Translation guide
The English term 'half-moon' can refer to the astronomical phase (first/last quarter), a semicircular shape, or a crescent shape. Japanese distinguishes these carefully, and the most natural translation depends on context.
Referring to the moon phase when exactly half of the visible disk is illuminated, i.e., the first quarter or last quarter moon.
The standard astronomical term for a half-moon (first or last quarter). Can also refer to a semicircular shape in some contexts.
You can see a half-moon tonight.
Specifically the first quarter moon (waxing half-moon). Used in astronomical or poetic contexts.
The first quarter moon can be seen in the southern sky in the evening.
Specifically the last quarter moon (waning half-moon). Used in astronomical or poetic contexts.
The last quarter moon can be seen around dawn.
Describing something shaped like a half-circle, such as a half-moon window, table, or design.
In casual English, 'half-moon' sometimes refers to a crescent shape. Japanese distinguishes this clearly.
Literally 'third-day moon', meaning a crescent moon. This is the most natural word for a crescent shape, even if English calls it a 'half-moon'.
If you mean a true half-circle (semicircle), use 半月形 or 半円形. 三日月 is specifically a crescent.
I baked half-moon shaped bread (crescent rolls).
Crescent-shaped. Used for objects like pastries, jewelry, or designs.
English 'half-moon' can be ambiguous. In Japanese, 半月 (はんげつ) is a half-circle (astronomical quarter moon or semicircle), while 三日月 (みかづき) is a crescent. Using the wrong one can cause confusion.
半月 is a semicircle, 三日月 is a thin arc shape.
I bought a half-moon table.
She's wearing half-moon earrings.