There are some situations wherein you need to find the distance. In such cases, you can either perform manual computations or use this distance formula calculator. Using this distance between two points calculator, you can find the distance between 2 points on a Cartesian coordinate system. This online tool makes use of the common formula. It computes the distance after you’ve entered the coordinates.

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## How to use the distance formula calculator?** **

This finds the distance between two points calculator is a simple tool that’s extremely easy to use. All you need to do is enter the required information, and it does the computation for you. Here are the steps to follow when using this calculator:

- First, enter the values for the first point, X
_{1}and Y_{1}. - Then enter the values for the second point, X
_{2}and Y_{2}. - After entering all of the required values, the distance formula calculator automatically generates the Distance value for you.

## How do you calculate the distance between two points?

Apart from using this online distance calculator math to find the distance, you can also perform the calculation manually using the distance formula. To learn how to calculate distance, let’s work with an example. Let’s say that our coordinates for (X_{1},Y_{1}) are (3,5) and the coordinates for (X_{2},Y_{2}) are (9,15), and you want to solve for the distance. To do this, we need to use the distance formula that’s related to the Pythagorean Theorem, and this formula is:

d = √(x₂ – x₁)² + (y₂ – y₁)²

** **

The formula relates to the Pythagorean theorem formula which is:

a² + b² = c²

**where:**

**a** refers to one leg of a right triangle

**b** refers to one leg of a right triangle

**c** refers to the hypotenuse

In our example, (x₁,y₁) and (x₂,y₂) are the coordinates of the hypotenuse’s endpoints. This means that (x₂ – x₁)² in our distance equation corresponds to the Pythagorean Theorem’s a² while (y₂ – y₁)² corresponds to b². We prove that the distance formula relates to the Pythagorean theorem since:

c = √a² + b²

When calculating the distance between the points in our example, here are the steps to follow:

- Replace the values in the distance formula.
- Start by subtracting the values on both parentheses.
- Take the square of both values.
- Add the values.
- Take the final square root.

Using these steps with our example, here are the steps:

**d = √(9-3)²+(15-5)²**

**d = √(6)²+(10)²**

**d = √36 + 100**

**d = √136**

**d = 11.66**

Remember that when you take the square root of a certain value, you can get a value that’s either negative or positive. But since you’re solving for the distance, you only need to concern yourself with a positive result. After you’ve made the computations by hand, you can use the distance between two points calculator to check if you performed the calculation correctly.

## What is the formula for distance?** **

The distance formula is a very important equation which you use to find the distance value between two points. You can derive this formula from the Pythagorean Theorem as we illustrated in the previous question. Because of this, some people claim that this formula is nothing but the “disguised version” of the Pythagorean Theorem.

In other words, it’s a derivative of the said theorem. If you need to find the distance, use the distance formula calculator. But if you want to perform the calculation manually, use the formula for the distance which is:

d = √(x₂ – x₁)² + (y₂ – y₁)²

where:

(X_{1},X_{2}) refer to the coordinates of one point

(Y_{1},Y_{2}) refer to the coordinates of the other point

** **

## What is the meaning of the distance formula?** **

Use the distance formula to find or calculate the distance between one point to another. These points can exist in any kind of dimension. For instance, you can calculate the distance between two points on

- a line which is 1D
- a plane which is 2D
- in space which is 3D

Let’s use another example to illustrate the meaning of the distance formula. In this example, let’s use the distance in a line or 1D. Consider a number line with only one dimension. This is the easiest computation to perform because the distance between any of the two points on the x-axis is the absolute value of the difference of the points’ coordinates. In the same way, the distance between any of the two points on the y-axis is the absolute value of the difference of the points’ coordinates.

In some cases, you get four sets of coordinates for you to comment on the nature of the shape that’s formed when you join these points. To do this, you need to find the distance between them. But before that, try to remember the characteristics of the different kinds of quadrilaterals:

- it’s a parallelogram if it has equal opposite sides;
- it’s a rectangle if it has equal diagonals and equal opposite sides;
- it’s a rhombus if it has all equal sides;
- it’s a square if it has equal diagonals and equal sides.

** **

With this information, you can solve for the distance as needed.

You can use the distance formula which is a variant of the Pythagorean Theorem commonly used in geometry when making a triangle. For instance, you have two points with coordinates of (1,5) and (-2,1), and you’re tasked to find the distance between them. Draw lines which form a triangle with a right-angle while using these coordinates as the points of the triangle’s corners.

In this situation, it’s easy to find the length of the vertical side and the length of the horizontal side of the triangle. All you have to do is subtract the x and y-values. Then use the distance formula (or the Pythagorean Theorem) to calculate the length of the remaining side or the hypotenuse.

This value is the same value for the distance between the two points. As you can see, this is a very important formula which you can use to perform manual calculations. Then you can check your answer using the distance formula calculator.