Penkala was born in Liptovský Mikuláš (in what is now Slovakia), to a Polish/Dutch family. He finished schooling in Vienna and Dresden. He then immigrated with his family to Zagreb and subsequently added "Slavoljub" to his name, becoming a naturalized Croat.
He became renowned for his inventions of the first mechanical pencil (1906) (then called "automatic pencil") and the first solid-ink fountain pen (1907). Together with an enterpreneur by the name of Edmund Moster, he started a factory of pens and pencils "Penkala-Moster" that was one of the bigger in the world at the time, and still exists today (named "TOZ-Penkala", where TOZ stood for "Tvornica olovaka Zagreb", meaning "Zagreb pencil factory").
Among his patented inventions are a hot water bottle (his first patented invention, the "Termofor"), a type of bluing detergent, a rail-car brake and an anode battery. He also founded another factory named "Elevator" that produced various chemistry-related items, such as "Radium Vinovica", a patent-medicine-like product sold as curing various forms of rheumatism.