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QUICK ANSWER
"Cuál" is a form of "cuál", a pronoun which is often translated as "which". "Por qué" is a form of "por qué", a phrase which is often translated as "why". Learn more about the difference between "cuál" and "por qué" below.
cuál(
kwahl
)A pronoun is a word that stands in for a noun (e.g., she).
a. which (among a group of options)
¿Cuál de estas camisas me queda mejor?Which of these shirts suits me best?
b. which one (among a group of options)
No sé cuál quiere.I don't know which one she wants.
¿Cuál es mejor?Which one is better?
An adjective is a word that describes a noun (e.g., the big dog).
a. which (among a group of options)
¿Cuál color iría mejor en el salón?Which color would look best in the living room?
por qué(
pohr
keh
)A phrase is a group of words commonly used together (e.g., once upon a time).
A masculine noun is used with masculine articles and adjectives (e.g., el hombre guapo, el sol amarillo).