Learn Spanish (Spain): No tengo ningún plan.

In Spanish, double negatives are perfectly normal and required! When you put no before the verb, any indefinite word after it must also be negative. So, No tengo ningún plan literally means "I don't have no plan", which is the correct and natural way to say "I don't have any plans."

Why is the word ningún used here instead of ninguno?

Ninguno drops its final -o and becomes ningún whenever it is placed directly before a masculine singular noun. Since plan is a masculine singular noun, it must be ningún plan.

The English translation says "any plans" (plural). Why is plan singular in the Spanish sentence?

In Spanish, negative words like ningún emphasize the idea of "not even one single thing." Because of this, they are almost always used with singular nouns. Even though English speakers naturally say "any plans" in the plural, Spanish strongly prefers the singular ningún plan.

Why does ningún have a written accent mark when ninguno does not?

When ninguno drops its final -o, the spoken stress stays on the "gun" part. According to Spanish spelling rules, words ending in -n that are stressed on the very last syllable need a written accent mark. We add it to make ningún so that the pronunciation stays correct.