance between two points in 3-dimensional space as well. The formula used for determining the distance between two points whose coordinates are (x_{1}, y_{1}) and (x_{2}, y_{2}) is given by:

**Distance between two points = √[(x _{2 }- x_{1})^{2 }+ (y_{2 }- y_{1})^{2}]**

## Solved Examples on Distance Calculator

**Example 1:**

Find the distance between two points if the coordinates are (5,2) and (7,8) and verify using the distance calculator.

**Solution:**

Distance between two points = √[(x_{2 }- x_{1})^{2 }+ (y_{2 }- y_{1})^{2}]

= √[(7_{ }- 5)^{2 }+ (8_{ }- 2)^{2}]

= √[(2)^{2 }+ (6)^{2}]

= √[4 + 36]

= √[40]

= 2√10

= 6.32 units

**Example 2:**

Find the distance between two points if the coordinates are (12,6) and (9,2) and verify using the distance calculator.

**Solution:**

Distance between two points = √[(x_{2 }- x_{1})^{2 }+ (y_{2 }- y_{1})^{2}]

= √[(9_{ }- 12)^{2 }+ (2_{ }- 6)^{2}]

= √(-3)^{2 }+ (-4)^{2}

= √ [9 + 16]

= √25

= 5 units.

Similarly, you can try the calculator to find the distance for the following:

- (5,2) (6,2)
- (-5,2) (6,5)
- (6,-5) (7,-8)

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