The humble cardboard box comes in many shapes, most of which are variants on the rectange. Round boxes can be difficult to find specialty items. However, when your storage, gifting or decorating needs call for a circular cardboard receptacle, you can cobble one together easily enough.
Draw a circle on the cardboard with a compass.
Measure the diameter of the circle. Multiply this figure by pi (approximately 3.14) to get the circumference.
Draw a rectangle on the cardboard with two sides equivalent to the desired height of the finished box and two sides equivalent to the figure obtained from Step 2.
Cut out the circle and the rectangle.
Roll the rectangle into a tube, with the sides that are not the circumference touching each other. Glue the touching edges together. Reinforce the seam with packing tape on both sides of the cardboard.
Apply a thin layer of glue to the edges of the cardboard circle. Lay the tube, edge-down, on top of this layer. Reinforce with packing tape on both sides.
If you wish to have a lid for your box, repeat all seven of these steps. Make the diameter of the lid circle about a half-inch longer than that of the box bottom, and make the height of the lid much shorter. If you'd like your box to be larger than a compass can accommodate, rig up a larger circle-drawing mechanism by tying a pencil to a thumbtack with a string the length of your desired radius. Push the thumbtack into the cardboard and keep the string taut as you draw your circle.