Barrels used for Pilates are short and wide, meaning they store extremely well and take up a small amount of space. They are also immensely lightweight, designed so anyone no matter their strength can carry them.
The average dimensions for a barrel are 34″ tall x 20″ wide, meaning it will fit in the vast majority of exercise spaces.
Measure the dimensions of where you intend to keep it in and compare it to the specific model you wish to buy to be sure.