How to Do Time Arithmetic: Add, Subtract & Convert Time
Quick Answer
Time uses base 60: 60 seconds per minute, 60 minutes per hour. Add or subtract each unit separately and carry/borrow when a unit exceeds 60. Convert between formats by adding 12 for PM hours (24-hour) or dividing total seconds by 3,600 for hours.
Understanding the Base-60 System
Time math uses sexagesimal (base 60), a system the Babylonians developed around 2000 BC. We inherited it through Greek astronomy, and now it's embedded in every clock and watch on the planet. The key relationships:
| Conversion | Value |
|---|---|
| 1 minute | 60 seconds |
| 1 hour | 60 minutes = 3,600 seconds |
| 1 day | 24 hours = 1,440 minutes = 86,400 seconds |
| 1 week | 168 hours = 10,080 minutes |
Adding Time: The Three-Column Method
Think of time like a three-column number: hours | minutes | seconds. Add each column independently, then normalize by carrying excess.
Example: 2:45:30 + 1:20:45
Seconds: 30 + 45 = 75. That's 60+ so carry: 75 − 60 = 15 seconds, carry 1 minute.
Minutes: 45 + 20 + 1 (carried) = 66. That's 60+ so carry: 66 − 60 = 6 minutes, carry 1 hour.
Hours: 2 + 1 + 1 (carried) = 4.
Result: 4:06:15
Subtracting Time: Borrowing from the Left
Same principle as decimal subtraction, but you borrow 60 instead of 10.
Example: 5:10:20 − 2:35:50
Seconds: 20 − 50? Can't do it. Borrow 60 from minutes: 5:09:80. Now 80 − 50 = 30 seconds.
Minutes: 09 − 35? Can't do it. Borrow 60 from hours: 4:69:80. Wait — we already adjusted minutes to 09. So: 4:69:30 (after the seconds step). Now 69 − 35 = 34 minutes.
Hours: 4 − 2 = 2.
Result: 2:34:30
12-Hour vs. 24-Hour Time
The 24-hour format (military time) eliminates AM/PM ambiguity. Converting between them:
| 12-Hour | 24-Hour | Rule |
|---|---|---|
| 12:00 AM (midnight) | 00:00 | 12 AM = 0 |
| 12:30 AM | 00:30 | 12 AM = 0 |
| 1:00 AM – 11:59 AM | 01:00 – 11:59 | Same number |
| 12:00 PM (noon) | 12:00 | 12 PM = 12 |
| 1:00 PM | 13:00 | Add 12 |
| 11:00 PM | 23:00 | Add 12 |
| 11:59 PM | 23:59 | Add 12 |
The confusing parts: 12 AM is midnight (00:00), not noon. 12 PM is noon (12:00), not midnight. This trips people up constantly. In 24-hour time, there's no ambiguity: 00:00 is midnight, 12:00 is noon, 13:00 is 1 PM.
Converting Total Seconds to Hours:Minutes:Seconds
Software often stores time as total seconds. To convert 10,250 seconds to readable time:
Hours: 10,250 ÷ 3,600 = 2 (remainder 3,050)
Minutes: 3,050 ÷ 60 = 50 (remainder 50)
Seconds: 50
Result: 2:50:50
Time Zone Arithmetic
Every time zone is defined as an offset from UTC (Coordinated Universal Time). Eastern Time is UTC−5, Pacific is UTC−8, Central European is UTC+1, Japan is UTC+9.
To convert between zones, calculate the difference between their offsets. EST to PST: −5 to −8 = 3 hours behind. So 3:00 PM EST = 12:00 PM PST. EST to CET: −5 to +1 = 6 hours ahead. So 3:00 PM EST = 9:00 PM CET.
Daylight saving time shifts offsets by one hour (EST/UTC−5 becomes EDT/UTC−4). Not all regions observe DST, which adds another layer of complexity when scheduling across time zones.
Common Time Unit Conversions
| From | To | Formula |
|---|---|---|
| Minutes | Hours | ÷ 60 |
| Hours | Minutes | × 60 |
| Seconds | Minutes | ÷ 60 |
| Minutes | Seconds | × 60 |
| Hours (decimal) | Hours:Minutes | Whole = hours, decimal × 60 = minutes |
| Hours:Minutes | Decimal hours | Hours + (minutes ÷ 60) |
Use the time calculator for instant time addition, subtraction, and conversion between any time formats.