The Swedish krona (SEK) is almost exactly 10:1 against the euro, meaning that for SEK 100 is equal to €10. Since most of us are more familiar with euros, we’ll probably use that for most of our costs to keep things nice and intuitive - just remember to multiply by ten if you want to work in Swedish currency.
The cost of living in Gothenburg, for a student with an eye on the purse strings, isn’t as excessive as some major Scandinavian locations (we’re looking at you, Norway) but it isn’t cheap either. Where you could get by on €600-700 euros per month in the likes of Valencia, you’d be doing well to stay under €1,000 here. It’s doable, but will require a bit of planning regarding meals, travelling and socialising.
Because some students are willing to pay more to live the exchange life, this rough budget should be taken with a pinch of salt - a determined student could easily spend 2.5 times as much enjoying themselves in Gothenburg!
As a rough figure, you’re likely to spend €350-600 on rent alone, plus your utility bills and internet. Add in your phone contract (€30), food (€200), public transport (€45), health insurance (€30) and a few other bits and pieces and you’re quickly up at the €800-1000 mark for the month.
Of course you can plan your meals effectively to keep the food costs down, and if your budget won’t stretch to €500+ accommodation, then you’ll simply have to choose somewhere less expensive.
You’ll notice this estimate doesn’t include "socializing" in any tangible way, and that’s where most students invest a large part of their budget. As long you’re careful, there’s no reason you can’t have a great time exploring Gothenburg within the €1000 (or so) bubble.
This is probably the most variable cost you’re going to meet, as it depends entirely on how much you travel, what you’re willing to pay and how much you enjoy cycling, as that’s by far the cheapest way to navigate the city. Full use of the city’s public transport will cost between €40-55 per month, though if you prefer to use single tickets/don’t use public transport every day, it’ll surely be less.
In general public transport costs can be kept quite low. If you have your own car, make sure you choose an apartment which has free parking, either permit-only or well-lit street parking.
Eating in Sweden is a bit more expensive than most of Central/Western Europe, but drinking is quite a lot more. Expect to pay about €5 minimum for a beer or wine, and a few extra for a good one. It’s just part of their economy, but it’s a pain going from a couple of euros a pint to what seems like extortion.
The Swedes also drink quite in moderation (as a rule) so you won’t spend as much money as you think, if you fall in line and consume a little less than you might at home.