Distance Calculator 2D

Basic Calculator

Calculators

Geometry

Plane

Distance Calculator 2D

Distance Calculator | 2D

use numbers, fractions or decimals

(x₁ y₁)

(x₂ y₂)

Answer:

\[ \text{distance} = 2 \, \sqrt{34} \] As a decimal:
\[ \text{distance} = 11.661904 \]

Distance Solution

\[ d = \sqrt {(x_2 - x_1)^2 + (y_2 - y_1)^2} \]\[ d = \sqrt {(4 - (-2))^2 + (-7 - 3)^2} \]\[ d = \sqrt {(6)^2 + (-10)^2} \]\[ d = \sqrt {36 + 100} \]\[ d = \sqrt {136} \]\[ d = \sqrt{4 \cdot 34} \]\[ d = 2 \, \sqrt{34} \]\[ d = 11.661904 \]

Graph of the Line Connecting the Two Points

Graph tools will zoom, move and enter full screen mode.
Or, use <Shift> with a mouse to zoom and move.
Press esc to exit full screen mode.

Find the slope of this line, line equations,
x and y intercepts at the Slope Calculator ↗

Share this Answer Link: help
Paste this link in email, text or social media.

Get a Widget for this Calculator

Share this Calculator & Page

Calculator Use

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.