刀 is a side-view pictograph of a single-edged blade — the handle and curved cutting edge captured in just two strokes. CJK calligraphy distinguishes carefully between two cutting weapons: 刀 (single-edged, like a saber or kitchen knife — slashing) and 劍 (double-edged, like a Western sword — thrusting). The pair encodes a subtle weapons taxonomy that English collapses into the single word "sword."

As a radical, 刀 takes the compressed form ⺉ (the "standing knife" radical, written on the right side of compounds) and anchors the entire vocabulary of cutting and dividing: 分 (fēn, to divide), 切 (qiē, to slice), 初 (chū, beginning — originally "first cut" of fabric), 別 (bié, to separate / different), 制 (zhì, to make / control — originally cutting with a knife to shape something), 剣 (the modern shinjitai for 劍). Few two-stroke characters punch as hard as a radical.

Korean reading "do." 短刀 (dando, short sword / dagger), 軍刀 (gundo, military saber), 名刀 (myeongdo, famous sword), 竹刀 (jukdo, bamboo sword used in Korean kendo / 검도), 一刀兩斷 (ilto-yangdan, "one stroke, two pieces" — to decisively cut through indecision; a famous Sino-Korean idiom for clean resolution).

Mandarin dāo, 1st tone. 刀 (dāo, knife — generic), 菜刀 (càidāo, "vegetable knife" = kitchen knife — the Chinese cleaver), 剪刀 (jiǎndāo, "cutting knife" = scissors — Chinese conceptualizes scissors as a kind of two-bladed knife rather than a separate object), 刀子 (dāozi, knife in casual speech), 一刀切 (yīdāoqiē, "to cut with one blade" = to apply uniform treatment to all without nuance).

Japanese on-reading トウ (tō) — 日本刀 (nihontō, "Japanese sword" — the curved single-edged blade central to samurai culture, samurai weaponry, and Japanese metallurgical tradition), 刀剣 (tōken, swords / blades), 木刀 (bokutō, wooden sword for kendo training). Kun-reading かたな (katana) is the famous one — 刀 read as katana names specifically the long Japanese sword carried by samurai. Japanese culture invests 刀 with far more cultural weight than Korean or Chinese, where it remains a generic word for knife. The katana is to Japan what the gladius was to Rome — a national symbol with its own metaphysics.

Memory aid: a side-view of a curved single-edged blade with handle. Two strokes = the entire weapon.