How Time Durations Work — A Complete Guide

A train leaves at 9:20 and arrives at 11:45. A film starts at 23:40 and ends at 1:15 the next morning. A recipe needs 1 hour 45 minutes in the oven and 30 minutes to cool. Every one of these is a question about a duration: how much time passes between one moment and another, or how long two stretches of time make when they are put together. The arithmetic is ordinary addition and subtraction, but time does not behave like ordinary numbers, because it groups in sixties rather than in tens. Once that one difference is understood, duration problems become straightforward.

This guide explains what a duration is, how to add durations together, how to subtract one duration from another when borrowing is needed, how to handle times that cross midnight, and how to convert between seconds, minutes and hours. It works through finding an elapsed time, adding two journeys together, and subtracting a break from a working day, and it shows where people most often go wrong, so you can check your own answers with confidence.

What a duration is

A duration is an amount of time, not a moment in time. “11:45” is a moment: it tells you where the hands of a clock are pointing. “2 hours 25 minutes” is a duration: it tells you how much time has passed. The distinction matters, because moments and durations are written in similar ways and are easily confused. If a journey starts at 9:20 and lasts 2 hours 25 minutes, the arrival moment is found by adding the duration to the start moment, giving 11:45. The duration itself is the gap between the two moments, and finding it is usually the harder direction.

Durations are measured in seconds, minutes, hours, days and weeks, and each step up uses a different conversion. There are 60 seconds in a minute, 60 minutes in an hour, 24 hours in a day, and 7 days in a week. The sixty is the awkward one. Money and ordinary counting group in tens, so 1.5 in money means one pound and fifty pence, a clean half. In time, 1.5 hours means one hour and thirty minutes, not one hour and fifty minutes, because half of sixty is thirty. Almost every duration mistake traces back to treating the minutes as if they were decimal places.

Finding an elapsed time

The simplest way to find how much time has passed is to count forward in whole hours first, then add the remaining minutes. From 9:20 to 11:45, count from 9:20 to 11:20, which is exactly 2 hours, and then from 11:20 to 11:45, which is 25 minutes more, giving a duration of 2 hours 25 minutes. Counting forward avoids subtraction altogether, and it is the easiest method to check, because you can land on each hour mark as you go.

The same forward counting works when the end time is on the hour. From 8:15 to 10:05, count to 10:00 first, which is 1 hour 45 minutes, and then add the final 5 minutes, giving 1 hour 50 minutes. A useful check is to add the duration back to the start time: 8:15 plus 1 hour 50 minutes is 10:05, which is the end time you started with. If adding the answer back does not land on the end time, the duration is wrong, and the counting-forward steps will show exactly where it went astray. This round-trip check is worth using on every elapsed-time problem, however easy it looks.

Adding durations together

To add two durations, add the hours together and add the minutes together, and then convert any minutes over 60 into hours. A journey of 1 hour 45 minutes followed by a wait of 2 hours 30 minutes gives 3 hours and 75 minutes when the parts are added separately. Seventy-five minutes is 1 hour and 15 minutes, so the total is 4 hours 15 minutes. The rule is the same as carrying in ordinary addition, except that the carry happens at 60 rather than at 10, and forgetting that is the single most common error in this whole topic.

The same method handles three or more durations, and it is often easier to add all the minutes first. Three study sessions of 35 minutes, 1 hour 20 minutes and 50 minutes give 1 hour and 105 minutes when the hours and minutes are grouped: 35 plus 20 plus 50 is 105 minutes, which is 1 hour and 45 minutes, and adding the single hour gives 2 hours 45 minutes in total. Adding the minutes in one column, rather than carrying after every step, keeps the working tidy and makes the final conversion happen only once. When the minutes total more than 120, convert twice: 150 minutes is 2 hours and 30 minutes, because 150 divided by 60 is 2 with 30 left over.

Subtracting durations and borrowing

Subtracting durations is the mirror image of adding them, with borrowing replacing carrying. If the minutes you need to subtract are larger than the minutes you have, borrow one hour, which is worth 60 minutes, from the hours column. A working day of 5 hours 10 minutes with a break of 2 hours 45 minutes is worked out by borrowing: 5 hours 10 minutes becomes 4 hours 70 minutes, because one hour has been turned into 60 minutes and added to the 10. Then 4 hours minus 2 hours is 2 hours, and 70 minutes minus 45 minutes is 25 minutes, giving 2 hours 25 minutes of working time.

Borrowing feels strange the first time because the borrowed hour looks like it vanishes, but nothing has been lost: 5 hours 10 minutes and 4 hours 70 minutes are the same amount of time, written differently, just as 1 hour 75 minutes and 2 hours 15 minutes are the same amount. A quick check is to add the answer to the amount that was subtracted: 2 hours 25 minutes plus 2 hours 45 minutes is 4 hours 70 minutes, which converts to 5 hours 10 minutes, the amount you started with. If that check fails, the borrowing step is the first place to look, because the most common slip is borrowing 100 minutes instead of 60, as if the hour were decimal.

Crossing midnight and the 12-hour clock

Durations that cross midnight need one extra idea: the clock restarts at 24:00, which is the same moment as 0:00. The cleanest method is to split the duration at midnight and add the two parts. A film that starts at 23:40 and ends at 1:15 the next morning runs for 20 minutes to midnight, because 60 minus 40 is 20, and then for 1 hour 15 minutes after midnight, giving 1 hour 35 minutes in total. Splitting at midnight keeps every step inside a single day, so no borrowing across the date change is needed.

The 24-hour clock makes this splitting easy, which is why timetables and travel use it, but everyday life often uses the 12-hour clock with am and pm. Converting first prevents the classic midnight error: 11:40 pm is 23:40, and 1:15 am the next morning is 1:15, so the film calculation above is the same problem in either system. The dangerous pair is 12 am and 12 pm: 12 am is midnight, the start of the day, and 12 pm is midday. A meeting from 12:00 pm to 2:00 pm lasts 2 hours, while a shift from 12:00 am to 2:00 am also lasts 2 hours, but they are twelve hours apart, and writing one as the other changes the answer completely. When in doubt, write the 24-hour time beside the 12-hour time before you start.

Converting between seconds, minutes and hours

Converting a duration means multiplying or dividing by 60, depending on the direction. To change a larger unit into a smaller one, multiply: 2 hours is 2 times 60, which is 120 minutes, and 2 hours in seconds is 2 times 3,600, which is 7,200 seconds, because there are 60 minutes in an hour and 60 seconds in each of those minutes. To change a smaller unit into a larger one, divide: 150 minutes is 150 divided by 60, which is 2 hours with 30 minutes left over, so 2 hours 30 minutes.

Decimal hours need the same care. The figure 3.5 hours does not mean 3 hours and 50 minutes: the 0.5 is half an hour, and half of 60 minutes is 30, so 3.5 hours is 3 hours 30 minutes, or 210 minutes. Working the other way, 45 minutes is 45 divided by 60, which is 0.75 of an hour, because 45 is three quarters of 60. Writing a duration as a decimal is sometimes useful for a calculator, but for everyday problems the hours-and-minutes form is clearer, because it matches how clocks and timetables actually show time.

Worked example 1: elapsed time across the afternoon

A repair visit is booked from 14:30 to 16:05. How long is the visit? Count forward from 14:30 to 16:00, which is 1 hour 30 minutes, and then from 16:00 to 16:05, which is 5 minutes more, giving 1 hour 35 minutes. The subtraction method gives the same answer: 16 hours 5 minutes minus 14 hours 30 minutes needs borrowing, because 5 is less than 30, so 16:05 becomes 15:65, and 15 minus 14 is 1 hour while 65 minus 30 is 35 minutes.

Both methods agree, and either one can be used to check the other. The forward-counting method is usually quicker when the times are close together, while the subtraction method is steadier when the times are far apart or cross several hours. What matters is not which method is chosen but that the answer is checked by adding it back: 14:30 plus 1 hour 35 minutes is 16:05, which is the end of the visit, so the duration is right.

Worked example 2: adding up a day of travel

A day out has three legs: a bus ride of 35 minutes, a train ride of 1 hour 20 minutes, and a walk of 50 minutes. How long is the travelling in total? Add the minutes first: 35 plus 20 plus 50 is 105 minutes. Convert 105 minutes into hours and minutes: 105 divided by 60 is 1 hour with 45 minutes left over, so the minutes column is worth 1 hour 45 minutes. Add the hour from the train ride, and the total travelling time is 2 hours 45 minutes.

This total is the travelling time only, not the length of the day out, because waiting time between legs has not been included. If there were also two waits of 15 minutes each, those 30 minutes would be added in the same way, giving 3 hours 15 minutes from the first departure to the final arrival. Keeping travelling time and waiting time in separate columns, and adding them only at the end, stops the two from being mixed up, which is a common source of error in timetable problems.

Worked example 3: a repeated duration

Four episodes of a programme each last 42 minutes. How long do all four last? Multiply the duration by 4: 42 times 4 is 168 minutes. Convert 168 minutes: 168 divided by 60 is 2 hours with 48 minutes left over, because 2 times 60 is 120 and 168 minus 120 is 48, so the four episodes last 2 hours 48 minutes. A quicker estimate confirms the answer is sensible: each episode is a little under three quarters of an hour, so four of them should be a little under 3 hours, and 2 hours 48 minutes fits that estimate.

Repeated durations also appear in the other direction, when a total is shared equally. If 2 hours 48 minutes of viewing is split into 4 equal episodes, dividing 168 minutes by 4 gives 42 minutes each, which is the original episode length. The conversion to minutes first, before multiplying or dividing, is the step that makes both directions easy: hours and minutes cannot be multiplied directly, but a single number of minutes can, and the result is converted back to hours and minutes at the end.

Common mistakes to avoid

Treating minutes as decimals is the most common error: writing 1 hour 45 minutes as 1.45 hours, or adding 1:45 and 2:30 to get 3:75 and leaving it there, both come from forgetting that the minutes carry at 60. The second is borrowing 100 instead of 60 when subtracting, so that 5 hours 10 minutes minus 2 hours 45 minutes wrongly becomes 2 hours 65 minutes. The third is forgetting to convert the answer back: 150 minutes is a correct intermediate answer, but it is not the finished answer, which is 2 hours 30 minutes.

Two more traps are worth watching for. One is the 12-hour clock at midnight and midday, where 12 am and 12 pm are swapped: 12 am is midnight and 12 pm is midday, and a duration calculated across the wrong one will be twelve hours out. The other is mixing durations with moments, such as answering “how long did it take?” with the arrival time instead of the gap between start and arrival. Writing the unit beside every number — hours, minutes, seconds — and adding the answer back to the start time makes all five traps visible before they do damage.

Frequently asked questions

Why is there 60 minutes in an hour instead of 100?

The sixty comes from the ancient Babylonian number system, which used base 60, and it survived because 60 divides neatly by many numbers: 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30. That makes halves, thirds and quarters of an hour into whole minutes — 30, 20 and 15 minutes — which a decimal hour could not do as cleanly. The cost is that time arithmetic needs carrying and borrowing at 60 instead of at 10, which is exactly the skill this guide practises.

How do I find a duration when the end time is earlier than the start time?

That usually means the end time is on the next day, so split the duration at midnight. Count from the start time to midnight, then from midnight to the end time, and add the two parts, as in the film example that runs from 23:40 to 1:15 and lasts 1 hour 35 minutes. If the end time is genuinely on the same day and earlier than the start, the times have probably been read in the wrong order, or am and pm have been swapped, and it is worth checking both before calculating.

What is the difference between 1.5 hours and 1 hour 50 minutes?

They are different amounts. The figure 1.5 hours is a decimal: 0.5 of an hour is half of 60 minutes, which is 30 minutes, so 1.5 hours is 1 hour 30 minutes. The figure 1 hour 50 minutes is 110 minutes in total, which as a decimal is about 1.83 hours, because 50 divided by 60 is 0.83. The confusion comes from reading the minutes as if they were decimal places after the point, and it disappears once the 60-minute hour is kept in mind.

Can I use a calculator for durations, or should I do them by hand?

Both have their place. Doing the counting-forward or borrowing steps by hand builds the understanding that makes calculator answers checkable, and for short durations it is often faster than setting up a tool. For longer lists of times, or for checking a result, a calculator is sensible: the Time Duration Calculator on this site finds the gap between two times and adds durations together, and the Scientific Calculator handles the multiplication and division when durations are first converted to minutes. Whichever route is used, the round-trip check — adding the answer back to the start — is what confirms the result.

If you want to check a result, try the matching tools on this site: the Time Duration Calculator finds elapsed times and adds durations, and the Scientific Calculator handles the conversion arithmetic for larger amounts.