To work out by fixed steps. Also the capacity to do so — the same word for the act and the resource.
Latin computare (to reckon, calculate), from com- (together) + putare (to think, reckon, prune); to work a result out by fixed steps rather than by judgment.
Latin putare also means to prune, and computing keeps that sense of cutting a problem down by fixed steps until only the answer remains. The same word names both the pruning and the blade it is done with.