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"By yourself" is a phrase which is often translated as "por ti mismo", and "on your own" is a phrase which is often translated as "por tu cuenta". Learn more about the difference between "by yourself" and "on your own" below.
by yourself( 
bay
yuhr
-
sehlf
)A phrase is a group of words commonly used together (e.g., once upon a time).
1. (general)
a. por ti mismo  (informal) (singular, masculine or mixed gender)
A word or phrase used to refer to the second person informal “tú” by their conjugation or implied context (e.g., How are you?).
You must make this decision by yourself.Debes tomar esta decisión por ti mismo.
b. por ti misma  (informal) (singular, femenine)
A word or phrase used to refer to the second person informal “tú” by their conjugation or implied context (e.g., How are you?).
Are you going to the dance by yourself, or do you have a date?¿Vas al baile por ti misma, o tienes una pareja?
c. por tu cuenta  (informal) (singular)
A word or phrase used to refer to the second person informal “tú” by their conjugation or implied context (e.g., How are you?).
I can't believe you moved the couch by yourself.No puedo creer que hayas movido el sofá por tu cuenta.
e. por sí mismo  (formal) (singular, masculine)
A word or phrase used to refer to the second person formal “usted” by their conjugation or implied context (e.g., usted).
Do you plan to deliver the presentation by yourself?¿Planea hacer la presentación por sí mismo?
f. por sí misma  (formal) (singular, feminine)
A word or phrase used to refer to the second person formal “usted” by their conjugation or implied context (e.g., usted).
Are you going to the conference by yourself?¿Va a ir a la conferencia por sí misma?
g. por su cuenta  (formal) (singular)
A word or phrase used to refer to the second person formal “usted” by their conjugation or implied context (e.g., usted).
You don't have to organize the meeting by yourself.No tiene que organizar la reunión por su cuenta.
on your own(  
an
yor
on
)A phrase is a group of words commonly used together (e.g., once upon a time).
1. (general)
a. por tu cuenta  (informal) (singular)
A word or phrase used to refer to the second person informal “tú” by their conjugation or implied context (e.g., How are you?).
Do you need help Benjy? Or can you do it on your own?¿Necesitas ayuda Benjy? ¿O puedes hacerlo por tu cuenta?
b. por su cuenta  (formal) (singular)
A word or phrase used to refer to the second person formal “usted” by their conjugation or implied context (e.g., usted).
I'm sorry sir, but you'll have to do it on your own.Lo siento señor, pero tendrá que hacerlo por su cuenta.
c. por su cuenta  (plural)
Now that you all know how to build a robot, are you ready to build one completely on your own?Ahora que todos saben cómo construir un robot, ¿están listos para construir uno completamente por su cuenta?
e. sin ayuda 
Do you think you're ready to try to do it on your own now?¿Crees que estás listo para tratar de hacerlo sin ayuda ahora?
f. por cuenta propia 
This should be done under a doctor's supervision. One should not do it on their own.Esto debe hacerse bajo la supervisión de un médico. No se debe hacer por cuenta propia.