If you wanted quite exact number, you’d have to uproot the tree and put it on a scale. However if you want a reasonably exact number of the kind used by foresters, you’ll need to measure the diameter and the height. Then there are simple formulas to get a good approximation of weight.
The reference below is an interactive page that defines terms and shows you how to walk through the process.
Note that the effort for these precise methods is oriented toward logging/farming concerns. If you’ve got a lovely, old, carefully tended oak that’s standing by itself in a park, that weight will have little to do with the statistical average for a youngish oak in the forest that’s crowded for resources such as light and water. The tree in the park, having plenty of resources, is liable to be more compact, because it “doesn’t have to stretch for resources”. I.e., the park tree will be much heavier for its height (?)
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