How the time calculator works
Time does not add up the way ordinary numbers do, because it carries at 60 rather than at 10. Two hours forty-five plus one hour thirty is four hours fifteen, not three hours seventy-five. This calculator does the carrying for you and shows every step, so you can check it rather than trust it.
It handles two jobs. Add or subtract two times works with durations: how long two tasks take together, or how much of a budget is left. Clock time plus or minus starts from a point on the clock and moves forward or back, which is the one that has to know about midnight. If instead you want the stretch between two moments, that is a different question and our time duration calculator answers it.
The formula
Everything is converted to seconds first, the arithmetic happens in plain whole numbers, and the answer is carried back into hours, minutes and seconds at the end. Doing it that way means base 60 is only ever handled twice, at the start and the finish, instead of at every step where it could go wrong.
Worked example
2 hours 45 minutes plus 1 hour 30 minutes.
2:45:00 is 9,900 seconds. 1:30:00 is 5,400 seconds. Together that is 15,300 seconds.
15,300 ÷ 3,600 = 4 hours with 900 seconds left over, and 900 ÷ 60 = 15 minutes. So the answer is 4:15:00, four hours and fifteen minutes.
As decimal hours, which is what a timesheet wants, that is 4.25. Not 4.15. That distinction is the subject of the next section, and it is the single most expensive mistake in time arithmetic.
4.15 is not 4 hours 15 minutes, and the error is always 40%
This is worth more attention than it usually gets, because it costs real money and it is completely invisible while you are making it.
Minutes are sixtieths of an hour. Decimals are hundredths. So when somebody works four hours fifteen minutes and writes 4.15 on a timesheet, they have not written 4 hours 15 minutes, they have written 4 hours and 9 minutes. The correct decimal is 4.25.
The size of the error is not random and it is not approximate. If you mean mm minutes and you write them as hundredths instead of sixtieths, you are out by exactly 0.4 × mm minutes, every time, whatever the hours figure is. The arithmetic: the true value is mm ÷ 60 of an hour, the written value is mm ÷ 100, and the difference is mm ÷ 150 of an hour, which is 0.4 × mm minutes.
| You mean | You write | It reads as | Error |
|---|---|---|---|
| 4 h 15 m | 4.15 | 4 h 09 m | 6 minutes |
| 4 h 30 m | 4.30 | 4 h 18 m | 12 minutes |
| 4 h 45 m | 4.45 | 4 h 27 m | 18 minutes |
| 4 h 59 m | 4.59 | 4 h 35.4 m | 23.6 minutes |
Note which way it runs: writing minutes as decimals always understates the time, so the person doing it is short-changing themselves. At 18 minutes a day it is an hour and a half a week, and nobody notices, because 4.45 looks exactly like what you meant to say.
Every result on this page prints the decimal hours figure alongside the hours-and-minutes one, so the two are never confused. Our time card calculator does the same across a whole week.
Crossing midnight
Clock arithmetic has one genuinely awkward case. Nine in the evening plus five hours is two in the morning, but it is two in the morning tomorrow, and a clock face has no way of telling you that. Plenty of calculators return the right time and quietly say nothing about the day.
This one says so. In clock mode the result names the day it lands on, and the working shows the moment the total went past 86,400 seconds, which is where the day boundary actually sits. If you are working out when a shift ends, when a flight lands, or when something in the oven needs taking out, the day is not a detail.
Negative results are shown as negative
Subtract a larger time from a smaller one and this calculator returns a negative duration rather than flipping the numbers around and pretending you meant it the other way. Which direction the difference ran is usually the thing you were checking. If you genuinely want the distance between two moments, where direction does not apply, the time duration calculator is the right tool and it measures the gap regardless of the order you type them in.
Hours, minutes, seconds and the units in between
Every answer is given four ways: as hours, minutes and seconds; as decimal hours for payroll and invoicing; as total minutes, which is what schedulers and cooking timers usually want; and as total seconds, which is what the arithmetic actually ran on. They are the same quantity, and having all four in view removes the step where somebody converts by hand and drops a factor of 60.
Where to go for the other time questions
- How long between two moments? The time duration calculator takes two dates and times and gives the exact span, including across months and leap years.
- How many days until a date? The date calculator adds and subtracts days, weeks and months from a calendar date.
- A whole week of shifts? The time card calculator totals a timesheet, including overtime and breaks.
- One shift, start to finish? The work hours calculator handles a single day, including unpaid breaks.
What this calculator deliberately does not do
It does not convert between time zones, and it does not simulate daylight saving. Both are questions about where you are as much as when you are, they depend on a rules database that changes when governments change it, and getting them subtly wrong is worse than not offering them. Clock arithmetic on a single local clock is a stable, exactly correct thing, and that is what this page does.