How to Add and Subtract Time: Hours, Minutes and Seconds Explained

Time does not behave like ordinary decimal numbers. Minutes and seconds roll over at 60, hours at 24, and that is why adding up "2:45 plus 1:30" on paper often goes wrong. This guide explains the carry-and-borrow method, a faster way using seconds, how to handle overnight shifts, and how to turn hours and minutes into decimal hours for payroll.

Adding time: carry every 60

Add each unit separately, then carry. Every 60 seconds becomes 1 minute, and every 60 minutes becomes 1 hour. Example: 2:45:40 + 1:30:35.

• Seconds: 40 + 35 = 75, which is 1 minute and 15 seconds. Write 15, carry 1 minute.
• Minutes: 45 + 30 + 1 (carried) = 76, which is 1 hour and 16 minutes. Write 16, carry 1 hour.
• Hours: 2 + 1 + 1 (carried) = 4.

The result is 4:16:15.

Subtracting time: borrow 60

If a unit would go negative, borrow 1 from the next larger unit and add 60 to the current one. Example: 5:10:20 − 2:45:50.

• Seconds: 20 − 50 is negative, so borrow 1 minute: 80 − 50 = 30. The minutes become 9.
• Minutes: 9 − 45 is negative, so borrow 1 hour: 69 − 45 = 24. The hours become 4.
• Hours: 4 − 2 = 2.

The result is 2:24:30.

The seconds shortcut

If carrying feels error-prone, convert everything to seconds, do ordinary arithmetic, and convert back. Using the first example: 2:45:40 is 9,940 seconds and 1:30:35 is 5,435 seconds. The sum is 15,375 seconds. Divide by 3,600 to get 4 hours with 975 seconds left over, then divide that by 60 to get 16 minutes and 15 seconds. Same answer: 4:16:15.

Time between two clock times

To find how long something lasted, subtract the start from the end. A shift from 8:45 AM to 5:15 PM is 8 hours and 30 minutes. If you take an unpaid 30-minute break, you worked 8 hours.

When the end time is earlier on the clock than the start time, the period crosses midnight. Add 24 hours to the end time before subtracting. A shift from 10:00 PM to 6:00 AM is 24 − 22 + 6 = 8 hours.

Converting to decimal hours

Payroll and invoices often need decimal hours rather than hours and minutes. Divide the minutes by 60 and add them to the hours:

For example, 7 hours 45 minutes is 7 + 45 ÷ 60 = 7.75 hours. At $20 per hour, that is 7.75 × 20 = $155. A common error is treating 7:45 as 7.45, which understates the pay.

Common mistakes to avoid

• Treating minutes as decimals. 1:30 is 1.5 hours, not 1.3 hours.
• Forgetting AM/PM. 12:00 AM is midnight and 12:00 PM is noon; use 24-hour time when in doubt.
• Not carrying when adding many durations. Sum each column first, then carry once at the end.
• Ignoring breaks. Subtract unpaid breaks before converting to decimal hours.

If you need to count days instead of hours, see How Days-From/Until Calculators Work (And Why the Count Can Look Off by One).