The exact tax rate will depend on which municipality you live in. Municipal tax generally is around 25%, but varies a little from place to place. It's for instance 24.4% here in Århus municipality. And Gentofte (very rich area) for instance at least used to have a pretty low rate (no idea whether it still is really low), though they had to raise taxes when Mærsk died back in 2012 since with his death they got a hole of around 30 million € a year. Similarly church tax varies too; on average it's around 1%; in Århus it's 0.74%. Generally you'll get a very good estimate by just using 37%. Though to get more precise you'd have to calculate every tax rate individually and some taxes are applied to the amount pre deductions and others on the amount post deductions. Hence why just using 37% is the way to go if you don't need anything 100% accurate. Also I'm not sure of how they do the rounding when calculating the sub amounts, which is another reason to just use 37%. (For the final amount the always round down if you paid too much and round up if you paid too little; so if you paid say 0.99 too much they'll round down and say that you paid the exact amount. On the other hand if you paid 0.01 too little they'll round up and say you need to pay an additional 1...)
Note that some deductions can be substantial and would need to be accounted for. For instance if you have to drive a considerable distance to work (something like over 10 to 15 miles) you get the driving deduction. There's also an interest deduction if you have loans.
And note that various things can be taxable income. For instance my insurance company is owned by the insurers and hence pays out profits to the insurers. Instead of lowering the insurance prices they pay out actual money though and that then counts as taxable income so you pay tax of the money you get back from the insurance due to the insurance doing well... On the other hand union membership fees are deductable.
Lets keep it simple though. Everybody has a personal deduction which this year is 44k (using crowns since that's easier; a Swedish crown is around 0.8 Danish crowns). There's also the green check which depends on exactly how much you earn. Setting it at a thousand shouldn't be too wrong.
That means that you have and income of around 285k, but the amount taxed will be 285k - 45k; 37% of 240k is 89k meaning that you'll have around 26k € left of the original 38k € after taxes. Umgefähr jedenfals.
With regard to Copenhagen then it's expensive---and it's expensive compared to elsewhere. 38k € a year is a pretty low wage and you'll therefore probably have trouble finding a place to live in central Copenhagen and will have to go to the outskirts or possibly even further away. Things like restaurants and cafés probably are more expensive in Copenhagen too, though I don't know for sure. Some people also live in Malmø, though with the rising housing market in western Skåne that has become less economically beneficial---plus the border controls means that it takes very considerably longer to go from Copenhagen to Malmø which also should be factored in. If possible it most definitely is cheaper to live elsewhere--even in Århus. And Århus also is small enough that even if you live quite far in the outskirts you still are really close to center---at least compared to the distance between the far outskirts of Copenhagen and the center of Copenhagen. Odense, Aalborg, or Esbjerg probably will be cheaper yet though. And if you don't have a requirement to live in one of the 5 biggest cities then living in one of the smaller ones probably will be even cheaper. And at least in Eastern Jutland it's perfectly possible to do something like living in say Randers or Horsens and then working in say Odense, Esbjerg, or Kolding. It's because of the motorway---you'd have something like an hour, perhaps an hour or a half, drive in those cases.
Are you contemplating moving to Copenhagen?
Also being low income there'll be various benefits. For instance if you rent you'll get some of the rent covered. And various other things. Those things will be highly dependent on the situation, but can be substantial so would need to be accounted for in a detailed budget.
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