# How to calculate the center of gravity with shapely in python?

## Question:

I discovered shapely but I did not find how to calculated the center of gravity of a polygon!

Does someone have the solution?

## Answers:

If your polygon has a uniform density, its center of mass coincides with its centroid. In shapely, the centroid can be directly calculated as:

```
from shapely.geometry import Polygon
P = Polygon([[0, 0], [1, 0], [1, 1], [0, 1]])
print(P.centroid)
#POINT (0.5 0.5)
```

The above answer is right. But some times you do not want to work with such format. So to get the values you can use:

```
from shapely.geometry import Polygon
centroid = list(Polygon([[0, 0], [1, 0], [1, 1], [0, 1]]).centroid.coords)
#[(0.5, 0.5)]
```

I have tested this method for more complex geometries and it works nicely.

**A solution without shapely**

You can also calculate it by hand, using just `numpy`

.

```
import numpy as np
def polygon_area(xs, ys):
"""https://en.wikipedia.org/wiki/Centroid#Of_a_polygon"""
# https://stackoverflow.com/a/30408825/7128154
return 0.5 * (np.dot(xs, np.roll(ys, 1)) - np.dot(ys, np.roll(xs, 1)))
def polygon_centroid(xs, ys):
"""https://en.wikipedia.org/wiki/Centroid#Of_a_polygon"""
xy = np.array([xs, ys])
c = np.dot(xy + np.roll(xy, 1, axis=1),
xs * np.roll(ys, 1) - np.roll(xs, 1) * ys
) / (6 * polygon_area(xs, ys))
return c
print(polygon_centroid(xs=[0, 1, 1, 0], ys=[0, 0, 1, 1]),
'expect: [.5, .5]')
print(polygon_centroid(xs=[0, 0, 2], ys=[1, -1, 0]),
'expect: [2/3, 0]')
print(polygon_centroid(xs=[0, 0, 2], ys=[-1, 1, 0]),
'expect: [2/3, 0]')
# https://wolfram.com/xid/0e5bspgmqyj9a5-cfx5ps
print(polygon_centroid(xs=[0, 1, 1.5, 1, 0, -.5], ys=[0, 0, .5, 1, 1, .5]),
'expect: [.5, .5]')
```

**Output**

```
[0.5 0.5] expect: [.5, .5]
[0.66666667 -0. ] expect: [2/3, 0]
[0.66666667 0. ] expect: [2/3, 0]
[0.5 0.5] expect: [.5, .5]
```