7.5 = 7 hours, 30 minutes. 0.25 = 0 hours, 15 minutes. Payroll software, time tracking apps, and project budgets all use decimal hours so they can multiply by an hourly rate without unit-conversion gymnastics.
What “decimal hour” actually means
The number 7.5 is read as “seven and a half hours.” The integer part (7) is hours; the decimal part (0.5) is the fraction of one hour — in this case, half. Multiply 0.5 by 60 to get the equivalent in minutes: 30. So 7.5 decimal hours = 7:30 in HH:MM.
The trick is that the “.5” doesn’t mean “5” or even “5/10” in the conventional sense for time. It means “halfway through one hour,” which is 30 minutes. This causes confusion when people first see 7.30 on a screen and assume it’s 7 hours and 30 minutes. It’s not. 7.30 decimal hours = 7 hours + 0.30 × 60 = 7 hours 18 minutes.
0.30 × 60 = 18 min · 0.50 × 60 = 30 min · 0.75 × 60 = 45 min.
Why payroll uses decimal hours instead of HH:MM
Three reasons, in order of importance:
-
Multiplication. Decimal hours can be multiplied by an hourly rate directly.
7.5 × $20 = $150. HH:MM can’t:7:30 × $20doesn’t mean anything in standard arithmetic. -
Aggregation. Adding decimal hours is normal addition:
7.5 + 8.25 = 15.75. Adding HH:MM requires careful handling of the 60-minute borrow:7:30 + 8:15 = 15:45— same answer, but you have to remember not to carry at 100. - Computer storage. A decimal number fits one floating-point register. HH:MM is two integers (or a string) that need parsing every time you do anything with them. Multiply this by a million paystubs a week and you understand why payroll engineering teams settled on decimal.
Where the convention came from
The decimal hour didn’t emerge from any single decision. It’s the natural result of three converging forces:
1. The metric idea (1790s)
During the French Revolution, mathematicians proposed “decimal time” — a 10-hour day, 100-minute hour, 100-second minute. It was officially mandated in France from 1793 to 1795 before being abandoned. The legacy survives in surveying (where minutes and seconds of arc are sometimes given as decimal degrees) and, oddly, in payroll — though we still use base-60 minutes, the partial-hour portion gets expressed in base 10.
2. Mechanical time clocks (1880s–1950s)
Daniel M. Cooper’s 1888 punch-card time clock and its IBM successors recorded times in HH:MM (with a punch wheel). Payroll clerks then transcribed those punches to ledgers. Computing a week’s pay in HH:MM was annoying, so clerks converted to decimal in their heads or on calculators. By the 1950s, the convention “store the punches in HH:MM, calculate pay in decimal” was standard practice.
3. Mainframe payroll (1960s–1980s)
Early payroll programs ran on IBM mainframes with limited memory. Storing a single decimal number per employee per day was vastly cheaper than storing two integers plus a unit. The decimal-hour format became the lingua franca of payroll data formats. ADP, Paychex, and dozens of regional bureaus all adopted it, and by the time PCs arrived in the 1980s, decimal was already the standard.
4. Modern web tools (2010s–present)
Time-tracking apps like Toggl (founded 2006), Clockify (2017), and Harvest (2008) all default to decimal display because their core use case is invoicing — and invoices need decimal-times-rate arithmetic. The HH:MM display is sometimes available as a toggle but is no longer the default.
How to read a decimal-hour paystub
Most U.S. paystubs show two columns: hours and amount. The hours column is decimal. To translate it back to "real" time:
| Paystub shows | Means |
|---|---|
| 40.00 | 40 hr 0 min — full week, no overtime |
| 38.50 | 38 hr 30 min — full week minus a half-day |
| 40.25 | 40 hr 15 min — full week plus a quarter-hour |
| 32.42 | 32 hr 25 min — partial week (0.42 × 60 ≈ 25 min) |
| 0.50 | 30 min — e.g., a single bereavement increment |
| 1.75 | 1 hr 45 min — e.g., overtime breakdown |
The two trick rows
Two paystub values commonly cause panic:
X.99 — this means just under one whole hour. 0.99 × 60 = 59.4 min, basically 1 hour minus a few seconds. If your paystub shows 7.99 hours, you worked 7 h 59 m — one minute short of 8.
X.01 — one minute. 0.01 × 60 = 0.6 min, which is roughly 36 seconds, but 0.01 is the rounded version of any value between 0.005 and 0.015 hours, i.e., between 18 seconds and 54 seconds. Treat it as “about a minute.”
Common conversion shortcuts
The four anchors to memorize:
- 0.25 = 15 min
- 0.50 = 30 min
- 0.75 = 45 min
- 1.00 = 60 min
And five more useful ones:
- 0.10 = 6 min (every tenth of an hour is 6 minutes)
- 0.20 = 12 min
- 0.33 = 20 min (one third of an hour)
- 0.50 = 30 min (half)
- 0.67 = 40 min (two thirds)
When NOT to use decimal hours
Some situations are clearer in HH:MM:
- Schedules — "the meeting is at 14:30," not "14.5 o’clock."
- Cooking timers — "set the timer for 0:45" beats "0.75 hours."
- Communicating durations — "this will take 1 h 15 m" is more natural than "1.25 hours" in conversation.
- Anything timed in seconds or sub-seconds — HH:MM:SS is easier to read than 0.083333.
The general rule: use decimal whenever a number is going to be multiplied or summed, and HH:MM whenever a human will read it directly without doing math.
Common myths
“Decimal hours are inherently less precise.”
False. A decimal hour can represent any time you want, to any precision your storage allows. 7.7833 is 7 hours 47 minutes exactly; 7.7833333 is 7 hours 47 minutes plus a fraction of a second. Imprecision shows up only when you choose to round — same as with HH:MM.
“7.30 means 7 hours 30 minutes.”
False. 7.30 means 7 hours plus 0.30 of an hour, which is 18 minutes. Always multiply the decimal portion by 60.
“Decimal hours can’t cross midnight.”
They can. A 12-hour shift starting at 22:00 ends at 10:00 the next morning, but as a duration it’s simply 12.0 decimal hours. Decimal hours don’t carry "time of day" semantics — they’re elapsed time only.
