Online Calculators

Distance Calculator 2D

Distance Calculator | 2D
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$\text{distance} = 2 \, \sqrt{34}$ 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

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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,

$$d = \sqrt {144 + 25}$$

$$d = \sqrt {169}$$

finally,

$$d = 13$$

Need Distance in 3 Dimensions?

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

Cite this content, page or calculator as:

Furey, Edward "Distance Calculator 2D" at https://www.calculatorsoup.com/calculators/geometry-plane/distance-two-points.php from CalculatorSoup, https://www.calculatorsoup.com - Online Calculators

Last updated: February 6, 2024