Time Duration Calculator
Minutes run in base sixty, so 45 plus 45 is an hour and a half rather than 90 of anything. That is why an ordinary calculator gets time arithmetic wrong.
Total
5h 0m
- Hours and minutes
- 5h 0m
- Total minutes
- 300
- Decimal hours
- 5.00
- Days
- 0.208
- Decimal hours are what payroll systems use, and they are not the same as the clock reading. Seven hours thirty is 7.5 decimal hours, not 7.30 — the most common mistake in a timesheet.
- Minutes are added in base sixty, so 45 plus 45 is an hour and a half rather than 90 of anything. That is why a plain calculator gets time arithmetic wrong.
About adding durations
Everything else you add is base ten. Time is not: sixty minutes carry into an hour, and a calculator that does not know this treats 2:45 as 2.45 and produces an answer that is wrong by a quarter of an hour before you have started.
The clean way is to convert everything to minutes, add them, and convert back. Two hours 45 is 165 minutes, one hour 30 is 90, and 45 is 45 — 300 minutes altogether, which is exactly five hours.
Decimal hours are the other form worth understanding, because payroll runs on them. Seven and a half hours is 7.5 in decimal and 7:30 on a clock, and reading one as the other understates a shift by twenty minutes. Over a year that error is real money, and it is the single most common mistake on a timesheet.
The conversion is division by sixty rather than moving a decimal point: 15 minutes is 0.25 hours, 20 is 0.333, 45 is 0.75. Only 30 minutes lands on a tidy 0.5, which is probably why the error persists.
What it works out
- Adding up to five durations
- Subtracting the rest from the first
- Decimal hours for payroll
- Totals in minutes and days
The formula
Convert each to minutes, add, then divide back: hours = total ÷ 60, minutes = total mod 60
Two hours 45 is 165 minutes. One hour 30 is 90. Forty-five is 45. Added together that is 300 minutes.
Three hundred divided by sixty is exactly five, with nothing left over — five hours and no minutes. Where there is a remainder, that is the minutes: 310 minutes would be 5 hours 10.
Decimal hours are the same total divided by sixty without taking the remainder separately: 300 ÷ 60 is 5.00. For 310 it would be 5.17, not 5.10, and that distinction is the entire problem with reading clock time as a decimal.
The conversions worth memorising: 15 minutes is 0.25, 20 is 0.333, 30 is 0.5, 40 is 0.667, 45 is 0.75. Anything else, divide by sixty.
Subtracting works the same way, taking the first duration and removing the rest. A negative result is shown rather than clamped, because knowing you are 20 minutes short is more useful than being told zero.
- Minutes
- The base everything converts to. Base sixty, not base ten.
- Decimal hours
- Total minutes over sixty. What payroll systems use.
- Clock time
- Hours and minutes separately. What a clock shows. Not the same thing.
A worked example
Two hours 45, plus one hour 30, plus 45 minutes.
That works out to 5h 0m .
- Hours and minutes
- 5h 0m
- Total minutes
- 300
- Decimal hours
- 5.00
- Days
- 0.208
Questions
How do I add hours and minutes?
Convert everything to minutes, add, then divide by sixty for the hours and take the remainder as minutes. 2:45 plus 1:30 plus 0:45 is 300 minutes, which is exactly five hours.
Why does my calculator get time arithmetic wrong?
Because it works in base ten and minutes work in base sixty. It treats 2:45 as 2.45, which is wrong by 18 minutes before you add anything.
What are decimal hours?
Total time expressed as a decimal — seven and a half hours is 7.5. Payroll systems use them. Reading a clock time of 7:30 as 7.30 understates the shift by twenty minutes.
How do I convert minutes to decimal hours?
Divide by sixty. 15 minutes is 0.25, 20 is 0.333, 45 is 0.75. Only 30 lands on a tidy 0.5, which is probably why the mistake is so persistent.
Can the answer be negative?
Yes, when subtracting more than you started with, and it is shown rather than clamped to zero. Knowing you are twenty minutes short is more useful than being told nothing.
How do I work out hours between two clock times?
That is a different question — use the timesheet calculator, which handles shifts crossing midnight. This one adds durations rather than subtracting clock times.