empathy (감정이입, 공감) : the feeling you understand and share another person's experiences and emotions the ability to share someone else's feelings
Example:
내 남편은 정말 공감능력이 제로라니까~ 내가 아프다고 하니까 글쎄 넌 왜 맨날 아프기만 하냐고 하더라고! 그 인간 태도에 정말 울고 싶었다니까..
My husband seems to have really zero empathy ability. I told him that I was sick the other day. Do you know what he said? He said I always get sick. I felt like crying over his bad attitude toward me.
이상, '공감능력'을 영어로 표현할 때는 empathy ability 정도로 표현하면 되겠습니다.