Why time arithmetic trips people up
Time is sexagesimal — base 60 — not decimal, so ordinary column arithmetic gives wrong answers. Adding 2:45 and 1:30 as though they were decimals produces 3:75, which needs carrying: 75 minutes is 1 hour 15 minutes, giving the correct 4:15.
The reliable approach is to convert everything to the smallest unit, do the arithmetic, then convert back. Two hours 45 minutes is 165 minutes; one hour 30 minutes is 90 minutes; the sum of 255 minutes is 4 hours 15 minutes. This is exactly what the calculator does internally.
| Unit | In seconds | Equals |
|---|---|---|
| Minute | 60 seconds | 1/60 hour |
| Hour | 3,600 seconds | 60 minutes |
| Day | 86,400 seconds | 24 hours |
| Week | 604,800 seconds | 7 days; 168 hours |
| Month (average) | 2,629,746 seconds | 30.44 days; 730.5 hours |
| Year (average) | 31,556,952 seconds | 365.2425 days; 8,765.8 hours |
Decimal hours for payroll
Payroll systems work in decimal hours, where 7 hours 30 minutes is 7.5 rather than 7.30. Converting means dividing the minutes by 60, not moving a decimal point — a distinction that causes real payroll errors.
The common values are worth knowing: 15 minutes is 0.25, 20 minutes is 0.333, 30 minutes is 0.5, and 45 minutes is 0.75. Awkward figures like 7 hours 20 minutes become 7.333, and some employers round timesheets to the nearest quarter hour, which US federal rules permit provided the rounding does not systematically favor the employer.
| Minutes | Decimal hours | Nearest quarter hour |
|---|---|---|
| 5 | 0.0833 | 0 |
| 6 | 0.1 | 0 |
| 10 | 0.1667 | 0.25 |
| 12 | 0.2 | 0.25 |
| 15 | 0.25 | 0.25 |
| 20 | 0.3333 | 0.25 |
| 25 | 0.4167 | 0.5 |
| 30 | 0.5 | 0.5 |
| 35 | 0.5833 | 0.5 |
| 40 | 0.6667 | 0.75 |
| 45 | 0.75 | 0.75 |
| 50 | 0.8333 | 0.75 |
| 55 | 0.9167 | 1 |
Overnight shifts and breaks
When an end time is earlier than a start time, the shift crossed midnight. A shift from 22:00 to 06:00 is 8 hours, not negative 16, and this calculator adds 24 hours automatically when it detects that case.
Whether breaks are paid depends on jurisdiction and length. Under US federal law, short rest breaks of 5 to 20 minutes are generally compensable, while bona fide meal periods of 30 minutes or more usually are not, provided the employee is fully relieved of duty. Many states impose stricter requirements, so subtract only genuinely unpaid time.
| Shift | Unpaid break (min) | Hours worked | Decimal |
|---|---|---|---|
| 09:00 – 17:00 | 30 | 7:30 | 7.5 |
| 09:00 – 17:30 | 30 | 8:00 | 8 |
| 08:00 – 16:30 | 60 | 7:30 | 7.5 |
| 07:00 – 15:30 | 30 | 8:00 | 8 |
| 10:00 – 18:45 | 45 | 8:00 | 8 |
| 14:00 – 22:30 | 30 | 8:00 | 8 |
| 22:00 – 06:00 | 30 | 7:30 | 7.5 |
| 23:00 – 07:30 | 60 | 7:30 | 7.5 |
Rounding to the quarter hour
US federal rules allow timesheets to be rounded to the nearest quarter hour, provided the rounding does not consistently favour the employer. The standard way to do that is the seven-minute rule: minutes 1 to 7 past a quarter round down, 8 to 14 round up. Over many punches the rounding averages out; on any single day it can add or remove up to seven minutes.
| Minutes past the hour | Rounds to | Example |
|---|---|---|
| 0 – 7 minutes | Round down to :00 | 8:07 → 8:00 |
| 8 – 22 minutes | Round to :15 | 8:19 → 8:15 |
| 23 – 37 minutes | Round to :30 | 8:33 → 8:30 |
| 38 – 52 minutes | Round to :45 | 8:40 → 8:45 |
| 53 – 59 minutes | Round up to the next hour | 8:56 → 9:00 |