Calculators

Geometry

Plane

Calculate the distance between 2 points in a two-dimensional plane.

Enter 2 points as x-y coordinates in the Cartesian coordinate system. Enter (x₁, y₁) and (x₂, y₂) to get the distance formula calculation in the 2D plane and find the distance between the 2 points.

Accepts positive or negative numbers, fractions, mixed fractions and decimals.

The calculator answer shows the work for:

• Distance formula using square root of (x₂ - x₁) + (y₂ - y₁)
• Graph of the line segment connecting the two points
• Below the graph find a link to the Slope Calculator for the same two points

Distance Formula:

The distance between two points is the length of the line connecting them, and the shortest distance is a straight line.

In a 2 dimensional plane, the distance between points (x₁, y₁) and (x₂, y₂) is given by the Pythagorean theorem:

\[ d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2} \]

Calculate Distance

To calculate the distance between 2 points, (x₁, y₁) and (x₂, y₂), for example, (5, 6) and (-7,11), plug the values into the distance formula:

\[ d = \sqrt {(-7 - 5)^2 + (11 - 6)^2} \]

combining terms inside parentheses you get:

\[ d = \sqrt {(-12)^2 + (5)^2} \]

squaring both terms you get,

\[ d = \sqrt {144 + 25} \]

adding the 2 results,

\[ d = \sqrt {169} \]

finally,

\[ d = 13 \]

Need Distance in 3 Dimensions?

For three-dimensional 3D space use the Distance Calculator for Three Dimensional Solids.