Why Paper Cuts Peak at 65 Micrometres

It has happened to everyone. You are quietly getting on with sealing envelopes or loading a ream into the printer when - tsssss, ouch! - a brand-new paper cut leaves ruby-red human juice across an otherwise pristine white surface.

Despite their frequency, the physics behind paper cuts remains surprisingly poorly understood. How can the edge of something so readily creased and torn penetrate skin deeply enough to draw blood?

Physicists at the Technical University of Denmark have now identified a key trait shared by the most troublesome sheets: paper around 65 micrometres thick.

That category includes dot-matrix printer paper, newspaper, and paper used for certain magazines and scientific journals.

Why 65-micrometre paper cuts are most hazardous

It might seem logical that the thinnest edge would pose the greatest risk. Yet very thin papers, including tissue, are so weak that their edges buckle when they meet the skin. At the other extreme, thicker paper is simply too blunt. At roughly 65 micrometres, paper occupies the paper-cut Goldilocks zone: rigid enough to retain its form, yet thin enough to produce a sharp cutting edge.

"These results allow us to assess the relative safety of various product categories broadly," physicists Sif Fink Arnbjerg-Nielsen, Matthew Biviano, and Kaare Jensen write in their paper.

"While tissues, books, and photos are generally safe, we cannot rule out certain risks of using office paper or magazines. In the future, paper manufacturers, printers, and publishing companies may wish to consider this during the product design process."

Paper cuts are not generally regarded as serious injuries - and in most cases, they are not. They cause a brief sting and irritation before we forget them and carry on.

Usually, at least.

For some patients, however, they can be genuinely dangerous. In any case, nobody likes getting a paper cut. The underlying physics also presented an intriguing puzzle, prompting Arnbjerg-Nielsen and colleagues to investigate it.

Testing paper thickness against gelatin

For the experiments, the team used sheets of paper in varying thicknesses and attempted to slice them through freshly prepared blocks of gelatin, formulated to mimic the consistency of flesh. A machine moved the paper over the gelatin at precisely controlled speeds and several angles, while a video camera captured the outcomes.

The tests showed that thin paper buckles under pressure and fails to cut. Thicker sheets, meanwhile, merely leave an indentation in the gelatin.

The scientists then created a formula to identify the paper thickness most effective at cutting human flesh. It indicated that paper between 50 and 100 micrometres is potentially the most dangerous, with 65 micrometres as the optimum point.

The Papermachete paper scalpel

As the researchers note, the results could help designers create paper products less likely to bite back. But the findings can also be applied in the opposite direction. Using their work, the researchers made an inexpensive paper scalpel named the Papermachete, which successfully cut apple, chicken, capsicum, and banana peel.

The Papermachete will not replace metal knives, but it can do the job in a pinch, which is rather neat. Free 3D-print files for its handle are available here.

Further research is needed to clarify how the slicing angle affects the ease with which paper cuts people. Until then, you can take control of your fate by handling paper more carefully.

"It is worth pointing out," the researchers write, "that the habits and dexterity of the user also play a role. In particular, most paper cuts can be avoided by adhering to a strict near normal-contact regimen, which minimizes the cutting likelihood."

We think they have just called us clumsy. Rude.

The research will be published in Physical Review E.