Dicing an Onion, the Mathematically Optimal Way

https://pudding.cool/2025/08/onions/

by surprisetalk • 11 months ago

359 146 11 months ago

pudding.cool

pfdietz6• 11 months ago

Throws it in the food processor.

SoftTalker• 11 months ago

Nice if you want onion mush.

criley23• 11 months ago

A few quick pulses doesn't make mush and is fine for a lot of applications. Otherwise, food processors have dicing kits https://i.imgur.com/cXbZ9aC.png

I enjoy the art of prep with my beautiful wa gyuto, I truly do. But if you put a 5 pound bag of large onion on front of me to dice, I will prefer the machine...

webstrand2• 11 months ago

Now you have to clean the food processor. Which is enough of a trouble to prevent me from using it very frequently.

pfdietz6• 11 months ago

Remove from the motor/base, separate parts, spray with water and toss in the dishwasher. And wouldn't you have to clean the cutting board and knife anyway?

The most important part: much less eye watering.

account4211• 11 months ago

Agreed. Food processors only make sense for larger amounts of processed foods. I'm glad to have one for those occasions though.

tptacek4• 11 months ago

The metric being optimized here is uniformity of cut.

altairprime2• 11 months ago

To translate the final answer from math to human (as I’m going to be explaining this to my mother when I chat with her next!):

Imagine the half onion is a half rainbow. You know there’s another half rainbow lurking below the surface, the onion’s ghost of the sphere it once was. Place your knife as usual for each of your ten dice cuts, but instead of cutting straight down towards the cutting board, angle it slightly inward towards the end of the onion’s ghostly half-rainbow sphere below the board. Check your fingers for safety and then make your cut. Assuming your knife isn’t a plasma cutter, you’ll be stopped at the cutting board without ever reaching the onion at the end of the rainbow, and that’s cool. Set your knife at the next dice point and try again :)

(This still improves on the other dicing cases and only costs 1% uniformity by using 100% radius as the target.)

fnord773• 11 months ago

Place your knife as usual for each of your ten dice cuts,

what does this mean, exactly? I don't cut onions. Also I assume there is some pre-step where you cut the onion in half on some axis, but I don't know which.

zeroonetwothree2• 11 months ago

If you don’t cut onions you probably shouldn’t bother with this thread. Or at least watch a video

altairprime2• 11 months ago

If you inspect the onion diagrams in the article carefully, they show various ways to cut an onion, as if origami diagrams but with knives. Still, I think you’ll want to learn the traditional methods of dicing an onion independently first, and then with that knowledge revisit this article and my description; this is last-10% optimization work that hinges on knowing that first-90% of how to dice an onion at all.

fnord773• 11 months ago

From their 2-d diagram, I'm having a hard time understanding what they mean by "vertical cuts" and "radial cuts"

immibis• 11 months ago

Vertical cuts go up and down. Radial cuts go towards a point. But you make a valid point that this 2D diagram doesn't tell the full story, unless your onions are cylindrical, which they're not.

criley23• 11 months ago

Enjoyed reading this. I've followed J Kenji Lopez-alt for a while and I've practiced the "aim below" method for a few years now.

I also like that the article ends with the perfect Kenji-ism. "Yes, technically my method is statistically ideal, but like, it's home cooking and it doesn't matter, heterogenity isn't the enemy". Reminds me of Adam Ragusea (https://www.youtube.com/watch?v=5cWRCldqrxM), we're not making fancy french cuisine, we don't need a perfect brunoise!

jader2013• 11 months ago

Why limit it to just two horizontal cuts?

I’ve always just made equal horizontal and vertical cuts, then slice the onion crosswise.

This results in pretty much no large pieces, and only some smaller pieces (which I prefer over larger ones, anyway).

I don’t care about standard deviation — I only care about minimizing the maximum size (but still without turning them to mush).

(Also, I know this was more of a fun mathematical look at chopping onions vs. practical. But still the “two horizontal cuts” thing seemed to be practical guidance, when it seemed like just equal horizontal and vertical cuts is far superior. But, granted, it’s a little trickier to do.)

EDIT: looking at Youtube, looks like the 2-cut thing is normal. But adding a few more cuts isn’t that much harder, and eliminates the larger pieces from the 2-cut method. I’ll stick to my method, even if it’s a little more work.

pinko• 11 months ago

The post's dataviz in fact allows you vary the # of horizontal cuts and compare the results. Take a look.

jader2013• 11 months ago

Right, but horizontal is limited to two, best I can tell. No?

otherme123• 11 months ago

Horizontal cuts does next to nothing, the onion is already "cut" horizontally.

In my experience it does worse, as the onion gets unstable to do the vertical cuts.

jader2013• 11 months ago

I mean, it’s also cut vertically — except for the adjacent edges (true for both horizontal and vertical, since it’s a sphere).

thunderbong• 11 months ago

Posted less than a day ago (8 points, 2 comments) -

https://news.ycombinator.com/item?id=44894302

1a527dd5• 11 months ago

This is fun!

I really struggled to effectively cut onions until this: https://www.youtube.com/watch?v=CwRttSfnfcc

Haven't looked back since.

morninglight• 11 months ago

That may be the most useful thing I've seen on the internet in months.

Thanks much!

finebalance• 11 months ago

I do it more or less this way - except I keep the root intact until the end. It keeps the onion structurally intact until I'm done with the dicing. At which point, the root takes a single chop to lop off, and then the whole thing scatters into tiny, mostly uniform dices. It's quite satisfying.

fifilura• 11 months ago

I also keep the root. But I am on the radial team!

tptacek4• 11 months ago

Hopefully you're not bothering to core the top and the bottom of the onion; fussy, a waste of time, and works against his later goal of keeping the root intact while dicing.

rjh292• 11 months ago

Yeah you know better than a classically trained French chef. LOL. Do you think he never considered that?

ndr42• 11 months ago

Sorry, but I had to link to this video as you said "effectively": https://www.youtube.com/watch?v=eQgIwwKmjdo

abcd_f2• 11 months ago

Lol, what an amateur hour :)

https://old.reddit.com/r/FastWorkers/comments/1dl1xpz/fast_o...

dyauspitr• 11 months ago

This is silly. I’ve seen Indian street vendors do it the most efficient way. You tilt the knife with the front part down and the back maybe a quarter inch above the surface. That way as you slice the onion the little quarter inch holds it together as you turn it 90 degrees and make the perpendicular set of cuts.

reddit_clone• 11 months ago

Yep. I arrived at the same solution after trial and error.

p1dda• 11 months ago

Chef Jean Pierre is the best, he explains so good that I really need to listen once to remember forever. Before discovering him, I wasn't interested in cooking at all and I listened to all the other chefs like Ramsay and Oliver but they don't tell you the complete story.

haunter• 11 months ago

Ah the famous oñyo video

the-mitr• 11 months ago

I came up with this way by trial and error. Though I don't pare away the root. Just slice is off when dicing is done. Removing the roots helps a lot

nojs• 11 months ago

Why does he peel the oño like an orange when he’s about to cut it in half, why not cut it first?

b1129• 11 months ago

Skin gets into the onion.

hashmap2• 11 months ago

I dislike easily 90%+ of the images I recognize as AI-generated, but the ones on this internet web site I think are a good use of the tech.

russsamora• 11 months ago

There was no AI used on this website!

ctenb• 11 months ago

Source?

hashmap2• 11 months ago

Well, so much for that sentiment! Those onion letters definitely struck me as the original "look we can make chairs out of avocados" use case for dall-e. I guess it's not surprising that good looking AI images turn out to not be AI images in the first place.

feoren• 11 months ago

This ignores the obvious solution of not cutting all the way through. If every other radial cut is only through half the layers, you avoid making the inner pieces too small. It's funny how common it is for people to claim some sort of optimality with lots of math and analysis while completely failing to consider a better possibility. Never take seriously claims that someone found a "mathematically optimal" way of doing something. They didn't.

dcrazy4• 11 months ago

I’m not going to try to make consistent partial cuts down through an onion. I’m going through to the cutting board every time.

RataNova5• 11 months ago

Real-world optimal is often just "whatever works best without making you cry (too much)"

re2• 11 months ago

It turns out that making horizontal cuts almost never helps with consistency.

They made the horizontal cuts evenly spaced between the cutting surface and the top of the onion, which is nonsensical to me. I believe that a single horizontal cut at around 15-20% height would be better for uniformity than a horizontal cut at 50% height.

indy• 11 months ago

Yes! They had all those visualisations and you could see the problem areas from vertical slicing were at the bottom of the onion, a couple of horizontal slices down there would have given the best solution.

jaxn• 11 months ago

Which is exactly how I was taught to do it while working in kitchens 25 years ago.

The other thing is that this seems to ignore that the onion is round in the other direction too. As far as I can see, it only covers the first dice cut.

dcrazy4• 11 months ago

The planar cuts just determine the thickness of the dice. You just want to make them equal to the thickness of the rings.

wkcheng• 11 months ago

Yeah, that's the way that I cut onions: you make vertical cuts followed by one single horizontal cut slightly above the cutting board.

This way of calculating doesn't take into account the creative ways you can make cuts. You could also do mostly vertical slices, and then slightly angle inwards when you do the final few cuts. That would get you a more optimal distribution as well.

jillesvangurp• 11 months ago

A lot of people insist that this is the way. However, at some point, I figured out that making the horizontal cut (or cuts) before you make vertical cuts is a lot easier. You can do it by simply putting the onion with the root on the board and cutting down at an angle of about 5-10 degrees. When the tip of the knife hits the board, simply don't press down all the way to keep the root intact. Then put it down normally and make the vertical cuts. You can easily manage 3 or 4 horizontal cuts this way. And there's no awkward cutting towards yourself with a sharp knife. All this business of first making lots of vertical cuts and then attempting a horizontal cut is a lot more fiddly. The vertical cuts affect the structural integrity of the onion. This makes the horizontal cuts harder. And it also makes the process of dicing harder.

Of course, as the article points out, the horizontal cuts don't really do much that a chef should care about. You can dice an onion super fine with just vertical cuts very close together. And it's a lot faster and easier. You might angle some of the cuts towards the edges. But honestly, even that is unnecessary and a bit overkill. With a good knife, you can put the vertical cuts really close together. So close that any kind of angle would mean the cuts cross each other. Once you are that close, a horizontal cut really does not matter. And if you do a rough cut, the size matters even less.

If you are interested in this topic, there's a French chef on Youtube called Jean Pierre who is full of practical wisdom and techniques. You can learn a lot from him. And he's highly entertaining to watch too. He's very opinionated on onions. Or Onyo as he pronounces it. You won't see him making horizontal cuts, ever.

ethan_smith• 11 months ago

A single low horizontal cut (15-20% from bottom) specifically targets the elongated base pieces - this would likely outperform the evenly-spaced horizontal cuts they tested while remaining practical for home cooks.

RataNova5• 11 months ago

Evenly spaced horizontal cuts might make sense from a modeling standpoint, but not from a practical one. In real-life onion dicing, no one's slicing horizontally all the way up like that, it’s usually one or two low cuts to help break up the base

Theodores• 11 months ago

Once upon a time, my father, who could not cook, harshly criticised my onion chopping technique. This knocked my confidence in the kitchen quite a bit. I refused to learn the fancy techniques of the TV gameshow celebrity chef that my dad was enamoured with.

In my opinion, so long as you are chopping onions, all is well. Sure it could be dangerous, with fingers and egos at stake, but far worse is to not be chopping onions as that means ready meals, take out meals and having a poorer diet.

1970-01-01• 11 months ago

Someone, somewhere, will now spend time growing square onions to fix the problem. Probably someone in Japan.

https://en.wikipedia.org/wiki/Square_watermelon

ginko• 11 months ago

Better yet onions that grow in large flat sheets.

account4211• 11 months ago

But that would also maximize the surface area which means more effort to peel the skin.

zeroonetwothree2• 11 months ago

Standard deviation is a poor measure because you care more about avoiding big pieces than small ones. Penalizing for having a few tiny pieces doesn’t make sense.

crazygringo4• 11 months ago

Thank you, this exactly! Seems like you want to reduce the standard deviation only considering pieces that are larger than the mean, but still relative to the mean. Would be very curious to see the results redone using that approach.

yunwal• 11 months ago

You probably don’t even care about the “standard” deviation at all. You care about the deviation from some desired size. Probably the more accurate problem is “what is the fewest number of straight cuts I can make such that all pieces are below some target size”.

RataNova5• 11 months ago

A few tiny bits will just melt away or brown faster, no big deal. But one big undercooked chunk in a bite of otherwise soft onions? That's noticeable

gndp• 11 months ago

Lol love the extent of clarity of the experiment, findings and interface. I think that for practical purposes, it would be better if the std-dev of pieces with size above a certain threshold is observed. From my experience, pieces above a certain size cause inconsistency in cooked onions. But maybe it depends on the recipe.

NKosmatos• 11 months ago

For sure this research can be nominated for an Ig Nobel Prize :-)

On a more serious note, thanks for posting this and letting me (us?) know about "The Pudding".

tetha• 11 months ago

But is uniformitiy the goal?

If you want diced onions, the cook generally wants onion chunks below a certain cubic mass, so they cook and dissolve easily and uniformly. It does not matter if some pieces are 50% of that size, some are 20% and some are 80%.

With that, 1-2 horizontal slices and a bunch of straight downward slices are the safest and easiest way to achieve that.

That technique also expands to onion rings, sauteed onions and such.

sdwr• 11 months ago

Yeah, measuring standard deviation from the average isn't an accurate way of scoring - "too big" pieces are worse than "too small"

joshwa2• 11 months ago

Just the opposite! When sautéing, too-small pieces have burned by the time the larger ones have cooked, giving the dish a bitter burnt flavor and ugly black flecks.

throwawayffffas• 11 months ago

Uniformity matters for even cooking.

If some pieces are twice the size of your average size, these pieces will be raw, when the others are done.

And if you have some pieces that are half the size of the average they will burn by the time the rest are done.

shakna• 11 months ago

But you don't want an even flavour profile. You do want things cooked, but not perfectly the same as each other.

jmrm• 11 months ago

IMHO yes. Sometimes if the deviation is too big yo can get coocked, overcooked, and mostly raw pieces in the same pan, and that's heavily undesirable.

Jarmsy• 11 months ago

When cutting potatoes into chunks, for something like a stew, I often find myself thinking about this problem, and how I would write a program for a robot to do it.

They are fairly well approximated as ellipsoids of different sizes. Typically, I want pieces around half the volume of the smallest potatoes, but with the range of sizes, this means cutting the larger ones into at least 5 pieces. While it would be simple to make parallel slices giving equal volume, these would have very different shape to the halved smalls. Some can be quartered to give nice chunks, others into thirds with 2 perpendicular cuts...

RataNova5• 11 months ago

As long as no chunk is big enough to stay crunchy while the rest caramelizes, you're good

account4211• 11 months ago

Yeah it's an interesting theoretical problem but the practical applicability is limited.

IAmBroom2• 11 months ago

Burnt bits add unpleasant acridness to the finished dish. And pieces that are 20% of the general size are very like to be overcooked when the rest are properly cooked, so limiting those is important.

tptacek4• 11 months ago

It's funny seeing people dunking on taking this much effort to analyze onion cuts. The rewards for improving your onion dice are indeed probably low. But in mainstream western cooking, you need to do it almost every meal, and the analysis/learning is a one-time cost rather than a cost applied at every prep. Seems like an extremely reasonable thing to noodle on!

dfxm12• 11 months ago

People are dunking on the fact that "mathematically optimal" is meaningless in this situation.

Even Lopez-Alt suggests, "It matters far more for winning internet debates and solving interesting math problems than it does for cooking."

tptacek4• 11 months ago

The mathematical verification doesn't matter, but:

* Radial is more convenient than the classic horizontal cut.

* Radial with an origin below the cutting board is a better outcome than naive radial with almost zero extra effort.

All this to say: it was worth figuring that out!

fuzzfactor• 11 months ago

I figure since it's only an onion I'm glad that that mathematical optimization is not really necessary.

After all there are many more approaches that can be more mathematically rewarding, might as well enjoy it when you can ;)

mafuku• 11 months ago

The authors rightly point out how the pieces near the bottom get elongated in a vertical cut, but don't realize that the whole point of the horizontal cut is to cut those elongated pieces in half. It's not meant to be a cut halfway up the onion.

buildsjets• 11 months ago

I make fresh Pico de Gallo twice a week so I chop a lot of onions. Besides an even dice, I’m interested in not dicing my fingertips. Radial slicing a 180 segment or adding horizontal slices is too unstable.

My method is to cut in quarters, give a quarter a vertical dice, rotate 90, do another vertical dice, then go longitudinal.

motbus3• 11 months ago

This remembers I have a challenge to figure out with some friends.

How to split a round cheese in in 5 perfectly without using any tools except the knife.

Assume you have the ability to cut in half perfectly always

Assume that if you can slice it in 10 equals pieces it is also a valid solution because you can just give two pieces for each

mtklein• 11 months ago

Okay, I'll bite: 2 and 5 are prime, this is the perfect fifth problem, only approximate solutions are possible. Make me wrong!

bravesoul2• 11 months ago

Cut into 8. Give 1 piece each.

For the remaining 3, repeat this method.

Let epsilon be a number as small as you like...

aidenn0• 11 months ago

Measure how many widths of the knife divide the circumference of the cheese. Divide by 5 and make a radial cut at each division.

saagarjha• 11 months ago

What I want is a cutting technique that’s good enough while still being practical for people to do. I am not sure I’m dexterous enough to slightly and consistently tilt the knife as I go through the onion.

uncletaco• 11 months ago

Sure.

First its feet, then its head then split its belly 'til its dead.

wahern• 11 months ago

Is that a regional adage?

fumeux_fume• 11 months ago

So using some complicated angle gets you 4% less std dev than just doing it the easy way that everone already does it. Ok.

burnt-resistor• 11 months ago

While math may offer "optimal" theoretical options, reality is messier. Likely the most efficient for humans and simpler technique to dice onions is the street food vendor way:

https://youtu.be/qDFc-5Zc3HU

https://youtu.be/LOqwl2KTzd4

DamnInteresting• 11 months ago

It's a fun intellectual puzzle, but I find it questionable that onion dice uniformity is always a worthwhile goal. Sure, it ensures more even cooking, but in most dishes, is that desirable? Texture and contrast are nice.

glitchc2• 11 months ago

The most uniform pieces come from this onion dicer: https://latacocarts.com/products/onion-dicer

I used to work in fast food and this bad boy has a rate of 0.5 onions/sec and all of the resulting pieces are perfectly uniform squares. If you've ever wondered where the perfectly diced onions garnishing your burger came from, this is it.

It was a pain to clean though, as the blades were exceedingly sharp. Someone would cut their fingers about once a week on those things.

0xDEAFBEAD• 11 months ago

Not dishwasher safe?

b1129• 11 months ago

I have a knife I use only to cut veggies, I never wash it with soap, just rinse it off and put it back in the block.

Veggies aren't meat.

This is the same for my frying pans. Just rinse them. When was the last time you saw someone use soap to clean a bbq?

glitchc2• 11 months ago

These commercial tools are often odd-shaped (this one is a foot and a half tall) and not dishwasher friendly. Even if you found a way to somehow fit it into the dishwasher, the jets may not reach the blades.

account4211• 11 months ago

It was a pain to clean though, as the blades were exceedingly sharp. Someone would cut their fingers about once a week on those things.

Much better than the various food cutting tools available to consumers which (apart from knives) are always exceedingly dull IME to the point of being useless. An the weird shapes make them impossible to sharpen yourself.

locallost• 11 months ago

I agree with the conclusion - it doesn't matter.

t_mann• 11 months ago

Small nitpick, it's not just the variation in area that you'd care about, but the variation in shape. Two pieces of the same area/volume can cook very differently depending on the shape. The thing is, there isn't a single canonical metric for measuring shape similarity afaik, but you could pick something e.g. based on Hausdorff distance https://en.wikipedia.org/wiki/Hausdorff_distance#Definition A quick search leads to some cool papers https://webspace.science.uu.nl/~veltk101/publications/art/sm...

Sharlin• 11 months ago

Bringing Hausdorff distance into a discussion about onion slicing. Love it.

bippihippi1• 11 months ago

also should consider how easy it is to hole each shape steady as you cut it. how hard is it to actually implement the radial cutting procedure?

b1129• 11 months ago

Sometimes I want this, other times I prefer random sizes.

For example, with tomato based sauces, I often have left overs. For those, sometimes it is not enough so I might add extra crushed tomato to the left overs.

Yet I won't cook that as long as the original dish. So I effectively end up with crushed tomatoes cooked to different amounts.

And you can taste it. It widens the flavour. Gives more depth. Since I noticed this, I often hold back a tablespoon or two of crushed tomatoes, giving long, short, and fresh tomato flavour. The fresh amount added is tiny, like adding spice!

For some dishes, I add fresh garlic but a tiny bit of garlic powder. Just a subtle hint of a slightly different garlic flavour.

Back to onions, different sized pieces cook more/less, and create more variance in flavour, as long as the cook isn't so long to completely cook them all.

I also like adding more than one type of onion to a dish.

Anyhow. Widen those flavours!

RataNova5• 11 months ago

This is exactly the kind of nerdy, hyper-specific deep dive that makes me love the internet

joshwa2• 11 months ago

https://onion-cutting-simulator.streamlit.app/

I made my own version of this a while back, and it lets you create your own cutting methods, plot the statistical distribution, and share your ideas via permalink. It also lets you tweak onion parameters, such as number of layers and the layer thickness distribution curve).

Along the way I discovered two things:

1. I came up with my own method ("Josh’s method" in the app above) where the neither the longitudinal cuts nor the planar cuts are full depth, so the number of cuts at the narrower core is less than at the wider perimeter.

2. After all this hyper-optimization about size, it turns out what really matters when cooking is the THICKNESS, since ultimately determines the cooking rate. The only way to avoid thin outliers that burn long before the rest are cooked is to discard more of the tip of the onion, where the layers are the thinnest.

The 3D version of the simulator is still in progress--turns out 3D geometry is a lot harder than 2D. :)

Pull requests are welcome! https://github.com/joshwand/onion-simulator

ctxc• 11 months ago

Beautiful!

sixtram• 11 months ago

and then there is Marco Pierre White, How to finely chop onions:

https://www.youtube.com/watch?v=UBj9H6z6Uxw

Dicing an Onion, the Mathematically Optimal Way

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