Distance between Two Points Calculator

Distance between two points calculator helps to calculate the distance between two points for the 2-dimensional plane. It provides the distance between any 2 points using the distance formula with the detailed steps in a fraction of a second after putting the value in respective fields.

What is the distance between two points?

The distance between two points is the length of the line segment that connects two points in a 2-dimensional plane. Mathematically, it represents how the two points are far from one another on the same line segment in a coordinate plane or xy-plane. 

It can be found by using the specific distance formula that is based on the Pythagoras theorem. The numerical value of the distance between the two points is always positive and mathematically represented by the symbol |d|.

Distance Formula for Two Points

To find the distance between 2-points use the distance formula which is an application of the Pythagorean Theorem. The formula is the square root of the sum of the squares of the difference of x-coordinate and y-coordinates. To use the distance formula, we need the coordinate value of the two points that lie on the same line segment. 

Suppose that, the 2 points P & Q lie on the line segment AB in the XY-plane. The coordinate’s values of the points P and Q are: P(x₁, y₁) and Q(x₂, y₂).  Then the mathematical form of the distance formula can be written as:

|d|= |PQ|= √ (x₂ – x₁)² + (y₂ – y₁)²    or √ (x₁ - x₂)² + (y₁ – y₂)²   

Where,

• x₁ & y₁ are the coordinates of point P.
• x₂ & y₂ are the coordinates of point Q.

Note: If the coordinates value of the P (x1, 0) and Q (x2, 0) then the distance between P and Q simply can be found by taking the difference of the x-coordinates value. However, if the coordinates value of the P (0, y1) and Q (0, y2) then the distance between P and Q simply can be found by taking the difference of the y-coordinates value.

|PQ| = |x₂ – x₁| for {P (x₁, 0) and Q (x₂, 0)}

|PQ| = |y₂ – y₁| for {P (0, y₁) and Q (0, y₂)}

How to find the distance between two points?

To find the distance between 2 points with the help of the distance formula follow the below steps.

• Note the coordinate’s value of the point-1 (x₁, y₁) and point-2 (x₂, y₂) from the line segment. 
• Put the point’s values in the distance formula and find the squares of the difference of the x & y coordinates.
• Simplify the terms by taking the square root of the sum of the squares of the difference and taking the distance value always positive.

Alternatively, use the above point distance calculator to find the values of the distance between two points without using any distance formula.

Example to Find the Distance between Two Points

Follow the below example to learn how to calculate the distance between two points using the distance formula with the detailed steps.

Example:

Find the distance between two points AB, If A (5, 3) and B (-2, 5).

Solution:

Step 1: Note the coordinates value of x & y from both points.

x₁ = 5, x₂ = -2 

y₁ = 3, y₂ = 5

Step 2: Put the values in the distance formula.

|d| = √ (x₂ - x₁)² + (y₂ - y₁)²​

     = √ (-2 - 5)² + (5 - 3)²

     = √ (-7)² + (2)^2​

     = √ 49 + 4​

     = √ 5​3

           |d| = 7.28

Example:

Calculate the distance of a point P(-4, 7) from the origin using the distance formula.

Solution:

Step 1: Write the coordinates value of x & y from the given point.

We know that the origin point such as O (0, 0)

x₁ = -4, x₂ = 0 

y₁ = 7, y₂ = 0

Step 2: Use all the above values in the distance formula.

|d| = √ (x₂ - x₁)² + (y₂ - y₁)^2​

     = √ (0 - (-4))² + (0 - 7)²

     = √ (0 + (4))² + (0 - 7)^2​

     = √ (4)² + (-7)^2​

     = √ 16 + 49​

     = √ 65

            |d| = 8.06

To cross-check the above result using the above distance between points calculator.

Frequently Asked Questions (FAQ’s)

What is the distance between two points called?

Answer: The distance between two points is called the length of the line segment. It is always positive and calculated by using the distance formula. Alternatively, use our above distance between two points calculator to find the length of the line segment. 

What is the distance formula?

Answer: The distance formula is the square root of the sum of the squares of the difference of x and y coordinates. The distance between P & Q represented as: |d|= |PQ|= √ (x₂ – x₁)² + (y₂ – y₁)².