Hours and Minutes Converter

This conversion exists because clock time is sexagesimal and money is decimal. An hour holds 60 minutes, so the decimal equivalent of a minute count is that count divided by 60, and the whole class of payroll errors comes from people treating the minutes field as if it were already a decimal fraction. Two hours thirty minutes is 2.50 decimal hours, not 2.30; two hours fifteen is 2.25, not 2.15. The conversions worth memorising are the sixths and quarters: 6 minutes is 0.10 hours, 10 minutes is 0.1667, 12 minutes is 0.20, 15 minutes is 0.25, 20 minutes is 0.3333, 30 minutes is 0.50 and 45 minutes is 0.75. Only minute counts divisible by 3 - that is 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54 and 57 - convert to exact two-decimal figures; every other value repeats or must be rounded. The rounding is where the practical caveats sit. Under United States federal wage-hour rules, 29 CFR 785.48 permits an employer to round recorded time to the nearest quarter hour provided the rounding is neutral over time and does not systematically favour the employer - the origin of the so-called seven-minute rule. Professional services more often bill in tenths of an hour, six-minute increments, so a 22-minute task becomes 0.4 hours. Rounding always rounds money, and at a $150 hourly rate a consistent 0.1-hour rounding is $15 per entry. The percentage figures use the same fixed denominators throughout: 1,440 minutes in a day and 10,080 in a week, which is exact for elapsed duration but not for wall-clock days containing a daylight-saving transition, where the civil day runs 1,380 or 1,500 minutes.

The 60-minute hour descends from Babylonian sexagesimal arithmetic transmitted through Hellenistic and medieval astronomy, where the hour was split into a first small part and a second small part - pars minuta prima and pars minuta secunda. The system survived every attempt to replace it. The most serious attempt was French decimal time, decreed during the Revolution and in official use from 1794, which divided the day into 10 hours of 100 minutes of 100 seconds; it required new clock faces, was widely ignored, and its mandatory use was suspended in 1795 after barely a year and a half. Decimal hours returned not as a replacement for the clock but as an accounting layer on top of it, driven by industrial wage payment. Mechanical time recorders spread through factories after Willard Bundy patented a workman's time recorder in 1888, and the firms built around such machines were among those merged into the company that became IBM. Once wages were computed as rate times hours, the fractional hour had to be decimal to multiply cleanly, and time-clock makers began printing dials in hundredths of an hour - still sold as industrial or decimal time. The Fair Labor Standards Act of 1938 made the recordkeeping legally consequential in the United States by requiring employers to record hours worked and pay overtime beyond 40 hours per week, and the rounding practices codified in 29 CFR 785.48 grew directly out of the limits of those mechanical punch cards.