Why Time Arithmetic Is Awkward
Time is not decimal. Sixty seconds make a minute, sixty minutes make an hour, twenty-four hours make a day — a mixed-radix system inherited from Babylonian astronomy, which counted in base 60. Adding 4:30 and 1:45 in your head fails if you treat the numbers as decimals, because 30 + 45 is 75, and 75 minutes is 1 hour 15 minutes, not 0.75 of an hour.
The reliable method is to convert everything to a single unit — normally seconds — do the arithmetic there, then convert back. That is exactly what this calculator does.
Total seconds = hours × 3600 + minutes × 60 + seconds
Conversion Table
| Unit | Seconds | Minutes | Hours | Days |
|---|---|---|---|---|
| 1 second | 1 | 0.01667 | 0.000278 | 0.0000116 |
| 1 minute | 60 | 1 | 0.01667 | 0.000694 |
| 1 hour | 3,600 | 60 | 1 | 0.04167 |
| 1 day | 86,400 | 1,440 | 24 | 1 |
| 1 week | 604,800 | 10,080 | 168 | 7 |
| 1 month (avg) | 2,629,746 | 43,829 | 730.5 | 30.44 |
| 1 year (avg) | 31,556,952 | 525,949 | 8,765.8 | 365.2425 |
Months and years use Gregorian averages, since neither has a fixed length. A calendar month is 28, 29, 30 or 31 days; the average of 30.44 is the only number that makes unit conversion consistent.
Decimal Hours
Payroll, billing and time tracking usually work in decimal hours rather than hours and minutes, because decimals multiply cleanly by an hourly rate. The conversion is minutes divided by 60.
| Minutes | Decimal | Minutes | Decimal |
|---|---|---|---|
| 5 | 0.083 | 35 | 0.583 |
| 10 | 0.167 | 40 | 0.667 |
| 15 | 0.25 | 45 | 0.75 |
| 20 | 0.333 | 50 | 0.833 |
| 25 | 0.417 | 55 | 0.917 |
| 30 | 0.5 | 60 | 1.0 |
The classic payroll error is writing 7 hours 45 minutes as 7.45 instead of 7.75 — a difference of 18 minutes per shift, which compounds quickly across a workforce.
12-Hour and 24-Hour Clocks
| 12-hour | 24-hour | 12-hour | 24-hour |
|---|---|---|---|
| 12:00 am (midnight) | 00:00 | 12:00 pm (noon) | 12:00 |
| 1:00 am | 01:00 | 1:00 pm | 13:00 |
| 6:00 am | 06:00 | 6:00 pm | 18:00 |
| 9:00 am | 09:00 | 9:00 pm | 21:00 |
| 11:59 am | 11:59 | 11:59 pm | 23:59 |
The two genuinely confusing points are noon and midnight. 12:00 am is midnight and 12:00 pm is noon — the opposite of what many people assume, because "am" means ante meridiem, before midday. Aviation, medicine and the military avoid the problem entirely by using the 24-hour clock, where 00:00 and 12:00 are unambiguous.
The calculator accepts both: enter 17:40 or 5:40 pm.
Overnight Spans
When the end time is earlier than the start, the calculator assumes the span crosses midnight and adds 24 hours. A shift from 22:00 to 06:00 is therefore 8 hours, not negative 16. This is almost always what is meant, but check it when the two times could legitimately be on the same day.
Leap Seconds
The Earth's rotation is gradually slowing and varies unpredictably, so atomic time drifts away from solar time. Leap seconds have been inserted 27 times since 1972 to keep them aligned, most recently in 2016. In 2022 the international body responsible voted to abandon the practice by 2035, since the irregular extra second causes more problems for computer systems than the drift it corrects. This calculator ignores leap seconds, as does essentially all civil timekeeping.
Frequently Asked Questions
How do I enter a time?
Use HH:MM or HH:MM:SS in 24-hour form, or add am/pm for the 12-hour form. Both 14:30 and 2:30 pm work.
Why is the negative result shown as a duration?
Subtracting a longer duration from a shorter one gives a negative span. The magnitude is displayed with a minus sign so the size of the difference is still readable.
Why is a month 30.44 days here?
Because months vary between 28 and 31 days and unit conversion needs a fixed value. For calendar arithmetic on specific dates, use the date calculator instead — it handles real month lengths.
How do I convert minutes to decimal hours?
Divide by 60. 45 minutes is 45 ÷ 60 = 0.75 hours. The unit converter above does this for any pair of units.