Distance Between Two Points Calculator

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This online Distance Between Two Points Calculator finds the distance between any two points in 2D or 3D spaces, which are represented as sets of Cartesian coordinates. To get the result just enter the known values of the vectors coordinates into the input fields of this calculator and click the ‘Calculate’ button.

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Dimensions: 2D3D

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Point 1

x₁:

y₁:

Point 2

x₂:

y₂:

Distance

  d:

Point 1

x₁:

y₁:

z₁:

Point 2

x₂:

y₂:

z₂:

Distance

  d:

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What is Distance?

In mathematics, distance is a quantitative measure of the separation between two points in a Euclidean space. Euclidean space, also known as Euclidean \(N\)-space, is a geometric space in which distances between points are determined using the Euclidean distance formula.

In a Euclidean space of dimension \(N\), the Euclidean distance between two points is calculated as the length of the shortest path (a straight line segment) between these points. This path is often referred to as the “line segment” connecting the two points.

Distance in 2D Space

In a two-dimensional (2D) space, such as a flat plane, distance between two points is calculated using the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This relationship can be applied to find the distance between two points \((x_1, y_1)\) and \((x_2, y_2)\) in a 2D plane.

The formula for calculating the distance \(d\) between two points in 2D space is:

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

Distance in 3D Space

In three-dimensional (3D) space, the concept of distance becomes slightly more complex, but the fundamental principles remain the same. To find the distance between two points \((x_1, y_1, z_1)\) and \((x_2, y_2, z_2)\) in 3D space, you can use the 3D Pythagorean theorem.

The formula for calculating the distance \(d\) between two points in 3D space is:

$$d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}.$$

Distance is an important concept with wide-ranging applications across various fields. Whether you are navigating, conducting scientific research, designing structures, or exploring virtual worlds, understanding how to calculate the distance between two points in 2D and 3D spaces is a fundamental skill. The Distance Between Two Points Calculator simplifies this process, making it easier for individuals in diverse professions to perform accurate distance calculations with ease.