Nepal Has the Only National Flag on Earth That Isn't a Rectangle — and the Shape Is Defined by an Irrational Number

Every other country on the planet flies a rectangle. Nepal's flag is built from two triangles, a 19th-century family rivalry, and eight steps of compass-and-straightedge geometry written directly into the constitution.

LR By Laxman Rawal · Jul 31, 2026 · 4 min read · Updated Jul 31, 2026

Nepal Has the Only National Flag on Earth That Isn't a Rectangle — and the Shape Is Defined by an Irrational Number

Look at almost any national flag and you'll see the same basic shape: a rectangle. Then there's Nepal. Its flag is the only national flag on Earth that isn't a rectangle or a square — two stacked crimson triangles, taller than they are wide — and by law it can only be drawn one way: with a compass, a straightedge, and eight numbered construction steps written directly into the country's constitution.

Key facts

Nepal's flag is the world's only non-rectangular, non-square national flag among 195 UN member states.
Its height-to-width ratio is an irrational number, roughly 1 : 1.21902 — it cannot be reproduced with a plain ruler alone.
The current design was adopted 16 December 1962; its exact geometry is set out in Schedule 1 of Nepal's constitution.
The two triangles represent the Himalaya; the moon and sun stand for the cool mountain climate and the heat of the southern lowlands.

The shape is not a design accident — it's a merger. For centuries, Nepali rulers and warlords flew triangular pennants rather than rectangular banners, a tradition traced back to King Prithvi Narayan Shah's unification campaigns in the 1700s. When the Rana family seized hereditary power as prime ministers in the mid-1800s, two rival branches of the dynasty each flew their own pennant — one bearing a moon, one bearing a sun, both originally shown with human faces representing the lunar and solar Rajput lines the Ranas claimed descent from. Rather than either branch dropping its symbol, the two pennants were stacked into a single double-pennon flag, moon above sun.

1700sTriangular pennants

King Prithvi Narayan Shah's unification-era forces fly triangular battle pennants rather than rectangular flags.

1800sTwo rival pennants merge

Rival branches of the Rana dynasty each fly a pennant, moon and sun, complete with human faces; the two are stacked into one flag.

16 Dec 1962Modern flag standardised

King Mahendra commissions engineer Shankar Nath Rimal to fix the flag's geometry by law; the faces are dropped from the sun and moon.

2015Geometry carried forward

Nepal's new constitution reproduces the identical Schedule 1 construction diagram, unchanged.

What actually makes the flag mathematically unusual is the border. The plain red pennon shape on its own has tidy 3:4 proportions. Add the constitution-mandated blue trim running around every edge, though, and the outer proportions shift to an irrational ratio, roughly 1 : 1.21902 — a number with no exact fraction, produced by drawing a uniform-width border around two joined triangles instead of a rectangle. It is the only national flag whose legally official shape cannot be captured by a whole-number ratio.

1of 195 UN flags that isn't a rectangle

8numbered construction steps in the constitution

1962year the current geometry was fixed by law

2triangles, representing the Himalaya

The colours carry their own meaning. Crimson is Nepal's national colour and the colour of the rhododendron, the national flower that blazes across the mid-hills every spring trekking season. The blue border stands for peace. The moon in the upper triangle represents the cool, calm temperament of the high Himalaya; the twelve-rayed sun below stands for the intensity of the southern plains. Together, they're widely said to carry the wish that the nation itself endure as long as the sun and moon.

What this means for travellers

What this means for you

You'll see this flag everywhere on a Nepal trip, and now you'll know why it looks the way it does — snapping from a bamboo pole over a teahouse in the Khumbu, painted on a porter's jacket, strung above Kathmandu's Durbar Square, or planted on a summit ridge. It's a small, sharp reminder that Nepal never fully adopted anyone else's template for anything, including how a flag is supposed to be shaped. The same independence shows up in its mountains: nowhere else on the planet packs eight of the world's fourteen 8,000-metre peaks into one country.

Everest Base Camp and Annapurna Base Camp are the two treks most people picture when they imagine the Himalaya, while Ghorepani–Poon Hill is the short, high-reward version for a first trip. Start planning with Everest Base Camp or Annapurna Base Camp. Source: Flags of the World.

Cover photo: HorstGerhard via Wikimedia Commons (CC0).

Source: Flags of the World (crwflags.com)

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