# Distance Measure

Distance Measure describes how we measure distance between two points.

In everyday life, we measure distance between two points using a straight line. This is called Euclidean distance.

There are other useful distance measures, such as Manhattan Distance.

### Euclidean distance

Euclidean distance is simply the distance between two points in a straight line. It is also called Pythagorean distance as it can be calculated using the Pythagorean theorem.

The formula for Euclidean distance between two points
`(p1,p2)`

and
`(q1,q2)`

is:

### Manhattan distance

Manhattan distance (L1 distance) is calculated by summing the absolute differences of the coordinates between two points.

It is usually used in a grid-like system, and is actually simpler to calculate than Euclidean distance as it does not involve square root.

The formula for Manhattan distance between two points
`(p1,p2)`

and
`(q1,q2)`

is:

### Example

In this **AI Simulator: Robot** example, we define the
coordinate at bottom-left as
`(0,0)`

. The
robot is at
`(3,1)`

, the
battery cell is at
`(0,3)`

.

The Manhattan distance between the robot and the battery cell is
**5**. This is calculated by summing the absolute
difference in horizontal direction (**3**) and vertical
direction (**2**).

The Euclidean distance between the robot and the battery cell is
approximately **3.6**. This is calculated using the
Pythagorean theorem, by taking square root of **13**,
which is sum of horizontal distance squared (**3*3**)
and vertical distance squared (**2*2**).

### Further readings

Distance Measure

Manhattan distance

Euclidean distance