While “remainder” and “remaining” are sometimes used interchangeably, the differences between the words are important to know if you want to use them correctly. The definitions of the terms change depending upon which grammatical form and context they are used in.
As Nouns
Both terms can be used as nouns. “Remaining,” as a noun, is an act by which someone or something remains. For instance, in the sentence “The remaining of two natures makes his acts questionable,” “remaining” is the noun. “Remainder,” used as a noun, is the part or parts that are left when something is removed. In the sentence “The remainder of the text will explore philosophical concepts,” “remainder” is the noun. “Remainder” is also used as a noun in mathematics: Here it is the part that is left after subtracting the divisor from the dividend as many times as possible without encountering a negative result.
As Verbs
Both terms can also be used as verbs. For instance, in the sentence “She will be remaining behind,” “will be remaining” is the progressive verb tense of “remain.” “Remainder” is used as a verb by added “-ed” to the end of the word. It refers to items being marked as unsold and being subject to price reductions. For instance, in the sentence “The store remaindered the unsold shirts at the end of the season at a discounted price,” "remaindered” is the verb.
As Adjectives
Only “remaining” may be used as an adjective. For instance, in the sentence “May I have the remaining drink?” “remaining” is the adjective. “Remainder” is never used as an adjective. If you want to resort to an adjective form of “remainder,” it becomes “remaining.”