The etymology of the name is from Latin: computatio (account, calculation), and Old Polish komput—an army budget which was voted for by the Commonwealth parliament, the Sejm.
Wojsko kwarciane was composed from various units, both Commonwealth-born soldiers and foreign mercenaries.
Personnel number (which was kept a state secret) varies, because often the commanders (hetmans) paid for additional manpower themselves.
During peacetime, the Commonwealth komput army numbered about 12,000 for the Crown (Poland proper) and 6,000 for the Grand Duchy of Lithuania.
In addition, wojsko kwarciane was supplemented with peasant-based recruits of piechota wybraniecka and from 1653, piechota łanowa, registered Cossacks (until 1699), pospolite ruszenie, royal guard, armies of magnates and cities, and wojsko ordynackie.