International Time Zones
Every question with a fully worked solution.
- International Time Zones - Video - International Time Zones Watch
Theory
Every place sets its clocks ahead of or behind UTC (Coordinated Universal Time), the world’s standard time. The offset behaves like an integer: Moscow (UTC\(+3\)) and Tokyo (UTC\(+9\)) are \(9 - 3 = 6\) hours apart. This Year 8 maths page shows how to convert times between zones.
UTC is the time standard the world uses to set clocks. An offset such as UTC\(+10\) or UTC\(-5\) says how far a place is ahead of (\(+\)) or behind (\(-\)) UTC. On a number line, the place further right is further ahead.
Time difference \(=\) bigger offset \(-\) smaller offset. Across UTC this is an integer subtraction: \(6 - (-3) = 9\) h.
Converting a clock time. Going to the place with the bigger offset, add the difference; going to the smaller offset, subtract it. Past midnight the date changes too.
Half and quarter hours. Some zones are not whole hours, such as UTC\(+9{:}30\) and UTC\(+5{:}45\). Take a whole hour first, then give back the minutes: \(10\) h \(-\) \(5\) h \(45\) min \(=\) \(4\) h \(15\) min.
Australia’s standard zones are AWST (UTC\(+8\): WA), ACST (UTC\(+9{:}30\): NT and SA) and AEST (UTC\(+10\): QLD, NSW, ACT, VIC and TAS). Daylight saving moves clocks forward \(1\) h from the first Sunday in October to the first Sunday in April: NSW, the ACT, Victoria and Tasmania move their clocks forward \(1\) h, from AEST to AEDT (UTC\(+11\)), and SA moves from ACST to ACDT (UTC\(+10{:}30\)). WA, the NT and Queensland stay on standard time all year. The northern hemisphere has daylight saving in our winter, so the gap between two places can change during the year. Use the offsets for the month in the question.
The International Date Line runs down the Pacific. Offsets run from UTC\(-12\) to UTC\(+14\), so two places near the line can show the same clock time on different dates. Flying east across the line the date goes back one day.
Flights. Add the flight time to the departure time in the departure city’s own time, then convert. Working backwards, go through UTC.
Australia’s standard zones at one moment (no daylight saving):
| Zone | Offset | Clock |
|---|---|---|
| AWST | UTC\(+8\) | 10:00 am |
| ACST | UTC\(+9{:}30\) | 11:30 am |
| AEST | UTC\(+10\) | 12:00 pm |
Australian time zones (daylight saving runs from the first Sunday in October to the first Sunday in April):
| State or territory | Standard time | Daylight saving time |
|---|---|---|
| WA | AWST, UTC\(+8\) | none (stays UTC\(+8\)) |
| NT | ACST, UTC\(+9{:}30\) | none (stays UTC\(+9{:}30\)) |
| SA | ACST, UTC\(+9{:}30\) | ACDT, UTC\(+10{:}30\) |
| QLD | AEST, UTC\(+10\) | none (stays UTC\(+10\)) |
| NSW, ACT, VIC, TAS | AEST, UTC\(+10\) | AEDT, UTC\(+11\) |
Converting a time between zones
- Find the difference: bigger offset \(-\) smaller offset (use the offsets for that month).
- Decide: to a bigger offset add; to a smaller offset subtract.
- Change the clock, and the day if you pass midnight.
Flight times
- Add the flight time to the departure time, in departure time.
- Convert the arrival to the destination’s time.
- Backwards: arrival \(\to\) UTC \(\to\) back the flight time \(\to\) departure zone.
| \(9 - 3\) | \(=\) | \(6\) |
\(6\) hours (Tokyo is ahead).
| \(10 - (-8)\) | \(=\) | \(18\) |
| \(\text{2:00 am} + 18 \text{ h}\) | \(=\) | \(\text{8:00 pm}\) |
8:00 pm on the same day (\(2\) am \(+ 12\) h \(=\) \(2\) pm, then \(+ 6\) h).
(i) Find the time in Johannesburg (UTC\(+2\)).
(ii) Find the time in Lima (UTC\(-5\)).
(iii) How many hours ahead of Lima is Johannesburg?
| \(2 - (-5)\) | \(=\) | \(7\) |
(i) 1:00 pm (add \(2\) h)
(ii) 6:00 am (subtract \(5\) h)
(iii) \(7\) h
(ii) In January, the AEST city is on daylight saving (UTC\(+11\)) and the ACST city is not. What time is it in the ACST city at 7:00 pm in the eastern city?
(i) \(10\) h \(-\) \(9\) h \(30\) min \(= 30\) min, and ACST is behind.
(ii) \(11\) h \(-\) \(9\) h \(30\) min \(= 1\) h \(30\) min.
(i) 7:45 am
(ii) 5:30 pm
Departure time: 10:40 am Fri \(+\) \(12\) h \(55\) min \(=\) 11:35 pm Fri. Difference: \(10 - (-7) = 17\) h, and Los Angeles is behind.
| \(\text{11:35 pm} - 17 \text{ h}\) | \(=\) | \(\text{6:35 am}\) |
6:35 am on Friday: it lands on the morning of the day it left.
Step 1: Honolulu is UTC\(-10\), so add \(10\) h: 4:00 am Sunday UTC.
Step 2: back \(6\) h \(20\) min: 9:40 pm Saturday UTC.
Step 3: Nadi is UTC\(+12\), so add \(12\) h.
9:40 am on Sunday, Nadi time. It leaves on Sunday and lands on Saturday: flying east across the date line takes the date back one day.
(ii) London uses UTC\(+0\) in January and UTC\(+1\) in July. How far ahead of London is an AEST city in July, and in January when that city uses daylight saving (UTC\(+11\))?
| \(10 - 5.75\) | \(=\) | \(4.25\) |
| \(10 - 1\) | \(=\) | \(9\) |
| \(11 - 0\) | \(=\) | \(11\) |
(i) 5:45 am (\(4\) h \(15\) min behind)
(ii) \(9\) h in July, \(11\) h in January
Common pitfalls
Frequently asked questions
What is UTC?
Coordinated Universal Time, the world standard that time zones are measured from.
How do I find the time difference between two places?
Subtract the smaller UTC offset from the bigger one, such as 10 − (−7) = 17 hours.
Do I add or subtract the time difference?
Add when going to a place with a bigger offset (further ahead); subtract when going to a smaller offset.
What does daylight saving do to the offset?
Where it is used, clocks move forward \(1\) hour, so the offset goes up by \(1\): NSW, the ACT, Victoria and Tasmania go from UTC\(+10\) to UTC\(+11\), and SA from UTC\(+9{:}30\) to UTC\(+10{:}30\). WA, the NT and Queensland do not change.
What happens at the International Date Line?
Flying east across it the date goes back one day; flying west it goes forward one day.