Time to Decimal Calculator

Why payroll runs on decimal hours

Payroll software multiplies a rate by hours, and hours in that multiplication are decimal: 7.75 means seven and three quarter hours. The clock in your kitchen counts in sixties, so 7:45 has to be translated before it can be multiplied. The translation is one division:

decimal hours = whole hours + (minutes ÷ 60) + (seconds ÷ 3,600)

What people get wrong is treating the minute part as if it were already decimal. On a time card, 45 minutes is 0.75 hours, not 0.45. Adding 1:45 and 2:30 gives 4:15, which is 4.25 decimal hours. Add the printed numbers as decimals and you get 1.45 + 2.30 = 3.75, which is 3:45, half an hour short of the truth.

The gap grows with the length of the list. Ten shifts that each lose 0.05 of an hour to this mistake come out 30 minutes light, and a worker paid $21.50 an hour is missing $10.75 on that check. Nothing about the arithmetic is wrong; the units are.

One more distinction before the numbers: a decimal hour is not a billing unit. Plenty of firms bill in 0.1 hour blocks, and 0.1 hour is 6 minutes, which is why a five minute phone call shows up as six minutes on an invoice.

Converting by hand in three steps

Do it in this order and you will not need the table below:

1. Write down the whole hours and leave them alone.
2. Divide the minutes by 60. That result is always between 0 and 1.
3. Add the two pieces. Seconds, if you have them, get divided by 3,600 and added last.

Three examples:

• 7:45 becomes 45 ÷ 60 = 0.75, then 7 + 0.75 = 7.75 hours.
• 8:20 becomes 20 ÷ 60 = 0.333, then 8 + 0.333 = 8.33 hours.
• 6:07 becomes 7 ÷ 60 = 0.117, then 6 + 0.117 = 6.12 hours.

With seconds, work from the smallest unit up. A stopwatch reading of 2:03:40 is 40 ÷ 3,600 = 0.0111, plus 3 ÷ 60 = 0.05, plus 2 hours, for 2.0611 decimal hours. If you only need payroll precision, drop the seconds and keep the minutes: 2:03:40 rounds to 2.06 hours anyway.

The reverse direction is just as quick. Take the decimal part and multiply by 60 to get minutes: 7.35 hours is 0.35 × 60 = 21 minutes, so 7:21. A decimal of 4.25 hours is 0.25 × 60 = 15 minutes, or 4:15.

Minute to decimal conversion table

Printed versions of this chart hang next to time clocks in warehouses and clinics. The same numbers, to four decimals, so you can round where you need to:

Round to two decimals for payroll and the common values become recognizable: 5 minutes is 0.08, 10 minutes is 0.17, 15 minutes is 0.25, 20 minutes is 0.33, 30 minutes is 0.50, 40 minutes is 0.67, and 45 minutes is 0.75. Those are the values a time card uses in quarter hour steps, and they are the ones most payroll systems store.

Two entries catch people out. Seven minutes is 0.1167, not 0.12 exactly, and 23 minutes is 0.3833. If you are adding a month of entries, keep four decimals until the end; the difference between 0.1167 and 0.12 is 50 seconds per entry, which compounds across 20 shifts.

Rounding: what federal rules allow

The Fair Labor Standards Act does not require minute-by-minute tracking. The regulation at 29 CFR 785.48(b) lets an employer round start and stop times, and the Department of Labor's Fact Sheet 53 on hours worked spells out the practical limit: rounding to the nearest quarter hour is allowed, but a policy that always rounds down breaks the law.

The mechanics of quarter hour rounding are worth knowing because they decide whether you gain or lose minutes:

• 1 to 7 minutes past a quarter hour rounds back. A punch at 8:07 counts as 8:00.
• 8 to 14 minutes past rounds forward. A punch at 8:08 counts as 8:15.
• The pattern has to even out over time. Rounding up one day and down the next is fine; shaving seven minutes every single day is not.

The regulation also allows rounding to the nearest five minutes or the nearest one-tenth of an hour, and one-tenth of an hour is six minutes. Those are the three increments this calculator offers. Anything coarser, such as rounding to the nearest half hour, is outside what the rule contemplates. The Department of Labor's elaws guide to hours worked walks through the same rules with worked examples.

Both punch times and durations can be rounded, but not both in the same system without care. Rounding the punch and then rounding the shift total is a double correction, and it is the fastest way to end up with a number nobody can reproduce.

A week of pay, in decimal hours

Five shifts: 7:45, 8:15, 7:30, 8:00, and 7:15. Each converts to 7.75, 8.25, 7.5, 8, and 7.25. Added up, that is 38.75 decimal hours. At $21.50 an hour the gross is 38.75 × 21.50 = $833.13, before federal and state tax.

Now the rounding question. Suppose the same worker clocks in at 8:07 every morning, seven minutes early. Under quarter hour rounding each punch counts as 8:00, so five shifts lose 35 minutes, which is 35 ÷ 60 = 0.58 hours a week. At $21.50 that is $12.54 a week, or about $652 over a year of 52 weeks. The loss is legal only if the policy rounds up just as often on the other end, which is why the rule speaks of averages over time.

The order of rounding changes the answer too. Take five shifts of 7:52, which is 7.8667 decimal hours each. Round each one to the nearest quarter hour and you get 7.75, for a total of 38.75. Add first and round once, and 5 × 7.8667 = 39.333 becomes 39.25. Same punches, same rule, half an hour apart, which is $10.75 at the $21.50 rate.

That is the argument for recording the exact decimal hours and applying any rounding rule in one place. Your own record, kept as 38.75 or 39.33, is the only version you can audit later.

Going back from decimal to hours and minutes

Managers reading a payroll export see 6.72 and want to know what time that is. Multiply the decimal part by 60: 0.72 × 60 = 43.2, so 6.72 hours is 6:43, near enough to 6:43 a.m. if the shift started at midnight. Rounding to the nearest minute is standard here, since payroll rarely tracks seconds.

Two conversions worth having in your head:

• 0.1 hour = 6 minutes. A $300 legal bill in 0.1 hour blocks is 6 minute increments, not 10 minute ones.
• 0.01 hour = 36 seconds. This is why a decimal hour carried to two places is only accurate to about half a minute per entry.

If you need the clock time rather than the duration, add the decimal hours to the start time. A shift that begins at 6:00 and runs 3.35 decimal hours ends at 6:00 plus 3 hours 21 minutes, which is 9:21. The arithmetic is the same whether the shift crosses noon or midnight, but a shift that crosses midnight needs the date added back or it will look negative.

Where decimal hours show up outside payroll

Any system that multiplies time by a rate ends up in decimal hours: machine hour logs, lab instrument time, flight logs, and project billing. Spreadsheet exports from time tracking apps usually carry both columns, one as 7:45 and one as 7.75, and the decimal column is the one the formulas read.

A few practical checks when you are reconciling those exports:

• Sum the decimal column and the h:mm column separately and compare. If they disagree, one of the columns is being rounded on the way out.
• Watch for text that looks like a decimal but is not. A cell holding "7.45" typed by hand means 7 hours 27 minutes, and no amount of reformatting will make it mean 7:45.
• Keep durations in decimal hours and clock times in h:mm. Mixing the two in one column is how a 30 minute error survives a whole quarter.

The time calculator adds several spans together and reports the total, which is the page to use for a sum of shifts. This page takes one span and shows what a rounding rule does to it. For a whole week with overtime, the time card calculator applies the 40 hour rule to daily hours. Here, the job stops at the conversion.