Why is snow hexagonal?
― The way water molecules line up gives the answer
Look at a snow crystal under a magnifying glass and every fine pattern is different, yet the outline is always a hexagon, or a six-armed star. You'll almost never find a five-sided or seven-sided snow crystal. This "always six" rule comes from the way water molecules — far too small to see — arrange themselves.
On a snowy day, you may have once stared closely at a snow crystal that landed on your glove or a dark cloth. The branching patterns are complex, and no two look exactly alike — but look closely and you'll notice every one has a hexagonal skeleton.
Inside a cloud, countless snow crystals are growing separately, in completely different places. So why do they all end up hexagonal, as if they'd agreed on it in advance?
The answer is hidden in a molecular-level property of water itself, the substance snow is made from.
A water molecule (H₂O) has a bent shape, with a fixed angle.
When water freezes, molecules link together only in fixed directions, through a force called a hydrogen bond, producing a crystal structure built from hexagons.
Let's look step by step at how the shape of a single molecule leads to hexagonal snow.
Water molecules have a fixed shape
A water molecule (H₂O) is made of one oxygen atom and two hydrogen atoms. The two hydrogen atoms aren't attached straight across from each other — they're bent, at a fixed angle. As covered in why ice floats on water, this bent shape is the root of many of water's strange properties.
Water molecules link in "fixed directions" via hydrogen bonds
Water molecules bond to each other through a force called a hydrogen bond. A single water molecule can form hydrogen bonds with up to four surrounding molecules, each in a fixed direction. In liquid water these bonds are constantly breaking and re-forming, but once it freezes into ice, the molecules' positions lock in place, producing a regular, repeating structure.
When molecules stack up using this fixed bonding angle in four directions, a repeating hexagonal ring structure naturally results. This is the basic shape of ice (more precisely, of the most common ice crystal structure).
The angle at which water molecules bond "promises" a hexagon from the very start.
Same hexagon, so why so many different shapes?
Based on the explanation so far, you might expect every snow crystal to end up the same shape. But in reality there's a striking variety — flat plates, slender columns, branching tree-like shapes, and more.
What produces this variety is the temperature and humidity the crystal grows in. In the 1930s, the Japanese researcher Ukichiro Nakaya became the first in the world to grow artificial snow crystals in a laboratory, and worked out in detail how combinations of temperature and humidity change the resulting crystal shape. The relationships he found are still used today as basic reference material for understanding snow crystal shapes.
As a snow crystal falls through a cloud, it passes through places where the surrounding temperature and humidity change. So even within a single crystal, the branches that grew at different times end up slightly different shapes.
Why "no two snow crystals are exactly alike"
The path of temperature and humidity changes a snow crystal follows inside a cloud is thought to be slightly different for every single crystal. Because these tiny differences accumulate over the course of growth, the chance of two crystals matching down to the finest detail is astronomically low. The basic hexagonal skeleton is shared, but the fine patterns produce countless variations.
Depending on temperature and humidity, a crystal can end up a simple or irregular shape that isn't clearly hexagonal. The image of "snow as a beautiful hexagonal star" describes the most common, representative shape — it isn't true of every crystal.
Something you can check for yourself
- Where it snows, catch snow on a dark cloth or paper and look closely with a magnifying glass or phone camera
- Even where it doesn't snow, check your freezer for a thin layer of frost (frost is also ice formed directly from water vapor, and it can show hexagonal patterns too)
- On a cold morning, looking for ice-crystal patterns on a window is another good option
Even without snow, any ice crystal reflects the same arrangement of water molecules, and can show hexagon-related patterns.
Summary
Snow crystals are hexagonal because the fixed angle at which water molecules link via hydrogen bonds produces a repeating hexagonal structure. This molecular-level hexagon carries through to the outline as the crystal grows larger. However, the temperature and humidity where a crystal grows produce a surprising variety of fine shapes, and no two crystals are thought to match down to the last detail.
A hexagonal snow crystal isn't a trick of the weather.
It's a "promise" built into the water molecule from birth.
Some things in nature are hexagonal for an entirely different reason. The honeycomb's hexagon is the answer to a math problem: "how to tile with the least material." Compare the two: Why are honeycombs hexagonal?
For those who want to know more ― terms, numbers, and textbook linksWe label which level each topic belongs to, from middle-school science to open research questions
- Middle schoolCovered in middle-school science and math
- High schoolCovered in high-school "basic chemistry"
- High school+Covered in high-school "chemistry," or an advanced/sidebar topic in textbooks
- UniversityNot covered in high school — a university specialist subject (crystallography)
- ResearchNot settled even at university level — something researchers are actively studying
Middle schoolTerms: words used around snow crystals
- Crystal: a solid formed when atoms or molecules line up in a regular pattern.
- Hydrogen bond: a force by which molecules attract each other via a hydrogen atom acting as a go-between.
- Water vapor: water in gas form. Snow crystals grow when water vapor turns directly into ice (sublimation).
High schoolChecking with a formula: calculating the hexagon's angle directly
Let's confirm why snow crystals show hexagonal symmetry, using a property of the hexagon shape itself.
Sum of interior angles = (number of sides − 2) × 180°
| Number of sides | 6, since it's a hexagon |
| Sum of interior angles | the total of all the polygon's vertex angles added together |
| Subtract 2 from the number of sides | 6 − 2 = 4 |
| Multiply 4 by 180 | 4 × 180 = 720 |
| Sum of interior angles | 720° |
| Since it's a regular hexagon, one interior angle is | 720 ÷ 6 = 120 |
| One interior angle | 120° |
| Angle seen from the center (divided into 6) | 360 ÷ 6 = 60 |
| Angle from the center | 60° |
If you spot a snow crystal's branches splitting at angles of 60° or 120°, that's no coincidence — it's the hexagonal geometry built into the crystal's basic structure showing itself.
※ In real crystals, growth irregularities can shift the angle slightly away from exactly 60° or 120°.
High school+A water molecule bonds with up to four partners
The oxygen atom in a water molecule has two pairs of electrons not used in bonding (lone pairs). These can also form hydrogen bonds with hydrogen atoms on neighboring water molecules, meaning a single water molecule can form hydrogen bonds with up to four other water molecules. This property — "bonding in four directions" — is the key starting point that determines ice's crystal structure.
UniversityCrystal structure and the "Nakaya diagram"
The most common crystal structure of ice is called "ice Ih," in which water molecules arrange in a repeating structure built from hexagons. The diagram Ukichiro Nakaya produced, mapping temperature and supersaturation (how much water vapor builds up) against the resulting crystal shape, is known as the "Nakaya diagram" and is said to still serve as basic reference material in snow and ice science.
ResearchWhat's still unclear
- The detailed speed and rules governing how snow crystals branch as they grow (growth kinetics) is said to be still not fully understood. Atomic-level behavior of water molecules being incorporated at the crystal's edge is thought to play a role.
- Developing models that simulate the temperature and humidity distribution inside clouds more precisely, to predict the diversity of snow crystal shapes, is also an active research topic in meteorology and crystal-growth science.
- The idea that "no two snow crystals are exactly alike" is also, strictly speaking, near-impossible to verify completely at the molecular level, and is said to remain a statistical, probabilistic argument rather than a proven fact.
Even the familiar snow crystal touches on crystal growth, a deep physics topic still under active research.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Middle school | Science: states of matter / Math: polygons | Basic terms: crystal, hydrogen bond |
| High school | Basic chemistry: molecular structure | Calculating a hexagon's angle from the sum of interior angles |
| High school+ | Chemistry: intermolecular forces | Water's lone pairs and four-direction hydrogen bonding |
| University | Crystallography / snow and ice science | Ice Ih crystal structure, the Nakaya diagram |
| Research | Crystal growth science (ongoing) | Growth kinetics, in-cloud simulation |
- Ukichiro Nakaya, Snow (Iwanami Shinsho, 中谷宇吉郎『雪』) and other classic works on snow and ice science.
- Basic chemistry textbook explanations of water molecule structure and hydrogen bonding.
- Crystallography textbook explanations of the ice Ih crystal structure.
- Materials from the Japan Meteorological Agency and Hokkaido University's Institute of Low Temperature Science (北海道大学低温科学研究所) on the classification of snow crystals (the Nakaya diagram).
- Research reviews in the field of snow and ice science on crystal growth kinetics.
※ Figures such as molecular structure and angles are representative values. Real crystal shapes vary with growth conditions.
※This article is a general-audience science explainer. If you go observing snow or ice outdoors, please dress and act safely for cold-weather conditions.