Happy Kaomoji
Kaomoji that read as happy, from a quiet (^_^) to a full ヽ(・∀・)ﾉ. Each one lists the characters doing the work, because in this form the eyes carry the feeling and the mouth mostly sets the volume.
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Happiness is in the eyes here
A kaomoji is read upright rather than sideways, so the eyes sit at the top of the brackets and stay in view. That is why the mouth can be a flat underscore in (^_^) and the face still reads as a smile: the work is being done by the two circumflexes. A circumflex is an eye folded shut by the cheek pushing up under it. It comes in two widths — ASCII ^ and the full-width ＾ — which matters for spacing, not for meaning.
Intensity is a separate character, not a bigger smile. ≧ and ≦ are the closed eye with a second stroke under it, and they lean in toward each other. (≧▽≦) is not happier than (^▽^) because the mouth changed; it is the same mouth with the eyes screwed shut.
The mouth sets the volume
▽ is an open laughing mouth, and ∀ is the same triangle with a bar across it, which reads as teeth showing. ω is a mouth that stays closed — two humps and a dip — so (＾ω＾) is pleased where (＾▽＾) is loud. Watch for ∇, which is nearly identical to ▽ but belongs to the mathematical operators rather than the geometric shapes; in a font stack where the two blocks come from different fallback fonts, one of them will render heavier than the other.
Volume also lives outside the brackets
The loudest happy faces do not change the face at all. ヽ(・∀・)ﾉ is the deadpan (・∀・) with two arms bolted on: ヽ on the left and ﾉ on the right — a katakana iteration mark and a half-width katakana no, doing nothing here but leaning in opposite directions. ＼(^o^)／ does the same with slashes. If a face feels too much, take the arms off before you change the eyes. Asterisks and o pressed against the cheeks work from the inside in the same way, adding warmth without touching either the eyes or the mouth; blush kaomoji takes that one marker as far as it goes. Faces built to be loud from the start — arms, star eyes and a wide-open mouth all at once — are collected on excited kaomoji.
Mixing widths is what breaks them
Full-width forms such as ＾ and ＼ occupy one full cell in a CJK font; their ASCII equivalents occupy half a cell. Both are fine, but a symmetric face needs the same width on both sides. Writing ＼(^o^)/ with a full-width slash on the left and an ASCII one on the right is the usual reason a face arrives at the reader visibly lopsided. Width is not the only thing that mangles a face in transit, and copying and pasting kaomoji covers the rest of it.
Every character used above is in the Basic Multilingual Plane, so these faces survive systems that strip four-byte emoji. The kaomoji index lays out the parts these are assembled from; the same eye characters turned upside down give you the sad set, and ω reappears as a muzzle in the cat faces.