Remove the lamp shade from the lamp. Some shades have a small nut securing them to the lamp, and others use a spring-loaded clip that slides over the light bulb. Write down on a piece of paper what type of connector your drum lamp shade uses.
Place one end of the tape measure over one side of the top of the drum shade. Extend the tape measure directly across to the opposite outside edge. Write the measurement down as the top diameter. Measure the bottom diameter in the same manner. Even though it is a drum shade, there might be a slight variance. Write the measurement down as the bottom diameter.
Reposition the end of the tap measure onto the top edge of the drum lamp shade and measure straight down to the bottom edge. Write this measurement down as depth of the shade. This measurement is also used to determine the slant if the bottom diameter is slightly larger.
Measure the distance between the top of the drum lamp shade attachment and the top of the shade. This measurement is necessary to determine how much of an angle the center piece needs to be on for the new lamp shade. Write the measurement down.