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When something falls onto the floor, we usually expect it to break into pieces. But scientists say they have found a way to calculate how many pieces form and what sizes they are, whether it’s a broken mirror or a sugar cube—they seem to follow a universal rule.

As Karmela Padavic-Callaghan reports for New Scientist, researchers have long known that fragmentation follows a universal pattern. If you count how many fragments there are at each size and plot that as a graph, the distribution has the same shape no matter what object breaks.

Emmanuel Villermaux at Aix-Marseille University in France has now derived an equation that explains this shape, effectively creating a universal law for how objects break apart.

Instead of focusing on the details of how cracks form in an object before it breaks, he took a more zoomed-out approach. Villermaux looked at all possible ways an object can shatter into fragments. Some of these outcomes are very specific, like a vase breaking into four equal pieces.

He then selected the most likely set—the one with the highest entropy—which represents breakages that are messy and irregular. He says this is similar to how many laws about large groups of particles were developed in the 19th century.

He also used a physical law that describes how the total density of fragments changes as the object breaks, which he and his colleagues had previously discovered.

Together, these two ingredients allowed him to create a simple equation that predicts how many fragments of each size a breaking object will produce.

To test how well it worked, Villermaux compared it with many past experiments involving shattering glass bars, dry spaghetti, plates, ceramic tubes, and even plastic fragments in the ocean, as well as waves breaking in rough seas.

Across all these cases, the fragmentation patterns followed his new law, matching the same common graph shape that researchers had observed before.

Villermaux conducted a series of experiments where he shattered a sugar cube by dropping an object onto it from different heights. “That was a summer project with my daughters. I did this a long time ago when my children were still young and then came back to the data, because they were illustrating my point well,” says Villermaux.

The equation doesn’t work in cases where there is no randomness and the fragmentation process is too regular, for instance, when a jet of liquid breaks up into many droplets of uniform size following deterministic laws of fluid physics, and in some cases where fragments interact with each other during shattering, he says.

Ferenc Kun at the University of Debrecen in Hungary tells New Scientist that because the graph shape explained by Villermaux’s analysis is so common, it isn’t surprising that it comes from a larger principle. At the same time, he says it is impressive how widely it works and how it can be adjusted in some cases where there are extra constraints, such as in plastic, where cracks can sometimes “heal”.

Fragmentation isn’t just an interesting physics problem. Kun says understanding it better could have real-world implications, such as improving how energy is used to shatter ore in industrial mining, or helping us prepare for rockfalls that are increasingly occurring in mountainous regions as global temperatures rise.

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