Gross Pay from an Hourly Wage

Gross pay from an hourly wage is a rate times a time, with the overtime hours weighted by a multiplier before they are added in. Time and a half means $m = 1.5$, so six overtime hours are paid as nine — which is the trick that makes the whole calculation one multiplication instead of two.

The word gross is doing real work in the title. This is pay before income tax, before payroll deductions such as CPP and EI in Canada or FICA in the United States, and before union dues, benefit premiums, garnishments or anything else that arrives on the stub as a subtraction. Net pay is a different and much longer calculation that depends on jurisdiction, filing status and year-to-date totals, which is why no single formula can produce it.

The overtime threshold is set by law and it varies more than people expect. Many jurisdictions count overtime weekly, over 40 hours; several count it daily as well, over 8; some step from one and a half times to double time past a second threshold, or on a seventh consecutive day, or on a statutory holiday. Averaging agreements, salaried-but-overtime-eligible classifications, and banked time each change the sum again. Where more than one band applies, run each band through this page separately and add the results rather than trying to find one multiplier that covers them all.

A note on rounding: pay is usually computed to the cent and hours to a hundredth, and rounding hours to the nearest quarter — a common timeclock setting — is lawful in some places only if it does not systematically favour the employer. The arithmetic here is exact; the timesheet feeding it may not be.