Your onion
Halve it root to stem, peel it, and measure the flat face: its width at the widest point, and its length from the root to the stem tip.
Stem trim and root stub
The root stub is what holds the onion together while you cut, and it is almost all of the waste — see the last finding below.
How even will it come out?
Dices the model onion with this plan, once with every cut exactly where it should be and a dozen times with the knife as steady as you say — then scores the pieces by mass.
The article that started this
The Pudding's onion piece found that fanning the lengthwise cuts toward a point 96% of the onion's radius below the board gives the most even dice. It is a lovely piece of geometry, and the number is not the answer: it comes from cuts landing exactly between layer lines, which no cook can reproduce, and from a statistic that lets a handful of slivers outvote the rest of the onion. Here is its own model, rebuilt, and what it says once you fix both.
Where to aim, and what matters more
The article's model is one slice through the middle. A real onion narrows toward both ends, so this tab dices the whole thing in 3D — with the plan this page gives — and asks what each choice is worth.
Even cooking is about surface, not size
A pan does not cook a piece by its weight. Browning and moisture loss happen at the surface, so a piece's rate goes with its surface-to-volume ratio, S/V — and heat soaks in from the surface too. This tab scores every piece that way, as a cooking size: 6V/S, the side of the cube that cooks the same. A cube's cooking size is its side; a thin piece of the same weight has a smaller one and burns first.
The onions the model cuts
Every number on this page comes from a model onion. These are its shapes: how the layers are laid out, how much thicker the outer ones are, and the outlines real onions come in — each drawn as the face you see when you halve it root to stem, and each cut with the plan this page would give it.
What this model assumes
- An onion is a solid of revolution,
R(z) = R₀·√(1 − (z/L)²), and every layer runs root to stem and pinches in at both ends — which is what a real one does. The findings also hold for the other textbook shape, concentric spherical shells, and say so where they differ. - Every cut is a plane. Knife error is a Gaussian displacement of each cut, taken along the skin for the lengthwise cuts because that is where you aim.
- Pieces are scored by volume and surface-to-volume ratio, weighted by how much onion each piece is. S/V stands in for cooking rate: sweating, softening and browning all happen at the surface.
- None of it has been checked against real onions yet. Layer grading (how much thicker the outer layers are) is an assumption the findings show matters, and a photo of the cut face would measure it.