A half cup of melted butter is equivalent to a half cup of vegetable oil.
Added: One stick of butter usually is the same as a half a cup but usually would need to add bit more since butter is entirely fat like oil. 80fat/20water is butter while oil is 100%.
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One stick of butter is the same measure as half a cup of oil. However, oil and butter act differently in cooking. You can't always substitute them and get the result you expect.
That would also be 1 tablespoon, which is 1/8 of a stick of butter. Tablespoon amounts are marked on the paper wrapper, so you can slice off the amount you need with a knife.