A league is approximately 3 miles.
Unfinished Tales has a chapter named A Description of The Island of Numenor where its states that Numenor "resembled in outline a five-pointed star, or pentangle, with a central portion some two hundred and fifty miles across, north and south, and east and west, from which extended five large peninsular promontories."[/i] This is the narrowest distances across the island according to the map and its scale of miles. Using this map, one could work out the distance of the shoreline and get an approximation of the total square mileage. The 167,961 seems to be rather specific though.
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