Online Calculator Resource

# Two Dimensional Distance Calculator

2D Distance Calculator

d = 26.196374

For:
(X1, Y1) = (-7, -4)
(X2, Y2) = (17, 6.5)

Distance Equation Solution:

$$d = \sqrt {(17 - (-7))^2 + (6.5 - (-4))^2}$$

$$d = \sqrt {(24)^2 + (10.5)^2}$$

$$d = \sqrt {576 + 110.25}$$

$$d = \sqrt 686.25$$

$$d = 26.196374$$

## Calculator Use

Calculate the distance between 2 points in 2 dimensional space.

Enter 2 sets of coordinates in the x y-plane of the 2 dimensional Cartesian coordinate system, (X1, Y1) and (X2, Y2), to get the distance formula calculation for the 2 points and calculate distance between the 2 points.

Accepts positive or negative integers and decimals. (6 and/or 6.5)

## Distance Formula:

The distance between two points is the length of the path connecting them. The shortest path 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), we plug our values into the distance formula:

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

combining terms inside parentheses we get:

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

squaring both terms we get,

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

adding the 2 results,

$$d = \sqrt {169}$$

finally,

$$d = 13$$

Cite this content, page or calculator as:

Furey, Edward "2D Distance Calculator"; from https://www.calculatorsoup.com - Online Calculator Resource.