Overtime
Overtime in NSW Year 10 Core maths covers pay for hours beyond a normal working week or at weekends and nights (NESA outcome MA5‑FIN‑C‑01). Overtime is usually paid at time-and-a-half (\(1.5\) times the normal rate) or double time (\(2\) times), and some jobs add a percentage penalty loading.
You will find time-and-a-half and double-time rates, work out a week's pay that mixes normal hours with overtime, and work backwards from total pay to the normal hourly rate. You will also read start and finish times with unpaid breaks, check a payslip for an error, compare two ways an employer might count overtime, and find how many extra hours are needed to reach a target wage. It is part of Year 10 Core Earning Money.
Theory
Overtime is work beyond normal hours, paid at a higher penalty rate such as time-and-a-half (\(1.5\) times) or double time (\(2\) times). This Year 10 maths page covers weekend and night rates, equivalent normal hours, long days split into pay bands, and working backwards from a total.
Overtime is time worked beyond the normal hours, for example past \(38\) hours in a week or \(8\) hours in a day. It is paid at a penalty rate: a multiple of the normal rate.
Time-and-a-half is \(1.5\) times the normal rate. Double time is \(2\) times the normal rate. Weekends and public holidays often attract these rates too.
A penalty loading is a percentage added to the rate, such as \(15\%\) for night shifts: night rate \(=\) normal rate \(\times 1.15\). Percentage loadings that apply together are added before multiplying.
The equivalent normal hours count each overtime hour by its multiple: \(4\) hours at time-and-a-half are paid like \(4 \times 1.5 = 6\) normal hours.
How to calculate pay with overtime
- Find the hours worked each day: finish minus start, minus unpaid breaks.
- Split the hours into bands using the rule given: normal, time-and-a-half, double time.
- Multiply each band by its rate, or count equivalent normal hours and multiply once.
- Add the bands and the days.
Other questions you will meet
- Daily or weekly rule: under a daily rule, only hours over the limit on each day are overtime. Under a weekly rule, only hours over the weekly total are. The two rules can give different pay.
- Extra hours needed: find the money still needed and divide by the rate for those hours. With bands, fill the first band before moving to the next (Example 4).
- Checking a payslip: work out the correct pay and subtract what was paid to find an underpayment.
- Percentage increase: the extra pay from overtime \(\div\) the pay without overtime \(\times 100\%\).
- Choosing the calculation: rate \(\times\) normal hours \(+\) rate \(\times\) overtime hours \(\times\, 1.5\) is the pattern for time-and-a-half.
(i) Find his time-and-a-half and double-time rates.
(ii) One week he works \(38\) hours at the normal rate and \(5\) hours at time-and-a-half. Find his pay for the week.
(i) Multiply the normal rate by \(1.5\) and by \(2\).
| \(\text{time-and-a-half}\) | \(=\) | \(1.5 \times \$31.20 = \mathbf{\$46.80}\) |
| \(\text{double time}\) | \(=\) | \(2 \times \$31.20 = \mathbf{\$62.40}\) |
(ii) Work out the normal pay and the overtime pay separately, then add.
| \(\text{normal}\) | \(=\) | \(38 \times \$31.20 = \$1185.60\) |
| \(\text{overtime}\) | \(=\) | \(5 \times \$46.80 = \$234.00\) |
| \(\text{total}\) | \(=\) | \(\mathbf{\$1419.60}\) |
Change every hour into equivalent normal hours. One hour at time-and-a-half is worth \(1.5\) normal hours.
| \(\text{equivalent hours}\) | \(=\) | \(10 + 3 \times 1.5 + 2 \times 2\) |
| \(\) | \(=\) | \(10 + 4.5 + 4 = 18.5\) |
| \(\text{normal rate}\) | \(=\) | \(\$599.40 \div 18.5\) |
| \(\) | \(=\) | \(\mathbf{\$32.40}\) |
Check each band:
| \(10 \times 32.40\) | \(=\) | \(324.00\) |
| \(3 \times 48.60\) | \(=\) | \(145.80\) |
| \(2 \times 64.80\) | \(=\) | \(129.60\) |
| \(\text{total}\) | \(=\) | \(599.40 \ \checkmark\) |
Dividing by the \(15\) hours actually worked would give the wrong rate, because some hours paid more.
Find the paid hours, split them into bands, then pay each band.
| \(\text{6:30 am to 7:15 pm}\) | \(=\) | \(12.75 \text{ h}\) |
| \(\text{paid hours}\) | \(=\) | \(12.75 - 0.75 = 12 \text{ h}\) |
Bands: \(8\) h normal, \(2\) h at time-and-a-half, \(12 - 10 = 2\) h at double time.
| \(\text{equivalent hours}\) | \(=\) | \(8 + 2 \times 1.5 + 2 \times 2 = 15\) |
| \(\text{pay}\) | \(=\) | \(15 \times \$29.60\) |
| \(\) | \(=\) | \(\mathbf{\$444.00}\) |
6:30 am to 6:30 pm is \(12\) hours, and 6:30 pm to 7:15 pm is \(45\) minutes, or \(0.75\) h.
Find the normal pay, then fill the gap one band at a time.
| \(\text{normal pay}\) | \(=\) | \(38 \times \$28.80\) |
| \(\) | \(=\) | \(\$1094.40\) |
| \(\text{still needed}\) | \(=\) | \(\$1368.00 - \$1094.40\) |
| \(\) | \(=\) | \(\$273.60\) |
The first \(3\) overtime hours pay \(1.5 \times 28.80 = \$43.20\) each.
| \(3 \times \$43.20\) | \(=\) | \(\$129.60\) |
| \(\text{still needed}\) | \(=\) | \(\$273.60 - \$129.60 = \$144.00\) |
After that, each hour pays double time, \(2 \times 28.80 = \$57.60\).
| \(\$144.00 \div \$57.60\) | \(=\) | \(2.5 \text{ h}\) |
| \(\text{overtime}\) | \(=\) | \(3 + 2.5 = \mathbf{5.5} \text{ hours}\) |
Common pitfalls
Frequently asked questions
What does time-and-a-half mean?
Time-and-a-half means each hour is paid at \(1.5\) times the normal hourly rate. If the normal rate is \(\$34\) an hour, time-and-a-half is \(\$51\) an hour.
How do you calculate overtime pay?
Multiply the normal rate by the overtime multiple, such as \(1.5\) or \(2\), to get the overtime rate. Multiply that rate by the overtime hours, then add the pay for the normal hours.
How do you find the normal rate of pay from total earnings?
Work out the equivalent normal hours: normal hours \(+ 1.5 \times\) time-and-a-half hours \(+ 2 \times\) double-time hours. Divide the total pay by this number.
What are penalty rates?
Penalty rates are higher rates of pay for working overtime, late at night, on weekends or on public holidays. They are written as a multiple, such as double time, or as a percentage of the normal rate, such as \(150\%\).
Is double time the same as working twice as many hours?
In pay, yes. One hour at double time earns the same as two hours at the normal rate, so \(3\) hours at double time are worth \(6\) normal hours.