Hours to Decimal Converter

Background.

Timesheets, invoices and payroll systems want hours as a decimal. People write and read durations in hours and minutes. Those two habits collide every fortnight, and the collision has a wrong answer that looks right: seven hours forty-five minutes is not 7.45 hours, it is 7.75, and typing 7.45 into a payroll field quietly loses eighteen minutes of work. This converter goes both ways — enter 7 hours 45 minutes and get 7.75; enter 7.75 and get 7:45:00 back — and it will also apply the payroll rounding increments that turn an exact figure into the number a timesheet actually carries.

It converts a duration, not a clock reading. "7:45" on this page means seven hours and forty-five minutes of elapsed time, not a quarter to eight in the morning. If you have a clock-in and a clock-out and need the duration between them, the hours between times calculator does that; if you want to add two durations together, the time duration calculator does that; if you want to turn 19:45 into 7:45 PM, that is 24-hour to 12-hour clock notation and belongs on the military time converter. This page starts from a length of time you already have and changes how it is written.

The arithmetic is two exact equalities and nothing else. NIST Special Publication 330, the US edition of the SI Brochure, gives them in its table of units accepted for use with the SI: one minute is 60 seconds, and one hour is 60 minutes or 3,600 seconds. So decimal hours are the hours part plus the minutes divided by 60 plus the seconds divided by 3,600. There is no approximation anywhere in the conversion and no jurisdiction in which it differs. Minutes and seconds above 59 are allowed and simply carry, which means "how many decimal hours is 90 minutes" is one field and one answer: 1.5.

The rounding increments are the part that needs care, because they are where money changes hands. United States federal regulation 29 CFR 785.48(b) — the paragraph headed "Rounding" practices — records the long-standing practice of recording start and stop times "to the nearest 5 minutes, or to the nearest one-tenth or quarter of an hour", and accepts it for enforcement purposes on one explicit condition: that the practice does not, over a period of time, result in a failure to compensate employees properly for all the time they have actually worked. Those three increments are exactly the three offered here. A fourth, hundredths of an hour, is the column in the Department of Labor's own published hours-worked conversion chart, which is also the source this page's independent check is measured against.

Because rounding can cost as easily as it can credit, this page shows the signed difference. Round 7 hours 52 minutes to the nearest quarter hour and you get 7.75 hours — seven minutes of real work that disappeared. Round 7 hours 8 minutes the same way and you gain seven minutes. The exact figure, the rounded figure and the difference between them are all on screen at once, and the rounding note beside the result states the legal condition rather than burying it in an accordion. Nothing here is legal or payroll advice: state law, a collective agreement or an employer policy can be stricter than the federal floor, and several jurisdictions restrict rounding further. The exact figure is always the ground truth; the increment is a reporting convention layered on top of it.

What is hours to decimal converter?

Decimal hours express a duration as a single number in base ten, so that it can be multiplied by an hourly rate or summed in a spreadsheet without any sexagesimal arithmetic. Hours and minutes express the same duration in base sixty, which is how clocks and people work. Converting between them is one division, and the reason it needs a page is that the two notations look confusingly alike: 7.45 and 7:45 differ by a single character and by eighteen minutes.

The conversion itself is jurisdiction-free and exact. What is not exact — and not universal — is the rounding increment a payroll system applies afterwards. In the United States, 29 CFR 785.48(b) recognises rounding to the nearest 5 minutes, tenth of an hour or quarter of an hour, and accepts it only where it does not systematically shortchange the employee over time. That is a condition on the practice, not a licence: a rule that always rounds down fails it, even though each individual rounding looks like a rounding.

Rounding to the nearest quarter hour is the increment most people have heard described as a seven-and-eight-minute rule. That description is not a separate rule at all — it is what "nearest" means when the increment is fifteen minutes, because 7.5 minutes is the midpoint. This page derives the behaviour from the increment rather than hard-coding a folk rule, and it tests every boundary.

How to use this calculator.

1. 01Pick a direction. 'Hours & minutes → decimal' takes a duration and returns a decimal figure; 'Decimal → hours & minutes' does the reverse.
2. 02In 'Hours & minutes → decimal' mode, fill in hours, minutes and — if you need them — seconds. Values above 59 in the minutes or seconds field are fine and carry automatically, so 0 h 90 min gives 1.5.
3. 03In 'Decimal → hours & minutes' mode, enter the decimal figure. 7.75 becomes 7:45:00; a figure with a long tail like 0.256 becomes 0:15:22, with the seconds rounded once from 921.6.
4. 04Leave the rounding increment on 'None' if you want the true figure. Set it to whatever your employer or client uses if you need the number that will actually appear on the timesheet — quarter hour and tenth of an hour are the two most common.
5. 05Read the signed 'minutes gained or lost to rounding' figure before you accept a rounded number. Over a pay period a consistent loss in that column is the specific thing 29 CFR 785.48(b) does not permit.
6. 06Use the unrounded decimal-hours output for any further arithmetic — multiplying by a rate, summing a week — and round only once, at the end. Rounding each day and then adding compounds the error.

The formula.

Decimal hours are the hours part, plus the minutes divided by 60, plus the seconds divided by 3,600. Both divisors come from exact definitions rather than measurements — NIST Special Publication 330 lists one minute as 60 seconds and one hour as 60 minutes or 3,600 seconds — so the conversion introduces no error of its own. Running it backwards is the same equation rearranged: multiply the decimal figure by 3,600 to get total seconds, take whole hours out of it, then whole minutes, and what is left is seconds.

The rounding increment is applied in minutes rather than in hours, and that is a correctness decision rather than a stylistic one. One twelfth of an hour — the 5-minute increment — has no exact decimal representation, so a 0.0833… constant would be a truncation, and comparing a value against a truncated increment can push it across a boundary. In minutes, every increment this page offers is exact: 0.6, 5, 6 and 15. So the duration is converted to minutes, divided by the increment, rounded to the nearest whole number of increments with halves going up, multiplied back, and converted to hours again.

Rounding half up is what makes the quarter-hour increment behave the way payroll practice describes it. With a 15-minute increment the midpoint is 7.5 minutes, so a 7-minute remainder is nearer the lower boundary and rounds down, while an 8-minute remainder is nearer the upper one and rounds up. The same logic sets every other edge: the tenth-hour increment turns at 3 minutes, the 5-minute increment at 2.5 minutes, and the hundredth-hour increment at 18 seconds. Each of those edges is tested immediately below and immediately at or above it.

Two rounding stages are kept strictly apart. The exact decimal-hours output is unrounded to ten decimal places, and it is the value the increment is applied to. The answer sentence prints the exact figure to four places purely so it reads well — 7.8666666667 shows as 7.8667 — and that four-place rendering is never what gets snapped to an increment. The h:mm:ss labels round the total number of seconds once and only then split it into hours, minutes and seconds, which is why a value half a second below the minute prints as 0:01:00 and never as 0:00:60.

A worked example.

Frequently asked questions.

References& sources.

1. [1]National Institute of Standards and Technology, Special Publication 330 (9th edition) — The International System of Units (SI), Section 4, Table 8 "Non-SI units accepted for use with the SI". The source of the two exact equalities this converter is built on: "1 min = 60 s" and "1 h = 60 min = 3600 s" (and "1 d = 24 h = 86 400 s"). SP 330 is the United States edition of the BIPM SI Brochure; the BIPM site serves the same table only inside a PDF, so the NIST HTML edition is cited because it is the copy that was actually read.
2. [2]29 CFR § 785.48 "Use of time clocks", paragraph (b), headed "Rounding" practices — CFR 2024 edition, title 29, volume 3, via GovInfo. The source of the three rounding increments this page offers and of the condition printed beside every rounded result: the practice of recording start and stop times "to the nearest 5 minutes, or to the nearest one-tenth or quarter of an hour" is accepted for enforcement purposes "provided that it is used in such a manner that it will not result, over a period of time, in failure to compensate the employees properly for all the time they have actually worked". Retrieval note: the current eCFR copy redirects automated requests to an anti-bot page, so the 2024 GovInfo compilation was read instead; the 2011 compilation carries identical paragraph (b) text.
3. [3]United States Department of Labor, elaws FLSA Overtime Calculator Advisor — Hours Worked Conversion Chart. Used as the independent check on this page's conversion and on its hundredths-of-an-hour increment, which the CFR does not name. The chart instructs the reader to "convert minutes worked into hundredths or quarters of an hour" and gives a worked example: "8.38 would be the entry for a day during which an employee worked 8 hours and 23 minutes." This calculator returns 8.3833333333 exact and 8.38 at the hundredths increment — agreement, and there is a test asserting both halves. Note: the chart's numeric table itself is served as an image, so only the instruction line and that example were read.