Start from the billable-days convention: a standard Saudi working year has 260 days (52 weeks x 5 days on the common Sunday-Thursday week), but you don't get paid for all of them as a contractor. Subtract 10 private-sector public holiday days, 21 statutory annual leave days, and 4 sick or bench days, and you land at roughly 225 billable days, before accounting for any gaps between contracts.
From there, your rate needs a loading on top of the equivalent permanent salary, but unlike most markets, that loading isn't about tax: Saudi Arabia has none. A PAYG/agency contractor typically needs only a 5%-12% loading, since they still accrue end-of-service benefit (EOSB) as a formally employed staff member of the agency. A freelance-permit contractor invoicing directly needs a higher 12%-22% loading, since they forgo EOSB entirely, there's no employer-employee relationship to accrue it under.