Even otherwise highly numerate people have been known to throw up their hands in horror at the thought of adding together times.

A system like time, which is not decimal, can be counter-intuitive and requires concentration.

However, with a bit of application, you too can learn how to calculate with time, and gain confidence in manipulating hours, minutes and seconds.

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Basic Units of Time

The basic units of time, which allow you to do calculations involving time, are:

Unit		Notes
Second		The second is the International System of Units (SI) measurement for time. The symbol 's' is used to denote a second. Seconds are also commonly abbreviated to sec.
Minute	60 Seconds	A minute nearly always has sixty seconds. However, very occasionally (approx. once every 18 months) a minute can have 61 seconds. These 'leap seconds' are used to keep our clocks aligned to the earth's rotation around the sun.
Hour	60 Minutes	It is common to talk about 'half an hour' (30 minutes) and 'quarter of an hour' (15 minutes).
Day	24 hours
Week	7 days	It is also common for people to talk about a work week, usually 5 days (Monday - Friday) and weekends (Saturday and Sunday).
Month	28,29, 30 or 31 days.	Different months have different numbers of days. All months have either 30 or 31 days except for February. February has 28 days in a common year and an extra day in a leap year; the 29th day of February is called the leap day.
Year	12 Months	A year always has 12 months. A year has approximately 52 weeks. A common year has 365 days and a leap year (occurring mostly every 4 years) has 366 days.
Decade	10 Years
Century	100 Years
Millennium	1,000 Years

Years are commonly split into quarters, especially in business and education settings, with each quarter being three months or approximately 90 days. Quarters in a specific business or sector may not necessarily be the same as those indicated below:

The number of days in a month varies. All months have the same number of days each year except for February which has 28 days in a common year and 29 in a leap year.

Quarter 1			Quarter 2			Quarter 3			Quarter 4
Month	Days		Month	Days		Month	Days		Month	Days
January	31		April	30		July	31		October	31
February	28/29		May	31		August	31		November	30
March	31		June	30		September	30		December	31

As the number of days in a month varies, this also means that the number of weeks in a month varies too.

People often use approximations when calculating the number of days in months. For example, it is common to use the assumption that a month contains four weeks, even though only February in a common year actually does so.

This makes it hard to convert from months to weeks and vice versa, unless you know which months are being used, because there is no immediate ‘conversion factor’.

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Writing Time

There are many different ways to write time. The simplest (digital) form is as written hh.mm or hh:mm, for example 10.21 or 10:21.

Hours may be either divided into 24 (known as the 24-hour clock) or two lots of 12 (often referred to as the 12-hour clock).

When using the 24-hour clock, the 24 hour cycle starts with the time 00:00 (midnight) and runs all the way through to 23:59, before rolling over to 00:00 again. We never write ‘24:00’. You will often see the time in 24-hour clock written without a separator (‘.’ or ‘:’) between the hours and minutes. For example 1400, which may be referred to as fourteen hundred hours. This is especially common in military and seafaring situations.

When using the 12-hour clock the 24 hour period is divided into two 12-hour periods. Both midnight and midday are 12:00. Time before midday (noon) is designated am (ante meridiem) and time after noon is referred to as pm (post meridiem). For example, 4:10pm is the same time as 16:10. Note that we never write ‘16:10pm’ The use of am and pm is only for the 12-hour clock.

You can also describe time in words, such as 'ten minutes past/after twelve', or 'ten past twelve'. Up to half way through an hour, we describe ‘minutes past’ the hour; beyond ‘half past’ we talk about minutes to/before the next hour. A time ‘on the hour’, for example 2:00pm, can be referred to as ‘two pm’, ‘fourteen hundred’, or ‘two o’clock’.

Example time formats:

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Calculating the Passage of Time

In the normal way of things, to calculate how much one thing is greater than another you would simply subtract one from another. However, subtracting time is complicated because it’s not decimal. Instead of the columns being hundreds, tens and units, they are hours, minutes and seconds.

The other way of calculating how much time has passed between Time A and Time B is:

• Work out how many minutes from Time A to the next hour (or minute, if in minutes and seconds).
• Work out how many hours between that next hour, and the last whole hour before Time B.
• Work out how many minutes from the whole hour until time B.
• Add these three numbers together.

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Calculating the total amount of time spent

Sometimes you might need to add up how much time you have spent on a task that you have completed over several days or sessions. Adding a list of hours and minutes isn’t as straightforward as doing a normal addition calculation, because (as above) we are not working with a decimal system.

For example, you may be doing a gardening job for a neighbour, who has agreed to pay you an hourly rate of £10 per hour. On the first day you spend 3 hours and 25 minutes on the task, on the second day you spend 2 hours and 50 minutes and on the third day you finish it off in an hour and a quarter.

You need to add together the three amounts of time 3:25, 2:50 and 1:15. The first step is to add together all of the minutes: 25 + 50 + 15 = 90 minutes. If you need to remind yourself how to perform an addition calculation, have a look at our page on addition.

As there are only 60 minutes in an hour, the next step is to convert 90 minutes into hours and minutes:

90 ÷ 60 = 1.5 hours

The answer is a decimal, so we can convert it back into hours and minutes. You can use a scientific calculator with a degrees function as described above, or you can do a bit more maths.

We can convert 0.5 hours into minutes.

0.5 × 60 = 30

1.5 hours is therefore 1 hour and 30 minutes.

Next we need to add together the whole hours we have spent, which was 3 on the first day, 2 on the second day and 1 on the third day: 3 + 2 + 1 = 6 hours.

Add the total hours to the total minutes (in hours and minutes):

6h + 1h 30m = 7 hours and 30 minutes, or 7:30 spent gardening. In decimal form, this is 7.5 hours.

In order to calculate how much you have earned, we multiply the time (in decimals) by the hourly rate:

7.5 × 10 = 75. You have therefore earned $75.

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Conclusion

The most important thing when calculating with time is to check whether the answer looks about right?

If your two numbers are less than an hour apart, is your answer less than an hour? If they are about 2 hours apart when you look at them, is your answer? If not, you may have lost or gained some time somewhere!

If you want to know more about ‘about right’ take a look at our page on Estimation, Approximation and Rounding.

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