Overtime
Overtime and penalty rates pay more for extra hours, weekends and public holidays, usually at time-and-a-half (\(1.5\) times the normal rate) or double time. This NSW Year 9 Core maths subtopic is Stage 5 Core content under NESA outcome MA5‑FIN‑C‑01.
You will find time-and-a-half, double-time and double-time-and-a-half rates, work out pay for overtime hours, and add normal and overtime pay for a week, such as \(38\) normal hours plus \(4\) at time-and-a-half. You will read rosters and timesheets to decide which hours earn which rate, add a daily site allowance, and work backwards from total pay to the normal hourly rate. You will also compare two workers paid at different penalty rates. It is part of Year 9 Core Earning Money.
Every question with a fully worked solution.
- Overtime - Video - Hourly Rate and Overtime Rate Watch
Theory
Overtime and weekend work are paid at a higher penalty rate, such as time-and-a-half or double time. This Year 9 maths page shows how to find each rate, pay a week with several rates, add an allowance, and work backwards from the pay to the normal rate.
The normal rate is the usual pay for one hour of work.
Overtime is work beyond the normal hours, such as more than \(38\) hours in a week. Overtime, weekends and public holidays are often paid at a higher penalty rate.
Time-and-a-half is \(1.5\) times the normal rate. Double time is \(2\) times. Double time and a half is \(2.5\) times.
An allowance is an extra flat amount, for example for travel or working at heights. It is added on and is not multiplied by a penalty rate.
An award is the agreement that sets the rates for a job and says which hours get which rate.
The penalty rates, with \(r\) the normal hourly rate:
A week with several rates:
| Normal rate | Time-and-a-half | Double time | Double time and a half |
|---|---|---|---|
| $20.00 | $30.00 | $40.00 | $50.00 |
| $30.00 | $45.00 | $60.00 | $75.00 |
How to work out pay with overtime
- Sort the hours into groups by rate: normal, time-and-a-half, double time. Use the award or roster to decide.
- Find each rate by multiplying the normal rate.
- Multiply each rate by its hours and add. Then add any allowance.
- Working backwards? Divide the pay by the equivalent normal hours.
(i) Jo's normal rate is $32 an hour. Find her pay for \(5\) hours at time-and-a-half.
(ii) Raj's normal rate is $19.50 an hour. Find his pay for \(4\) hours at double time.
Find the penalty rate first, then multiply by the hours.
(i)
| \(\text{rate}\) | \(=\) | \(1.5 \times 32 = 48\) |
| \(\text{pay}\) | \(=\) | \(48 \times 5 = \mathbf{240.00}\) |
(ii)
| \(\text{rate}\) | \(=\) | \(2 \times 19.50 = 39.00\) |
| \(\text{pay}\) | \(=\) | \(39.00 \times 4 = \mathbf{156.00}\) |
Jo earns $240.00 and Raj earns $156.00.
The penalty rates are \(1.5 \times 24 = 36\) and \(2 \times 24 = 48\) dollars an hour. Pay each group of hours at its own rate, then add the allowance at the end.
| \(\text{normal}\) | \(=\) | \(38 \times 24 = 912\) |
| \(\text{time-and-a-half}\) | \(=\) | \(3 \times 36 = 108\) |
| \(\text{double time}\) | \(=\) | \(2 \times 48 = 96\) |
| \(\text{allowance}\) | \(=\) | \(5 \times 15 = 75\) |
| \(\text{total}\) | \(=\) | \(912 + 108 + 96 + 75\) |
| \(\) | \(=\) | \(\mathbf{1191.00}\) |
Ben's pay is $1191.00. The allowance is not multiplied by a penalty rate.
Find the hours for each day, then use that day's rate.
| \(\text{Sat hours}\) | \(=\) | \(6.5\) |
| \(\text{Sat rate}\) | \(=\) | \(1.5 \times 27 = 40.50\) |
| \(\text{Sat pay}\) | \(=\) | \(6.5 \times 40.50 = 263.25\) |
| \(\text{Sun rate}\) | \(=\) | \(2 \times 27 = 54.00\) |
| \(\text{Sun pay}\) | \(=\) | \(4 \times 54 = 216.00\) |
| \(\text{total}\) | \(=\) | \(263.25 + 216.00 = \mathbf{479.25}\) |
Priya earns $479.25 for the weekend.
(i) Tia worked \(5\) hours at time-and-a-half and earned $225.
(ii) Max worked \(2\) hours at time-and-a-half and \(5\) hours at double time and earned $377. Find each normal hourly rate.
Turn the hours into equivalent normal hours, then divide the pay by that number.
(i)
| \(\text{equivalent hours}\) | \(=\) | \(5 \times 1.5 = 7.5\) |
| \(\text{rate}\) | \(=\) | \(\dfrac{225}{7.5} = \mathbf{30.00}\) |
(ii)
| \(\text{equivalent hours}\) | \(=\) | \(2 \times 1.5 + 5 \times 2\) |
| \(\) | \(=\) | \(3 + 10 = 13\) |
| \(\text{rate}\) | \(=\) | \(\dfrac{377}{13} = \mathbf{29.00}\) |
Tia's normal rate is $30.00 an hour and Max's is $29.00 an hour.
Common pitfalls
Frequently asked questions
What does time and a half mean?
It means one and a half times the normal hourly rate. On $30 an hour, time-and-a-half is $45 an hour.
How do you calculate overtime pay?
Multiply the normal rate by the penalty, such as \(1.5\) or \(2\), to get the overtime rate. Then multiply by the number of overtime hours.
What is double time and a half?
It is \(2.5\) times the normal rate. It is often paid on public holidays.
How do you find the normal rate from total pay with overtime?
Change all the hours into equivalent normal hours by multiplying each group by its penalty, then divide the total pay by that number of hours.
Is an allowance paid at the overtime rate?
No. An allowance is a flat amount added to the pay. It is not multiplied by time-and-a-half or double time.