Te equivocas

In school you were taught that you're right is tienes razón. True enough. But how would you say you're wrong? This is a good for the verb equivocarse.

• Sí, te equivocas. You're mistaken about that.
• ¿O me equivoco? Or am I wrong? I'm right, aren't I?
• Yo nunca me equivoco. I'm never wrong.
• Están muy equivocados. They are very wrong, badly informed.

Equivocarse de

In the examples above, equivocarse refers to the correctness of belief. However, the verb also works for making choices or mistakes.

• Me equivoqué de hombre. I made a poor choice (by marrying him).
• Upon calling a wrong number: Me equivoqué de número.

As you can see, de is used here to say what you made a mistake about. Here's an example without de: Me equivoqué como cincuenta veces. I screwed up like fifty times.

Una equivocación is a misunderstanding. No es lo que piensas. Se trata de una equivocación. The word malentendido would also work here.

Error

Another way to say make a mistake is cometer un error. This is not as formal as its English counterpart. Although I have heard native speakers use hacer with error, this is not widely accepted and should not be imitated.