How to Find the Volume of a Piece of Paper

By Ariel Balter
A sheet of paper is thin, but they can add up.

The volume (V) of a rectangular solid is equal to the product of the length (L), width (W) and height (H): V = L_W_H. You can measure the length and width of a piece of paper with a ruler, but without a special tool it would be hard to measure the height, or thickness. But you can do this using a little trick: Stack up many pieces and measure the entire stack, then divide this measurement by how many pieces are in the stack. If you only have a few sheets, cut them into small pieces and stack the pieces.

Stack and Measure Method

Mark and cut out a rectangular sheet of paper.

Stack up 100 sheets of the same paper. If you only have a few sheets, cut them evenly into at least 100 pieces. Then clamp 100 of the pieces tightly together with a clothespin or binder clip. Make sure that all the edges line up evenly on one side of the stack.

Measure the thickness of the stack.

Divide that number by 100. If you used inches, you will need to find decimal values. For instance, if the stack was 9/64 of an inch thick, then each piece is (9/64)/100 = 0.0014 inches thick. It’s easier to work in metric. If the stack was 1.5 millimeters, then each piece is 0.015 millimeters thick.

Measure the length and width of the piece of paper.

Multiply the length, width and thickness to get the volume.

Tip

You can find the volume for pieces of paper that are not rectangles as well. Use the proper geometric formula for the area of the shape (circle, triangle, etc.) and then multiply by the thickness.

About the Author

Ariel Balter started out writing, editing and typesetting, changed gears for a stint in the building trades, then returned to school and earned a PhD in physics. Since that time, Balter has been a professional scientist and teacher. He has a vast area of expertise including cooking, organic gardening, green living, green building trades and many areas of science and technology.