Inelegance is the state of not being graceful or attractive. It is not always ugliness. Sometimes the thing just lacks polish: a clumsy sentence, an awkward movement, a solution that works but looks messy. You meet this word more in writing about art, manners, style, or design than in the street. In maths and computers, people also talk about the inelegance of a method — it gets the answer, though actually it takes the long, ugly road. Slightly formal. In speech, most people would just say it was clumsy, messy, or not elegant.