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Thaum is a unit of energy in the Four Corners, possibly equal to somewhere around 350 to 390 joules (as argued below).
According to Kvothe's answer in an admissions interview in WMF (deemed 'Good enough for me' by Elxa Dal) it takes approximately 180 thaums to boil away one ounce of water that has reached its boiling temperature. The required amount of energy in joules is 63,280 J (assuming that an ounce in the book universe equals approximately 28 grams as is the case with the modern Ounce avoirdupois ounce). Thus one thaum equals 351.56 J. However, the assumption regarding the exact mass of the ounce is open to questioning; for example an historically used Apothecaries' ounce equals to 31.1 grams, thus leading to one thaum equalling 389.22 J. Also, the accuracy of Kvothe's answer is unknown, as demonstrated by the following quote: I dragged up what I could remember from the vaporization tables I'd worked with in the Fishery. "A hundred and eighty thaums," I said with more assurance than I actually felt.
Manet tells Kvothe about an incident of thaumic overfill (or slippage) where a student "must have slipped two hundred thousand thaums inside two seconds". Using here 1 thaum = 370 J, this translates to an energy equivalent released in an explosion of 300 kilograms of TNT.
In Discworld, a thaum is the base unit of magic, the amount needed to create a pigeon, or three billiard balls.