ArcGIS has a built in scripts to calculate geometry properties such as area, length, and coordinate. For polygon features, we can also calculate the X and Y of centre points (centroids) of each polygon. The following tutorial shows us how to calculate those attributes from table. Some extensions exist however to make this step handy. Just in case we are using default arcgis installation.>> Open the table of layer
Right-click on the layer and open attribute table

>> Create a field for the property we will calculate.
Click on Option > Add Field…

>> Fill a form

Please carefully select what type of your field should be. In this example, I want to create a field contains 7 precision and 2 digits of decimal. If you have any question about what type of field suits you, you can ask me in comment below.
This step will give you an empty field like shown in the following image

>> Calculate the property
Righ click on our new field above > Calculate Geometry

>> Select some atributes

In this example, I want to calculate are using UTM projection with hectares unit. Adjust this if you want to do different one.
>> Done
Now our new field will have its data
