How to Calculate Time Duration Between Two Times: Hours & Minutes
Elapsed time math, 24-hour clock conversion, borrowing minutes across hours, and overnight shifts.
The Challenge of Sexagesimal (Base-60) Time Math
While modern mathematics operates on the base-10 decimal system, clock time is governed by the ancient Babylonian sexagesimal (base-60) system: 60 seconds in a minute, and 60 minutes in an hour.
Because you cannot simply subtract time like regular decimal numbers (e.g. 5:15 minus 3:45 is NOT 1:70), calculating elapsed time requires borrowing 60 minutes when subtracting across an hour boundary.
Step-by-Step Method: Calculating Elapsed Time
To subtract an earlier start time from a later end time:
- Convert both times to a 24-hour clock format (e.g. 1:15 PM = 13:15, 5:45 PM = 17:45).
- Subtract minutes first. If start minutes exceed end minutes, borrow 1 hour (60 minutes) from the end hour and add 60 to end minutes.
- Subtract the hours.
Worked Example: 08:30 AM to 05:15 PM (17:15)
- End time = 17:15, Start time = 08:30.
- Minutes: 15 is smaller than 30. Borrow 1 hour from 17 (becomes 16 hours) and add 60 minutes to 15: 15 + 60 = 75 minutes.
- Subtract minutes: 75 − 30 = 45 minutes.
- Subtract remaining hours: 16 − 8 = 8 hours.
- Result: 8 hours and 45 minutes.
Converting Hours & Minutes to Decimal Hours for Payroll
Employers and payroll software require working hours to be reported in decimal hours rather than minutes. To convert minutes to a decimal, divide by 60:
In our example above: 8 hours + (45 / 60) = 8 + 0.75 = 8.75 decimal hours. If an employee earns $20/hour: 8.75 × $20 = $175.00 gross pay.
Quick Reference: Common Minutes to Decimals Table
| Minutes | Fraction of Hour | Decimal Equivalent |
|---|---|---|
| 15 min | 1/4 hour | 0.25 hrs |
| 30 min | 1/2 hour | 0.50 hrs |
| 45 min | 3/4 hour | 0.75 hrs |
| 10 min | 1/6 hour | 0.17 hrs |
| 20 min | 1/3 hour | 0.33 hrs |
| 50 min | 5/6 hour | 0.83 hrs |
Calculating Overnight Shifts (Crossing Midnight)
When a shift starts in the evening and concludes the following morning (e.g. 10:45 PM to 06:15 AM), add 24 hours to the end time in 24-hour notation:
- Start time: 22:45. End time: 06:15.
- Add 24 hours to end time: 06:15 + 24:00 = 30:15.
- Subtract start time: 30:15 − 22:45.
- Borrow 1 hour: 29:75 − 22:45 = 7 hours and 30 minutes (7.5 decimal hours).
Compute Time Durations Instantly
Calculate work shifts, track billable hours, and convert decimal time effortlessly:
- Calculate elapsed time and decimal hours with our Time Duration Calculator.
- Add or subtract calendar days with our Add or Subtract Days Calculator.
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