Conversion factors – to obtain a weekly salary from an annual salary

Conversion factors – to obtain a weekly salary from an annual salary

Discussion: Since there are not exactly 52 weeks in every year, and more working days in some years than others, a divisor is used in payroll systems for calculating the weekly rate from an annual wage which takes account of leap years and/or working day cycles. The formula to be used might be mandated or you may have a choice, depending on your industrial legislation. The divisor range generally varies from 52.0 weeks to 52.25 weeks. The higher the divisor the lower will be the weekly wage.

Options & Explanation

Option 1 – divide the annual salary by 52 weeks. This method ignores the fact that there are slightly more than 52 weeks (52.1429 weeks excepting leap years). This formula results in the highest weekly rate.

Option 2 – divide the annual salary by 52.1429 weeks (sometimes expressed as 365/7, 365 days per year/7 days per week, 52.1428, or rounded to 52.14). This method recognises that there are more than 52 weeks in a year. A variation of this formula is 365.25/7 = 52.1786 or rounded to 52.18.

Option 3 – divide the annual salary by 52.1667 weeks (sometimes expressed as 313/6; 52.1666, or rounded to 52.167 or 52.17). The origins of this method lie in the working days last century (Sunday being a day of rest): thus 365 days less 52 Sundays = 313 working days, over 6 days per week. This was the default method in the Australian federal industrial jurisdiction when the conversion factor was not specified in the industrial award*. A problematic attempt to explain the logic of using this factor was made by Commissioner Bacon in the Australian Industrial Relations Commission in 2002**.

Option 4 – divide the annual salary by 52.1775 weeks. This method is favoured by those that appreciate scientific method but is somewhat rarely used for payroll purposes (at least in Australia).  This method is based on the Gregorian calendar, a refinement to the Julian calendar, amounting to a 0.0011% correction to the calculation of the weeks in a year. This method is more exact – based on a year of 365 days, five hours, 49 minutes, and 16 seconds – the decimal equivalent being 52.1775.

Option 5 – divide the annual salary by 52.1786 weeks. There are two ways this can be calculated.

a) The days’ method: over 4 years there are 1,461 days (3 x 365, plus 1 x 366) divided by 7 days to obtain weeks; divide the result by 4 (to get an annual rate) = 52.1786 weeks per year.

b) The working days’ method: in the United States a General Accounting Office (GAO) study published in 1981*** demonstrated that over a 28-year period (the period of time it takes for the calendar to repeat itself) there are, on average, 2,087.1429 working hours per calendar year (assuming a 40 hour week). This average results from the fact that there are usually 4 years with 262 workdays, 17 years with 261 workdays, and 7 years with 260 workdays. The divisor using this calculation is 52.1786. The alternative calculation is to take the Working Days average for the 28 year cycle – 260.8929 divided by 5 = 52.1786.

This method aligns with the Julian calendar of 365.25 days, or 52.1786 weeks.

Option 6 – divide the annual salary by 52.20 weeks (sometimes expressed as 261/5). The calculation for this option is as follows: 365 days each calendar year less 104 weekend days = 261 working days; ÷ 5 working days per weekly pay period = 52.20. A variation of this option would be: 365.25 days less 104 weekend days = 261.25 divided by 5 working days = 52.25.

* In Australia, on 3 June 2010, the Minimum Wage Panel issued its Annual Wage Review 2009–10 Decision to vary modern award minimum rates to take effect on 1 July 2010. Annual rates, where there was no calculation method in the modern award, were then adjusted by using the formula: $26.00 x 313/6.

The Fair Work Ombudsmen will suggest, in the absence of an explicit obligation, 52.1667 (or 313 divided by 6). The source of this recommendation is a clause from the previous (and now replaced) Workplace Relations Act Regulation 2.7.5.

Workplace Relations Act Reg 2.7.5

** AIRC – C2002/2532 at P. 1: “… The above divisor was introduced into the award during the review required by the Workplace Relations and Other Legislation Amendment Act 1996. The divisor and apparently the annual wage rates are based on the fact that each year consists of 52 weeks and one day. Thus (provided only one leap year is included) each 6 years comprises 313 weeks and not 312 weeks (ie 6 x 52 weeks). That is, this award reflects the fact that an additional week accrues each 6 years. Expressed another way (provided only one leap year falls in the 6 years) one year in each 6 is comprised of 53 weeks. Thus, on average, each year is not comprised of 52 weeks but is comprised of 52.1667 weeks”.

*** https://www.opm.gov/policy-data-oversight/pay-leave/pay-administration/fact-sheets/computing-hourly-rates-of-pay-using-the-2087-hour-divisor/

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4 comments

  1. In general the payroll divisor/multiplier is set up during configuration of the pay system. It is then used consistently.
    If the payroll divisor was set at (say) 52.1786 to get the weekly rate from an annual salary then this result (divided by weekly hours) would be the base hourly rate for starting to do shift calculations. That is the general position but you need to take account of the laws and industrial agreements that apply in your own jurisdiction. I trust that helps.

  2. Quite thorough, sir, thank you.

    I developed a passing interest in these calculations because the old-fashioned company where I worked (now retired) paid its salaried employees 24 times yearly, mid-month and month-end, when I began working there. (Since it’s Feb. 29 as I write this, I should note that all salaried staff joked about working an extra unpaid day every leap year.)

    When the company outsourced its payroll processing and started paying salaried staff weekly (every Friday), I noted that my weekly gross pay was calculated by dividing my annual salary by 261, then multiplying by 5…that is, by using the 52.20 factor in your option 6 above. It also occurred to me that now I did indeed “get paid” for Feb. 29, although I had no luck ever explaining that to anyone else.

    Because the HR department provided zero education about these calculations, this change to a weekly pay schedule caused a great deal of confusion, and some hard feelings.

    When the company declared bankruptcy and was purchased by another company, I noted that my new employers now calculated my weekly pay simply by dividing my annual salary by 52. I maintained a discreet silence on the subject and enjoyed my employer’s bit of generosity…just a bit over 1% annually, if my calculations are correct.

    Thanks again for this summary. It deserves wide distribution.

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