Time units, 24-hour time and elapsed time

Converting between seconds, minutes, hours and days, decimal hours versus hours and minutes, 12-hour and 24-hour time, and finding elapsed time, including across midnight.

Time is the one measurement that isn't metric. There are $60$ seconds in a minute and $60$ minutes in an hour, so the decimal habits that work for metres and litres can trip you up. Most errors in this topic come from treating $3.45$ hours as $3$ hours $45$ minutes.

Units of time

Unit	Equals
1 minute	$60$ seconds
1 hour	$60$ minutes $= 3600$ seconds
1 day	$24$ hours $= 86\,400$ seconds
1 week	$7$ days
1 year	$365$ days ($366$ in a leap year), $52$ weeks and $1$ or $2$ days

Calendars are human inventions too. Aboriginal and Torres Strait Islander peoples have long tracked time through seasonal calendars based on weather, plants and animals rather than fixed months. Many have more than four seasons. The Bureau of Meteorology's Indigenous Weather Knowledge pages show several, including the D'harawal calendar from the Sydney region.

Decimal hours and hours and minutes

A calculator gives time as a decimal, like $3.45$ h. The decimal part is a fraction of an hour, not a number of minutes. Multiply it by $60$ to get minutes.

Example 1●

(a) Write $3.45$ h in hours and minutes. (b) Write $2$ h $50$ min as a decimal number of hours.

(a) $0.45 \times 60 = 27$ min, so $3.45$ h $= 3$ h $27$ min

Keep the whole hours. The 0.45 is a fraction of an hour, so multiply by 60.

(b) $2 + \dfrac{50}{60} \approx 2.83$ h

50 minutes is 50 sixtieths of an hour.

12-hour and 24-hour time

12-hour time needs "am" (before midday) or "pm" (after midday). 24-hour time counts the hours from midnight, $00$ to $23$, and always uses four digits. Timetables, hospitals, the military and airlines use it because it can't be misread.

From $1$ pm onwards, add $12$ to the hour: $7{:}40$ pm $= 19{:}40$.
The hour after midnight is $00$: $12{:}25$ am $= 00{:}25$.
Midday is $12{:}00$, which is $12{:}00$ pm. Midnight is $00{:}00$, the start of a new day.

Elapsed time

The safest way to find the time between two clock times is to count up in jumps: to the next whole hour, then whole hours, then the leftover minutes. If the finish time looks earlier than the start, it must be on the next day, so count to midnight first.

Example 2●●

A nurse starts a night shift at $22{:}45$ and finishes at $06{:}20$ the next morning. How long is the shift?

$22{:}45$ to $00{:}00$ is $1$ h $15$ min

The finish looks earlier on the clock, so the shift crosses midnight. Count up to midnight first.

$00{:}00$ to $06{:}20$ is $6$ h $20$ min

Then count from midnight to the finish.

$1$ h $15$ min $+ 6$ h $20$ min $= 7$ h $35$ min

Add the hours and the minutes separately. 35 minutes is less than 60, so no carrying.

Example 3●

A movie starts at $7{:}50$ pm and runs for $2$ h $35$ min. When does it finish, in 24-hour time?

$7{:}50$ pm $= 19{:}50$

Convert the start to 24-hour time.

$19{:}50 + 2$ h $= 21{:}50$

Add the 2 hours.

$21{:}50 + 35$ min $= 22{:}25$

Add 35 minutes: 10 minutes takes it to 22:00, then 25 more.

Interactive24-hour dial

Try this

Set a start of $22{:}45$ and a finish of $06{:}20$. Check the dial agrees with Example 2.
Set the start to $09{:}35$ and find a finish time that gives exactly $4$ h $35$ min.
Read the decimal hours for a shift of $7$ h $45$ min. Why is it $7.75$ and not $7.45$?

Your turn

A bus leaves Sydney at $11{:}48$ pm and the trip takes $6$ h $25$ min. When does it arrive, in 24-hour time?

Show the working

$11{:}48$ pm is $23{:}48$. Twelve minutes takes it to $00{:}00$, leaving $6$ h $13$ min. It arrives at $06{:}13$ the next morning.

Flashcards

Decimal hours to minutes

Multiply the decimal part by $60$

$7{:}40$ pm in 24-hour time

$19{:}40$: add $12$ to pm hours from $1$ pm

Elapsed time across midnight

Count to midnight, then on to the finish

Practice

How many minutes are in $4.2$ hours?
$1.75$ h $= 1$ h and how many minutes?
Write $135$ minutes in decimal hours.
$15{:}40$ in 12-hour time is:
$12{:}30$ am in 24-hour time is:
How many minutes are there from $09{:}35$ to $14{:}10$ on the same day?
A security guard works from $21{:}50$ to $05{:}15$ the next day. How many minutes is that?
How many seconds are in one day?
Exam style: A nurse works from $19{:}00$ to $07{:}30$ the next morning. Write the shift length in decimal hours, ready to calculate pay.
Exam style: A bus leaves at $11{:}48$ pm and the trip takes $6$ h $25$ min. When does it arrive?