Meaning
弧 means arc — a smooth, curved line forming part of a circle or any gently curving path through space. The archery bow captures this same idea: a symmetrical bend, curved under tension. In mathematics and physics, 弧 turns up in discussions of circular arcs, radian measurement, and curved trajectories.
Etymologically, 弧 is built on the radical 弓 (yumi) — the archery bow. The left component 弓 evokes a bow drawn taut, and from that image comes the kanji's core idea: a line curved under tension, forming a smooth arc. The right-hand component derives from 瓜 (uri, melon or gourd), contributing the phonetic reading コ rather than any semantic meaning.
弧 is written in 9 strokes and classified as a secondary-education kanji in Japan. It joined the 常用漢字 (Jōyō Kanji) list in the 2010 revision, though it does not appear in the elementary-school 教育漢字 curriculum. You'll encounter it mainly in geometry textbooks, engineering documents, and physics papers. It also turns up in literary writing — the graceful arc of a rainbow, the sweeping trajectory of a ball in flight.
Watch out for 弧's near-homophone 孤, which shares the on'yomi コ but means orphan or alone. The distinction is visual: 弧 uses the bow radical 弓 on the left, while 孤 uses the child radical 子. Their meanings share nothing — 弧 always refers to physical shape and curvature, never isolation.
Readings
On'yomi (音読み) — Chinese-derived readings
弧 has one on'yomi: コ (Ko), derived from Middle Chinese. It is used in virtually all compounds and contexts involving 弧. Since there is no kun'yomi, コ is the only reading to know — but you need it solid.
コ appears consistently across mathematical and geometric terminology. The most important compound words:
- 円弧 (enko) — arc of a circle; the portion of a circle's circumference between two defined points. The most common compound using 弧 in mathematics education.
- 弧度 (kodo) — radian; the SI unit of angular measurement used in higher mathematics, physics, and engineering. The system based on this unit is called 弧度法 (kodohō).
- 弧線 (kosen) — curved line, arc; a general geometric term for any arc-shaped line, used in both pure mathematics and descriptive contexts.
- 弧状 (kojō) — arc-shaped, bow-shaped; used as an adjectival noun to describe objects, formations, or structures with a curved arc-like form.
Kun'yomi (訓読み) — Native Japanese readings
弧 has no kun'yomi. Many technical kanji that arrived through Chinese scholarly texts were never paired with native Japanese words — 弧 is one of them. In practice, 弧 almost always appears inside a compound or in the set phrase 弧を描く (ko wo egaku, "to trace an arc"). It rarely stands alone.
Common Words & Compounds
Specialized as it is, 弧 appears across mathematics, science, architecture, and literary writing. The compounds below are grouped by theme.
Mathematics and Geometry
- 円弧 (enko) — arc of a circle; the most fundamental term in geometry involving 弧
- 弧度 (kodo) — radian; the unit of angle measurement based on arc length
- 弧度法 (kodohō) — radian system; the method of expressing angles using radians rather than degrees
- 弧長 (kochō) — arc length; the measured distance along a curved arc between two endpoints
- 弧線 (kosen) — arc line; a curved geometric line forming an arc
- 放物弧 (hōbutsuko) — parabolic arc; the curved path followed by a projectile under gravity
Shape and Form
- 弧状 (kojō) — arc-shaped; bow-shaped in form
- 弧形 (kokei) — arc form; a shape characterized by a smooth curved profile
Common Expressions
- 弧を描く (ko wo egaku) — to draw or trace an arc; used in precise mathematical contexts and in evocative descriptions of movement or trajectory
- 虹が弧を描く (niji ga ko wo egaku) — the rainbow traces an arc; a common literary expression
Example Sentences
数学の授業で円弧の長さを計算した。
Sūgaku no jugyō de enko no nagasa wo keisan shita.
In math class, we calculated the length of an arc.
コンパスを使って紙の上に弧を描いた。
Konpasu wo tsukatte kami no ue ni ko wo egaita.
I drew an arc on the paper using a compass.
虹が雨上がりの空に美しい弧を描いていた。
Niji ga amaagari no sora ni utsukushii ko wo egaite ita.
A rainbow was tracing a beautiful arc across the sky after the rain.
投げられたボールは放物線の弧を描いて飛んだ。
Nagerareta bōru wa hōbutsusen no ko wo egaite tonda.
The thrown ball flew through the air tracing a parabolic arc.
弧度法では角度をラジアンで表す。
Kodohō de wa kakudo wo radian de arawasu.
In the radian system, angles are expressed in radians.
この橋の設計には弧状の曲線が多く用いられている。
Kono hashi no sekkei ni wa kojō no kyokusen ga ōku mochiirarete iru.
Arc-shaped curves are used extensively in the structural design of this bridge.
円弧の長さは半径と中心角から求められる。
Enko no nagasa wa hankei to chūshinkaku kara motomerareru.
The length of a circular arc can be determined from the radius and the central angle.
水しぶきが弧を描きながら空中に飛び散った。
Mizushibuki ga ko wo egaki nagara kūchū ni tobichita.
Water droplets flew through the air, each tracing its own arc as they scattered.
彼女は剣を振り下し、刃が空気に鋭い弧を描いた。
Kanojo wa ken wo furioroshi, yaiba ga kūki ni surudoi ko wo egaita.
She brought the sword down, and the blade carved a sharp arc through the air.
月が夜空を横切る弧を描く軌跡は、古来から人々を魅了してきた。
Tsuki ga yozora wo yokogiru ko wo egaku kiseki wa, korai kara hitobito wo miryō shite kita.
The arc the moon traces across the night sky has captivated people since ancient times.
Memory Tip
Focus on the left-side radical: 弓, the archery bow. Picture a bow drawn taut — that symmetrical bend is exactly what 弧 represents. The right portion of the character carries the phonetic reading コ, but the bow on the left is your visual anchor. Think: "A bow's curve — that's an arc."
To lock in the reading, picture a 虹 sweeping across the sky — a giant bow stretched from horizon to horizon. The reading コ is short and sharp, like the snap of a bowstring releasing an arrow.