Paper Column Strength Experiment: A Tube Beats a Slab

Four sheets of paper. Same paper, same height, same 5 cm of tape. One rolled into a tube, one folded into a triangle, one into a square, one folded flat into a thick strip. Stack books on each until it gives way and the spread is startling: the flat slab folds at a few hundred grams while the tube often holds three or four kilograms. This paper column strength experiment makes a point that no amount of telling achieves, which is that compression strength is a question of geometry, not quantity. The paper did not get stronger. It just moved.

Key Takeaways

• You’ll build four columns from four identical sheets, load each with books, and weigh the load that made it collapse.
• The concept is buckling. A column fails by bowing sideways, and how much it resists that depends on how far the material sits from the column’s centre line.
• Numbers to measure: paper thickness, failure mass for each shape, and the effect of halving the column’s height.
• Best for ages 7 to 13. An adult handles stacks of books above a couple of kilograms.
• The usual spoiler is an uneven top edge. If one side of the tube is 2 mm taller, it carries everything and collapses early.

What You’ll Need for the Paper Column Strength Experiment

Item	How much	Where to get it	If you don’t have it
Printer paper, A4 or US letter	4 identical sheets, plus spares	Printer tray	Any paper, as long as all four sheets are identical
Masking tape	20 cm, cut into four 5 cm pieces	Hardware drawer	Any tape, measured equally per column
A stiff flat platen	1 piece of thick cardboard, 20 × 20 cm	Recycling	A hardback book used as the first weight
Books of various sizes	10–15	Shelf	1 kg bags of rice or sugar, weighed
Kitchen scale	1	Kitchen	Weigh each book once and label it
Ruler and pencil	1 each	Stationery	Any straight edge
Scissors	1 pair	Kitchen drawer	Tear along a folded crease

Time: prep 15 min, experiment 30 min, cleanup 5 min Cost: four sheets of paper Mess level: low, as long as the books land on the table

Do the Experiment

Step 1 — Measure how thick your paper actually is

Stack 100 sheets, measure the stack with a ruler, divide by 100. Most printer paper lands near 0.1 mm. This number matters, because it is the smallest dimension in the whole experiment and it turns out to control everything.

Step 2 — Roll the cylinder

Roll one sheet so the short side becomes the height, bringing the long edges together with a 5 mm overlap, and tape the seam with one 5 cm piece. For A4 that gives a tube about 21 cm tall and 9.4 cm across; for US letter, about 21.6 cm tall and 8.8 cm across. Stand it up and check the top edge is level all the way round.

Step 3 — Fold the triangular and square prisms

Second sheet: score it into three equal strips the long way and fold into a triangular prism, taping the seam. Third sheet: four equal strips, folded into a square prism. Same height as the cylinder, same tape, same paper.

Step 4 — Fold the flat slab

Fourth sheet: fold it in half the long way, then in half again, and again, until you have a flat strip the same height as the others and roughly 8 layers thick. Press the folds hard. This is the column with all its material concentrated near the middle.

Step 5 — Load each column and weigh the failure

Stand a column on a table, rest the cardboard platen flat on top, and add books one at a time, placing each gently and centrally. When it collapses, weigh everything that was on top. Three runs per shape if you have the paper, because one run is a story and three is a measurement.

Step 6 — Halve the height and retest

Make a second cylinder, cut it to half height, and load it. Euler’s buckling theory says load should rise with the inverse square of length, so halving the height predicts four times the load. Measure what you actually get.

What you should see: The flat slab goes first, usually between 100 g and 400 g, folding neatly at mid-height. The square prism typically manages 0.5 to 2 kg, the triangle a little more, and the cylinder is the clear winner at 2 to 5 kg with a level top edge. Failure in the tube is sudden and local: a small crease appears in the wall and the whole column goes in about a tenth of a second. Halving the cylinder’s height gives more load, but usually two to three times rather than the four that Euler predicts, which is a result worth explaining rather than hiding.

What the Paper Column Strength Experiment Measures

Column	Shape	Typical failure load	How it fails
Flat folded slab	~37 mm wide, 8 layers	100–400 g	Bows sideways and folds at mid-height
Square prism	7.4 cm sides	0.5–2 kg	A wall panel buckles inward
Triangular prism	9.9 cm sides	0.8–2.5 kg	One face creases, then the corner folds
Cylinder	9.4 cm diameter	2–5 kg	A small local crease, then instant collapse
Half-height cylinder	Same diameter	2–3× the full-height value	Local crease, higher load

What’s Actually Going On

A tall thin column under load does not get crushed. It buckles, meaning it bows out sideways and then folds. The load at which that happens was worked out by Leonhard Euler in the eighteenth century and it depends on three things: how stiff the material is, how long the column is, and a geometric property called the second moment of area, usually written as I. Stiffness and length are the same for all four of your columns. Everything in your results is I.

I measures how far the material sits from the axis the column would bend about, and distance counts heavily. For a thin-walled tube of radius r and wall thickness t, I is approximately π r³ t, so the radius enters cubed. For a flat strip of width b and thickness t, I is b t³ divided by 12, and here the thickness enters cubed instead. Run the numbers for A4 paper at 0.1 mm thick. The cylinder has a radius of about 47 mm, giving an I of roughly 33,000 mm⁴. The flat slab, 37 mm wide and 0.8 mm thick after folding, gives an I of about 1.6 mm⁴. That is a ratio of about twenty thousand to one, from the same sheet of paper.

Your measured loads will not differ by twenty thousand to one. They will differ by perhaps ten or thirty to one, and the reason why is the most interesting part of this experiment. Euler’s formula describes a column that fails as a whole, bowing in one smooth curve. The flat slab does exactly that, and if you plug paper’s stiffness of roughly 2 to 5 gigapascals into Euler’s equation you get a predicted failure load of a couple of hundred grams, which is about what you measure. The cylinder does something different. Its Euler prediction is astronomical, hundreds of kilograms, and it is nowhere near that. Instead a small patch of the thin wall crumples first, a mode called local or shell buckling, and once the wall gives way locally the column is gone.

Thin shells are notoriously weaker than theory suggests, because tiny imperfections such as a dent, a crooked seam or an uneven top edge concentrate stress and trigger local failure early. The effect is large enough and important enough that NASA published design criteria for it in SP-8007 on the buckling of thin-walled circular cylinders, which exists precisely because rockets are thin-walled cylinders in compression. Euler’s own analysis and the classical treatment of these modes are set out in Timoshenko and Gere’s Theory of Elastic Stability, and the same material is taught in courses such as MIT’s Mechanics of Materials.

There’s a misconception this experiment kills. Children, and plenty of adults, assume that strength comes from amount of material, so the thickest column should win. The folded slab is the thickest thing on the table, eight layers deep, and it is the weakest by a wide margin. What matters is not how much material there is but where it is, and the useful way to say that to a child is that paper near the middle of a column does almost nothing. As Smith, diSessa and Roschelle argued, the thicker-is-stronger intuition is not a stupid error to be stamped out; it is a reasonable generalisation from experience that needs refining, and the four columns do the refining.

How to Explain It to Your Kid

Ages 5–8: paper standing up

Hand them a flat sheet and ask them to stand a book on it. Then roll the same sheet into a tube and try again. The tube holds, and the surprise is physical rather than verbal. Then let them build a four-tube table by standing a sheet of card on four paper tubes, and sit a teddy bear on it.

Ages 9–12: it’s about where, not how much

Have them write a prediction for all four shapes in order before testing. Most will rank the thick folded slab first. After the test, ask the key question: all four used the same paper, so what changed? Lead them to the word “shape” and then sharpen it to “how far the paper is from the middle”.

Ages 13+: compute and compare

Give them Euler’s formula and have them calculate the predicted load for the flat slab using a stiffness of 3 gigapascals, then compare with their measurement. The agreement is usually decent. Then calculate the cylinder’s Euler load and see it come out hundreds of times too high. Discussing why a formula works for one case and fails for another is a better lesson in physics than either case alone.

The question to ask: “If I gave you two sheets of paper instead of one for a single column, what would you do with the second sheet to add the most strength?”

Why Teaching This Early Pays Off

The idea that geometry can beat material is one of the most useful things a person can know about the physical world, and it explains a huge amount of what they see: why scaffolding is tubes, why bones are hollow, why an I-beam has that cross-section, why a bike frame is made of thin-walled tube rather than solid rod. One afternoon with four paper columns gives a child a physical memory to attach all of that to.

It also introduces a failure mode, buckling, that is genuinely different from breaking. Materials in tension break when the stress exceeds their strength, which is intuitive. Columns in compression fail suddenly at a load that depends on their length, which is not intuitive at all and catches people out. Meeting that distinction early helps.

The honest framing is worth keeping. The National Research Council’s framework treats structure and function as a crosscutting concept precisely because this pattern recurs across biology and engineering. What this experiment will not do is teach structural analysis, and a single afternoon changes nothing on its own. What it reliably does is make a rolled tube the first thing your child reaches for next time something needs to hold weight. For a bending version of the same idea, try how much a paper bridge can hold.

Before You Start: What Parents Should Know

Best age	7–13. From 12, add the Euler calculation. Below 7, do the stand-a-book-on-paper contrast only
Supervision	Light, but an adult places any load above about 2 kg and keeps the stack low and central
Real hazards	Falling books. Load over a table rather than a lap, keep fingers and toes clear, and stop adding weight at about 10 kg even if the column is still standing, because a toppling stack is the only real risk here. Nothing fragile on top of the platen
Don’t	Don’t put a glass or ceramic object on the platen as a weight, and don’t let a child lean over the column to watch the moment of collapse. Watch from the side, at a distance

When It Doesn’t Work

• The tube collapses at a low load, far below other people’s results. The top edge is not level, so one spot takes all the load. Stand the tube on a flat surface, press down gently and evenly, then trim the high points with scissors.
• The platen tips and everything slides off. The platen is too small or the column is off-centre. Use a 20 cm square of stiff cardboard and mark its centre so each column sits in the same place.
• Results vary hugely between runs. Paper humidity and seam quality both matter. Use sheets from the middle of a fresh pack, tape seams with the same 5 cm every time, and average three runs.
• The flat slab holds much more than expected. Check that you folded rather than rolled it. Any curve at all in its cross-section adds second moment of area and spoils the comparison.
• The triangle beats the cylinder. This happens with a badly formed cylinder, and it is a legitimate result for your particular tubes. Rebuild the cylinder carefully, check the seam overlap and the top edge, then retest.

Take It Further

1. Height sweep. Build cylinders at 21, 15, 10 and 5 cm from identical sheets, trimming rather than changing the diameter, and plot failure load against height. Euler predicts an inverse square relationship, and seeing where your data departs from it tells you where local buckling takes over.
2. Wall thickness. Roll a cylinder from two sheets instead of one, keeping the same diameter so the wall is twice as thick. The jump is larger than most kids expect, because local buckling resistance improves steeply with thickness.
3. Shape efficiency table. Divide each column’s failure load by the mass of paper used and rank the shapes. That column, load per gram, is the number structural engineers actually compete on. Combine it with the index card tower challenge to build something tall from the winning shape, or with straw truss bridges to see the same members working in tension.

What to Watch For Over the Next 3 Months

• Week 4: Reaching for a rolled tube unprompted whenever something needs to stand up or hold weight.
• Month 2: Noticing hollow structures in the world: scaffolding poles, chair legs, bicycle frames, the ribs of an umbrella. The comment to listen for is about things being hollow on purpose.
• Month 3: Predicting a failure mode rather than just a failure. “It’ll bend out sideways” is a different and better prediction than “it’ll break”, and it means the buckling idea landed.

Frequently Asked Questions

Why is the thickest column the weakest?

Because thickness in the direction of bending is what counts, and the folded slab is thick in one direction and extremely thin in the other. It bows sideways about its weak axis at a low load. The tube has material spread all the way around, so there is no weak direction to bow about.

How much weight should a paper tube hold?

With a level top edge and a decent seam, 2 to 5 kg is typical for a single sheet of printer paper rolled into a 21 cm tall cylinder. Results below 1 kg almost always mean an uneven top edge rather than weak paper.

Why doesn’t Euler’s formula predict the tube correctly?

Because Euler describes a column bowing as a whole, while a thin-walled tube fails by a small patch of its wall crumpling first. That local mode happens at a far lower load and is extremely sensitive to small imperfections, which is why NASA publishes separate design criteria for thin shells.

Does the type of paper matter?

Yes, but the ranking of the shapes does not change. Thicker or stiffer paper raises every number, and card can carry considerably more. What matters for the comparison is that all four columns come from identical sheets, so keep one paper type per experiment.

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About the author

Ricky Flores is the founder of HiWave Makers and an electrical engineer with 15+ years of experience building consumer technology at Apple, Samsung, and Texas Instruments. He writes about how kids learn to build, think, and create in a tech-saturated world. Read more at hiwavemakers.com.

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Sources

1. NASA. (1968). Buckling of Thin-Walled Circular Cylinders (NASA SP-8007). NASA Technical Reports Server. https://ntrs.nasa.gov/citations/19690013955
2. Roylance, D. (1999). Mechanics of Materials (3.11). MIT OpenCourseWare. https://ocw.mit.edu/courses/3-11-mechanics-of-materials-fall-1999/
3. Timoshenko, S. P., & Gere, J. M. (1961). Theory of Elastic Stability (2nd ed.). McGraw-Hill.
4. Smith, J. P., diSessa, A. A., & Roschelle, J. (1994). “Misconceptions Reconceived: A Constructivist Analysis of Knowledge in Transition.” Journal of the Learning Sciences, 3(2), 115–163. https://doi.org/10.1207/s15327809jls0302_1
5. National Research Council. (2012). A Framework for K-12 Science Education. National Academies Press. https://doi.org/10.17226/13165
6. White, R., & Gunstone, R. (1992). Probing Understanding. Falmer Press.