The short version three rules, from the model below
- Aim about 1.2 onion radii below the board. Anywhere from 0.8 to 1.5 radii comes within a point of the best in the model, so there is no need to be exact. Evidence
- Make the first and last slice 1.5× thicker. The onion narrows toward the ends, and this evens out the pieces from those slices: the size spread goes from 24% to 20%. Evidence
- Keep the knife steady. 1.2 mm of cut-to-cut error adds 16 points of size spread, 2.8× what every aim point from 0.6 to 3 radii changes. Evidence
All from the model on this page, which has not yet been checked against real onions.
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.
Dice it yourself
This game draws the onion with WebGL2, which this browser does not have. The planner on the Plan tab works without it.
Leaderboard
- Loading the board…
Every timed cut goes on the board as it is diced, under your name if you give one and as anon if you don't, so your three best cuts can all be on it. Signed in to an account, your cuts go up under your handle with a ✓, and nobody else can post under it. Every variety is scored alike, so they share one board, and every score has its speed bonus in it. The board stores the name, the score, the time, the onion and the cuts themselves, so anyone can watch an entry being made on its own onion. Zen and duels are never posted.
How it is scored
The cuts are yours: every lengthwise cut goes where you swipe or send the knife, at whatever lean, crossing another or not, and every slice where you put it. The knife turns round the onion and tilts about where it goes in; the readout says where its cut will meet the board, how far it leans and where it aims. The model onion is then cut exactly along them, every piece found and weighed — a cut that leans in over the middle can leave two separate chunks of one layer, and they count as two.
The score is the planner’s own yardstick, two numbers made one: the size spread by mass (how far a typical bite of onion is from the average piece, the number the Plan tab predicts) and how far the typical piece is from the size asked for, which is the typical piece of the planner’s cut of the same onion. Score = 100 × e−√(spread² + size²), so 100 is every piece the same and the right size. The planner’s own cut is the par, about 80.
A cook copying the plan with a knife steady to ±0.6 mm scores about 4 under par, ±1.2 mm about 11 under, and ±2.4 mm about 25 under; the tiers are named for those. Straight-down cuts lose about 14, even slices about 4. The root end, the six millimetres the cuts stop short of, is not scored.
Every onion is drawn at random: yellow and white are common, red uncommon, sweet rare, and about one in seventy is golden. The one you are dealt is yours until you have diced it, through a reload or a replay; after that you can cut it again or take a new one. Onions differ, and the planner’s own cut scores from about 75 to 82 depending on the onion, so the par beside each one is the number to beat.
The clock times each attempt from your first touch on the onion to Dice it!, held while the page is out of sight or you are watching a replay. In Play it scores: a quick cut earns up to a quarter of its own score again, the speed bonus. The whole quarter is yours inside 2½ seconds for each of the planner’s cuts and slices on the onion (50 seconds on an onion of twenty), and it runs down evenly to nothing at 8 seconds each (2:40); the clock burns it down as you cut. It is a share of the cut’s score, so a rushed rough chop gains little. The board ranks the score with the bonus in it; the stars, the par and the tips are the cut’s alone. A duel ranks the cut, against a clock of its own (below). Zen deals the same onions with no clock at all, a new one whenever you like.
Coins. Each onion pays once, the first time you dice it into something that counts (a score of 20 or more): 30 for beating the planner down to 2 for a rough chop, half as much again for an uncommon onion, twice for a rare one and ten times for a golden one, half in Zen and in duels, up to a quarter more for speed in Play, and 15 more for your first onion of the day. Spend them in the shop (🪙, beside Play and Zen) on knives, boards and kitchens, which are looks and change no score, and on goggles. One knife is more than a look: the legendary mirror knife makes every lengthwise cut twice, mirrored across the middle, and the board marks the cuts made with it.
Power-ups. About one onion in five diced in Play drops a power-up as its pieces land. It floats over the board for twenty seconds, blinking at the end: tap it to pick it up. Double coins pays every onion twice for 2½ minutes; Lucky onions deals rare onions more than twice as often for 3 minutes (a golden one still only after an onion that paid). They run on the clock on the wall whatever you are doing, and only in Play; the purse wears each one, its ring emptying as it runs. Neither changes a score.
Tears. Every cut stings, and onions add up: one leaves your eyes watering, three in a row and you can hardly see what you are cutting. Wipe your eyes, take a break, or buy goggles. Duels: Share sends a link carrying your onion and your cut; whoever opens it cuts the same onion, and every cut in it is re-diced on their screen, so a score in a link is only a claim. Pass it round and the link keeps everyone’s. A duel is against the clock: 8 seconds for each of the planner’s cuts and slices on the onion, the same on every phone, counting down as you cut. When it runs out the knife goes down and the onion is diced as it stands, and a cut that took longer counts for nothing.
The article that started this
“Dicing an Onion, the Mathematically Optimal Way”, by Andrew Aquino with Russell Samora and Jan Diehm for The Pudding (August 2025), found that fanning the lengthwise cuts toward a point 96% of the onion's radius below the board gives the most even dice. However, it seems that number 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.
The article builds on J. Kenji López-Alt's rule of aiming about 60% of the radius down, and on Dylan Poulsen's ~55.7% “onion constant” for infinitely many cuts and layers - the “Kenji's 60%” below is his.
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.
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.