How to Make Square Wheels?

You may not be able to put a square peg in a round hole—but you can make a square wheel roll on a round road.Square wheels roll smoothly on a surface with bumps of the right size and shape.

How to Make Square Wheels DIY Math Project 89
How to Make Square Wheels? 10


  • About 20 cardboard toilet paper tubes (all approximately the same diameter)
  • Foamboard, stiff cardboard, or matboard to serve as a base for the cardboard tubes, about 4 x 30 inches (10 x 75 cm)
  • Hot-glue gun and glue sticks
  • Poster board or matboard, approximately 8 x 10 inches (20 x 25 cm)
  • Scissors
  • Pencil or pen
  • Ruler
  • Pushpin
  • Drinking straw
  • Two bamboo skewers
  • Paper clip
  • String, about 12 inches (30 cm)


How to Make Square Wheels DIY Math Project
How to Make Square Wheels? 11

Using hot glue, attach a cardboard tube across one end of the base. Continue gluing on tubes, with each tube just touching the one before it, until you reach the other end of the base (see photo below).


Measure the diameter of three or four of the toilet-paper rolls. The diameters should be approximately 1 11/16 inches (4.3 cm). If this is the case, cut four square wheels from the poster board, with sides of 2 inches (5 cm). If the diameter of your tubes is significantly different from this measurement, then make the sides of the square wheels equal to 1.2 times that diameter. (See the Math Root below.)


How to Make Square Wheels DIY Math Project 2
Locate the center of each square wheel by drawing two diagonals, as shown in the photo below.


Use the pushpin to poke a small hole in the center of each square wheel, taking care not to bend or crease the wheel.


From the poster board, cut a rectangle measuring 2 x 5 inches (5 x 12 cm).


Cut two sections of straw, each 2 inches (5 cm) long.


How to Make Square Wheels DIY Math Project 3
Glue the straw sections to the rectangular piece of poster board 3/8 inch (1 cm) from each end (see photo below). This assembly will be the body of a small cart.


Cut the skewers into two 5-inch-long (12-cm) pieces, each with a point at one end. These will be axles. (If you can’t cut the skewers with the scissors, just break the skewers, or cut them with a utility knife.)


How to Make Square Wheels DIY Math Project 4
Slide one of the square wheels onto a skewer until it’s about 3/4 inch (2 cm) from the non-pointed end. Slide the pointed end through the straw, and then slide the other square wheel onto the skewer. Adjust the wheels so they’re aligned with each other, and are fairly close to the edge of the cart. The wheel-and-axle assembly should turn freely in the straws. Assemble the other set of wheels the same way. When all the wheels are on, the cart should look like the photo below.


How to Make Square Wheels DIY Math Project 5
Use the pushpin to poke a hole between the straw and one end of the cart body, equidistant from the edges, as shown below. Put one end of the paper clip through the hole, and adjust until it’s positioned as shown in the photo below.


How to Make Square Wheels DIY Math Project 6
Tie a loop in the end of the string, and place it on the paper clip (see photo below).


A smooth ride on square wheels—amazing, no? This works because, as the cart rolls, the vertical distance from each axle to the horizontal base of the road stays about the same. Study the cart carefully as it rolls and you’ll see that the axle neither rises nor falls: High spots in the lumpy road are exactly cancelled by flat spots on the square wheel.

Ali Kaya


Ali Kaya

This is Ali. Bespectacled and mustachioed father, math blogger, and soccer player. I also do consult for global math and science startups.

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