Hourly to yearly salary: the formula and the hours behind it

To turn an hourly wage into a yearly figure, multiply it by the hours you work in a week, then by the number of weeks you are paid for in a year. At 20 an hour, 40 hours a week and 52 paid weeks, the year is 20 × 40 × 52 = 41,600 before tax. Monthly pay is the yearly figure divided by 12. To go back to an hourly rate, divide by the weeks and then by the hours.

The steps, one at a time

Work through the figures in order:

1. Weekly pay is the hourly rate times the hours in a week: 20 × 40 = 800.
2. Yearly pay is weekly pay times the paid weeks: 800 × 52 = 41,600.
3. Monthly pay is yearly pay divided by 12: 41,600 ÷ 12 = 3,466.67.
4. Daily pay is weekly pay divided by the days you work: 800 ÷ 5 = 160, if every day is the same length. If your hours vary from day to day, the daily figure is only an average, and your actual shifts are the better record.

To go backwards from a salary, reverse each step. 41,600 ÷ 52 = 800 a week, and 800 ÷ 40 = 20 an hour. The converter does this as you type. Enter a figure in Hourly, Daily, Weekly, Monthly or Yearly, and the other four fill in. Its working line shows each step. For 41,600 typed into Yearly, it reads 41,600 a year ÷ 52 weeks = 800 a week; ÷ 40 h = 20 an hour.

The three settings under Your working week are Hours per week, Days per week and Paid weeks per year. They start at 40, 5 and 52. A 37.5-hour week is typed as 37.5 in Hours per week. At 20 an hour that is 750 a week, and 750 × 52 = 39,000 a year.

Where 2,080 hours comes from

A full-time year is often worked out as 40 hours times 52 weeks, which is 2,080 hours. Divide a yearly figure by 2,080 to get the hourly rate. 41,600 ÷ 2,080 = 20, the same answer as before. The same method works for an offer. A yearly offer of 45,000 for 40 hours a week and 52 paid weeks is 45,000 ÷ 52 = 865.38 a week, and 865.38 ÷ 40 = 21.63 an hour. The 52 comes from the calendar, because a year has 52 weeks and one or two days. The converter's FAQ says to keep 52 if your holidays are paid, and to lower it to the number of paid weeks if some are not. The 2,080 figure is a convenient working year, not a rule, so the hours in your own contract or timesheets are the ones to use.

Paid weeks and part-time hours

Paid weeks change the yearly figure but not the weekly one. If four weeks of the year are unpaid, you are paid for 48 weeks: 20 × 40 × 48 = 38,400 a year, while the weekly pay stays at 800. Unpaid leave, unpaid holidays and gaps between contracts all reduce paid weeks in the same way.

Part-time hours work the same way. At 20 hours a week and 52 paid weeks, the year is 20 × 20 × 52 = 20,800, and the week is 400. Over five days the daily figure is 80. Halving the hours at the same rate halves the yearly pay.

The table shows four common rates for a 40-hour week, with 52 paid weeks and with 48 paid weeks. Every row is the hourly rate times 40 times the weeks, and the monthly column is that yearly figure divided by 12.

Four unpaid weeks cost 3,200 a year at 20 an hour, which is the difference between the two yearly columns. The rate itself is the same in every row, so the gap comes entirely from the weeks.

Why monthly pay is yearly divided by 12

For a fixed salary, every month pays the same, so yearly pay divided by 12 is the right monthly figure. The converter uses that rule for every monthly figure. It is exact for salaried work, and for hourly work it is an average.

An hourly worker's months differ. A year has 52 weeks, so an average month holds about 4.33 of them. A month of four full weeks at 800 a week pays 3,200, and a month of five pays 4,000. The average of 3,466.67 sits between those figures and is useful for budgeting. It is not a payslip figure, because the hours in a given month depend on shifts, holidays and overtime.

What the figures leave out

Every figure is gross pay, before tax and other deductions. Net pay is what reaches your account after those deductions, so it is always lower than the gross figure. Those depend on where you live and on your own circumstances, and the converter applies no tax rules. Overtime is not included, because the converter uses one rate for every hour. Overtime rates are set by your employer and by any rules that apply, so check them separately. Bonuses, benefits and pension contributions are also left out.

To check real hours, the hours calculator totals each shift and gives decimal hours, and minutes to decimal hours explains the conversion. For a raise, the percentage calculator gives the new figure in one step. A 5% rise on 41,600 adds 2,080 a year, which is 40 a week, or two hours' pay at 20 an hour. The new yearly figure is 43,680. When two offers are compared, convert both to yearly pay with the same hours and weeks first, so that the comparison is like for like.