Mr_Vittles is absolutely right in that butter can be as little as 80% fat, by law, whereas oil is 100% fat. Certain cakes depend on the additional fat of oil to achieve a moist crumb. Also, many cake recipes call for creaming butter and sugar, incorporating air, until the batter is fluffy. You can never achieve this with oil. So they're not perfectly substitutable, but you'll end up with textural changes that can probably only be detected in a side-by-side comparison.
Yes you can make the substitution the problem being this: butter is milk fat, but it is also, milk, mostly water. So when you bake a brownie made with oil, the fat is all fat and gives you that luscious mouthfeel, but with butter your brownies are a liable to turn out bit more cakey or have less texture. If you go with butter, try browning it first, that way some of the water will evaporate and you'll have and even richer flavor in the end.
I do it all the time. If a recipe deigns to mention "vegetable oil", I automatically change it to butter. It tastes better, it bakes better, it's all around better.
No change in measurement needed. Really, if you're choosing to bake from scratch (and unless it's an Olive Oil Cake) never use oil. Just use the butter and eat the goodies in moderation.
Substituting butter for oil requires about 25% more butter. If you brown it, as suggested above, then measure out 25% more than called for in recipe or box (gasp), that'll help. If dubious just measure out a smidge over called-for amount on your 1st try.
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No change in measurement needed. Really, if you're choosing to bake from scratch (and unless it's an Olive Oil Cake) never use oil. Just use the butter and eat the goodies in moderation.