Decimal Hours Converter

Decimal hours restate a sexagesimal duration in base ten so that it can be multiplied directly by a rate: 8 hours 30 minutes becomes 8.5, and gross pay is simply 8.5 times the hourly rate. The conversion is H plus M divided by 60 in one direction, and floor of the decimal plus 60 times the fractional part in the other. Because 60 factors as 2 squared times 3 times 5, the quotient M over 60 terminates in decimal only when M is a multiple of 3; 20 minutes is 0.3333 repeating, while 21 minutes is exactly 0.35. That is why round-tripping a two-decimal timesheet entry can shift the result by a minute, as 6.33 hours returns 6 hours 20 minutes rather than the 6 hours 19.8 minutes it literally represents. In US payroll the practical question is not conversion but rounding. Wage and Hour Division regulation 29 CFR 785.48(b) permits recorded time to be rounded to the nearest 5 minutes, tenth of an hour (6 minutes), or quarter hour (15 minutes), provided the practice does not over time fail to compensate employees for all time actually worked. Quarter-hour rounding carries a worst case of 7.5 minutes per punch, so a shift with a clock-in and a clock-out can move by up to 15 minutes; at 20 dollars an hour that is 5 dollars a day, or roughly 1,250 dollars across 250 working days if the rounding is systematically one-directional. Tenth-hour rounding cuts the worst-case error to 3 minutes per punch. Rounding is also narrowing legally: California courts have restricted it sharply, holding in Donohue v. AMN Services (2021) that meal period time may not be rounded, and employers with systems capable of capturing exact minutes increasingly cannot justify approximation at all.

Decimal notation for time has two unrelated ancestries, and only one of them survives. The revolutionary French decimal day, decreed in 1793 and briefly in force from 1794, replaced the sexagesimal clock outright with 10 hours of 100 minutes of 100 seconds. It required new clock faces, gained almost no public adoption, and was suspended within about two years. The base-60 clock inherited from Babylonian arithmetic remained, and modern decimal hours are not a revival of the French scheme at all: minutes stay sexagesimal on the clock and are converted to a base-ten fraction only at the moment a duration enters an arithmetic pipeline. The practical need arose with mechanical time recording. Willard Bundy patented a workman time recorder in 1888, and the Bundy Manufacturing Company that followed was among the firms consolidated into the enterprise that became IBM in 1924, which kept a time equipment division into the 1950s. Punched cards recorded clock-in and clock-out stamps in hours and minutes, but wage computation demanded multiplication, so payroll clerks converted to hundredths of an hour before applying a rate. The Fair Labor Standards Act of 1938 then made accurate recording of hours worked a federal obligation, and the Wage and Hour Division interpretive material that became 29 CFR 785.48 recognized the industry rounding increments already in use around the mechanical clock. Modern timekeeping software captures seconds directly, but the tenth-hour and quarter-hour grids from that mechanical era persist in payroll and in professional billing, where legal and accounting work is still commonly billed in 0.1 hour units.