# Distance Formula Calculator

## How To Use Distance Formula Calculator

Lets first understand, what is distance formula and how we can calculate distance between two points in the cartesian plane using that formula?

Distance is a numerical measurement of how far apart objects or points are.

Distance Formula:

(a) The distance 'd' between any two points say P(x1, y1) and Q(x2, y2) is given by:

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

(b) The distance 'd' of a point P(x1, y1) form the origin is given by:

$$d=\sqrt{(x-0)^2+(y-0)^2}$$ $$\implies d=\sqrt{x^2+y^2}$$

Example: Calculate the distance 'd' between A(2,3) and B(6,8).

Solution:

$$d=\sqrt{(6-2)^2+(8-3)^2}$$ $$=\sqrt{(4)^2+(5)^2}$$ $$=\sqrt{16+25}$$ $$=\sqrt{16+25}$$ $$=\sqrt{41}$$ $$=\sqrt{41}$$ $$\therefore d=6.40\hspace{0.1cm}units$$

Distance traveled is the length of a specific path traveled between two points.

Straight-line (Euclidean) distance is the length of the shortest possible path through space, between two points, that could be taken if there were no obstacles.

"Circular distance" is the distance traveled by a wheel.

Distance versus Displacement:

Both distance and displacement measure the movement of an object. Distance cannot be negative, and never decreases. Distance is a scalar quantity, or a magnitude, whereas displacement is a vector quantity with both magnitude and direction. It can be negative, zero, or positive.

For calculating distance using above distance formula calculator, you have to just write both the coordinates in the given input box and press the calculate button, you will get the distance between the given points.

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