One Swedish matsked is exactly 15 millilitres. Unlike the American tablespoon, which lands on an awkward 14.79 ml through a chain of older units, the Nordic kitchen measures were defined directly in metric terms and are therefore exact round numbers.
About the units
Sweden reformed its kitchen measures during metrication and ended up with an unusually clean system: kryddmått 1 ml, tesked 5 ml, matsked 15 ml, and deciliter 100 ml. Each step is a whole number of millilitres and each is a simple multiple of the one below. Norway and Denmark use the same values with their own names. The contrast with the English-speaking world is stark: the US tablespoon is 14.787 ml, the imperial tablespoon 17.758 ml, and the Australian tablespoon 20 ml, and all three are called a tablespoon. The Swedish measures were designed after the metric system rather than retrofitted to it, which is the whole reason they are tidy.
The exact factor
The factor is exactly 15, so conversion is trivial in both directions: 3 msk is 45 ml, 100 ml is 6.67 msk. Within the Swedish system, 1 msk is exactly 3 tsk and exactly 15 krm, and 1 dl is 6⅔ msk — the only untidy relationship in the set, and the reason recipes jump from matsked to deciliter rather than stacking tablespoons. Against the American tablespoon the difference is 1.4 per cent, small enough that Swedish and US recipes can be swapped for most purposes without noticeable effect.
Where you meet this conversion
Every Swedish recipe uses it, for oil, cream, sugar, flour, mustard, soy and spices. Swedish measuring spoon sets contain a matsked, tesked and kryddmått as a matter of course, and they are sold graduated in millilitres so the equivalence is printed on the object. The conversion matters most when a Swedish recipe is scaled up: eight matskedar is 120 ml, which is more usefully measured as a little over one decilitre in a jug than counted out one spoon at a time.