1. Two Odd Shapes, Two Different Kinds of Trouble
The short answer is that these two shapes do not have the same cause. A forked carrot is mostly a story about the root: something hurt it or got in its way while it was growing down through the soil. A crooked cucumber is mostly a story about the fruit: something was uneven while the small fruit behind the flower was swelling up.
Home-gardening guides from several US universities agree on this split. Utah State University says carrots "form multiple roots (fork) when damage to the primary root occurs" [3]. Penn State says field-grown cucumbers grow straight when their flowers get enough pollination and curve when they do not [5]. So the next sections look at the carrot's underground trouble first, then at the cucumber's, and then at what you can and cannot tell from a shape alone.
2. Why a Carrot Grows Forked Roots When Its Main Root Is Hurt or Blocked
A carrot is mostly one fat root, called the taproot, that grows straight down. If the tip of that taproot is damaged, the carrot can end up with multiple roots, so it may show two or more "legs" [1].
What can damage or block the taproot? Utah State University lists dense, compact soil and obstructions such as rocks, which can deflect root growth [1]. The University of Minnesota's plant-problem guide names compacted or rocky soil as the first cause of forked or misshapen carrot roots [4]. A simple way to picture it is a plant root meeting a stone and finding a way around, although the guides themselves only describe the result, not the root's "decision."
That leaves a question: if there are no stones, can a carrot still fork?
3. Fresh Manure, Too Much Water, Tiny Worms: Other Ways a Carrot Root Gets Hurt
Yes. Even in loose, stone-free soil, a root can be injured in other ways. Utah State University lists fertilizer placement, damage from insects or disease, too much nitrogen, and fresh manure as things that injure the root and lead to branching [1]. Its home-garden guide adds that overwatering makes "hairy roots" form and forking occur [3].
Microscopic roundworms called root-knot nematodes are another cause. They live in soil and feed on plant roots, and in carrots their activity makes the root forked, distorted or stunted [2]. The University of Illinois also lists root-knot nematodes, stones, and deep, close cultivation as possible causes of forking, and says poor soil preparation is the most common one [6].
Crowding makes a different kind of mess. When seeds are sown too thickly and the seedlings are not thinned out, the roots twist and wrap around each other [6]. This is not forking, but it comes from a similar problem: the root does not have room to grow freely. The gardening advice that follows from all this is consistent too: deep digging, adding compost, and controlling pests help reduce forking [3].
4. Why a Cucumber Curves: Missing Pollination First, Then Water and Temperature
Now to the cucumber. A cucumber starts as a tiny swelling at the base of a female flower. For a regular garden cucumber to fill out evenly, the flower needs enough pollen from visiting bees. Penn State's guide says that if a flower is "pollination deficient," the fruit is deformed and curved, and it can also have fewer seeds and weigh less [5]. The University of Maryland describes the same thing: poorly pollinated fruit is deformed on one end, and the photo caption mentions an increase in "crooked and nubbed fruit" [7]. The guides say that poor pollination goes with curving, but they do not explain exactly how the bend forms.
Why would pollination fail? Maryland lists weather that is too rainy or too cool for bees to fly, very high heat that injures flowers and pollen, and pesticides that kill bees [7].
Water matters too. Utah State's cucumber guide says misshapen cucumbers may come from poor pollination, low soil moisture, or low soil fertility, and that water stress makes fruit bitter, pointed at the end and misshapen [8]. A Purdue University plant-clinic note adds two more suspects: cooler temperatures early in the season, which it links to curved cucumbers in high tunnels, and physical contact from clips, strings, stems or tendrils pressing on a growing fruit [9].
One twist: some greenhouse cucumber varieties are bred to make fruit without pollination at all. Penn State notes that such varieties can set fruit this way, so pollination matters much less for them [5].
5. What a Crooked or Forked Shape Can and Cannot Tell You
It is tempting to treat a shape as a clear clue: "This carrot hit a rock." But the guides list several possible causes for each shape, and the causes can overlap. A forked carrot could have met a stone, been bitten by nematodes, or been touched by fresh manure. A crooked cucumber could have had poor pollination, thirsty roots, or a string pressing on it. The shape alone cannot tell you which cause was at work; the causes the guides list are mostly growing problems.
Two more limits are worth knowing. First, the sources describe what usually causes the shape, but they do not describe exactly how a carrot's side roots decide to thicken or how a cucumber's uneven seeds bend the fruit, so those pictures are only our way of imagining it. Second, the shape alone cannot tell you whether a vegetable is fit to eat. The guides here deal mainly with growing causes, not food safety, so they do not settle that question. Utah State even advises removing badly misshapen young cucumbers from the vine, because they will not grow into normal ones [8].
6. How to Read the Clues on Vegetables From a Store or Garden
You can practise being a vegetable detective without cutting anything. Use only your eyes, and wash your hands after touching garden soil.
For a carrot, look at where the fork starts and how thick each leg is. Legs of different thickness are a clue worth noting, but thickness alone cannot tell you the cause or how the carrot grew. If the carrot has many thin, hairy roots, recall that overwatering is one of the listed suspects [3]. For a cucumber, look at which side it curves toward and whether the bend starts near the middle or the tip. Draw it or take a photo, then write down one guess about what caused the shape and one clue that might show your guess is wrong. If you grow vegetables, the guides give things to try next season: loosen the soil deeply, remove stones, thin seedlings, water evenly, and plant flowers that attract bees [3] [8].
If you want to read more, the University of Minnesota's one-page carrot diagnosis [4] and Penn State's cucumber pollination article [5] are good places to start.