Decimal Hours Explained: Why 7:45 Is Not 7.45

Payroll and billing systems usually want time as a decimal: 7.75 hours rather than 7 hours 45 minutes. The confusion comes from mixing two number systems, one based on 60 and one on 100.

The conversion

An hour has 60 minutes, so a minute is 1/60 of an hour.

Decimal hours = hours + minutes ÷ 60
Minutes       = decimal part × 60

So 7 hours 45 minutes is 7 + 45 ÷ 60 = 7 + 0.75 = 7.75 hours. Writing 7.45 would mean 7 hours and 27 minutes, since 0.45 × 60 = 27.

Common conversions

Values such as 10 minutes (0.1667) do not end, so they are rounded, usually to two decimals.

Going the other way

To convert 8.4 hours to hours and minutes, keep the 8 hours and multiply 0.4 by 60, which gives 24 minutes. So 8.4 hours is 8 hours 24 minutes.

Adding up a week

It is much easier to add decimals than clock times. Five days of 8.25 hours each come to 41.25 hours. To check, 8 hours 15 minutes × 5 is 40 hours plus 75 minutes, which is 41 hours 15 minutes, and 0.25 hours is 15 minutes, so the two agree.

Rounding rules

Some employers round time to the nearest quarter hour, or to the nearest tenth of an hour. Rounding rules and their legality vary by country and contract, so follow the rule that applies to you. Whatever the rule, it helps to record the exact clock times as well as the rounded figure.

Pay from decimal hours

Multiply the decimal hours by the hourly rate. For 41.25 hours at 22 an hour the gross pay is 41.25 × 22 = 907.50. Using 41.15 by mistake for 41 hours 15 minutes would understate the pay.

Common mistakes

• Treating the digits after the decimal point as minutes.
• Rounding each day before adding up the week, which can drift the total.
• Forgetting an unpaid break before converting.

The hours calculator shows both forms, and the work hours calculator adds up a full week.