backlog / deficit / residue
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backlog
A task that has not yet been completed, an unpaid bill, or another form of deficit. You are behind with something.
Er muss am Wochenende arbeiten, um seinen Rückstand bei dem Projekt aufzuholen.
He has to work on the weekend to catch up on his backlog in the project.
'Rückstand' consists of 'rück-' (back) and 'der Stand' (state, level). It describes a state in which one has 'fallen behind' a target state or an opponent.
Durch seine Krankheit ist er mit den Hausaufgaben in Rückstand geraten.
Because of his illness, he fell behind with his homework.
In connection with work or payments, there are fixed expressions. You can say 'im Rückstand sein' (to be behind/in arrears) or 'in Rückstand geraten' (to fall behind). To end the deficit, you have to 'den Rückstand aufholen' (catch up on the backlog).
Ich bin mit meinen Rechnungen im Rückstand.
I am behind on my bills.
In a sports context, 'Rückstand' describes the gap to the leader. Typical phrases are 'in Rückstand geraten' (to fall behind), 'einen Rückstand aufholen' (to make up a deficit), or 'mit einem Rückstand in die Pause gehen' (to go into the break trailing).
Die Mannschaft geriet schon nach fünf Minuten in Rückstand.
The team fell behind after just five minutes.
This meaning is used almost exclusively in scientific, technical, or ecological contexts. It refers to material remains that are left over after a process, often in connection with the preposition 'von' (of/from).
Die Analyse zeigte Rückstände von Mikroplastik im Trinkwasser.
The analysis showed residues of microplastics in the drinking water.
rest / remainder
'der Rest' and 'der Rückstand' can both refer to something that remains. 'der Rest' is the general word: it works for food, money, time, or things that are still there after something has been used up. 'der Rückstand' is more specific. It can mean unfinished work or an outstanding payment. In a technical or chemical context, it can also mean a small amount of a substance that remains after a process. Learners may confuse the words because both can express 'something left over'. In everyday language, 'Rest' is usually more natural; 'Rückstand' fits better for debts, work that is overdue, or substances left after cleaning or a reaction.
Nach dem Urlaub hat sie einen großen Rückstand bei den E-Mails.
After her vacation, she has a large backlog of emails.
Den Rest der Suppe hebt Maria für morgen auf.
Maria saves the rest of the soup for tomorrow.