How to Add, Subtract & Convert Time — A Complete Guide

Core Concepts: Time vs. Duration

Before calculating, distinguish between two key ideas:

• Time of Day: A specific point on the 24-hour clock (e.g., 2:30 PM or 14:30). This is not a quantity you can directly add or subtract.
• Duration: A length of elapsed time (e.g., 3 hours 20 minutes). This is what you add, subtract, multiply, or divide.

Example:

• Time: “My meeting starts at 9:15 AM.”
• Duration: “The meeting lasts 1 hour 45 minutes.”
• Resulting Time: 11:00 AM

Always convert time of day problems into duration problems first.

The Base-60 System: Why It’s Tricky

Unlike decimal math (where 10 units = 1 higher unit), time uses:

• 60 seconds = 1 minute
• 60 minutes = 1 hour
• 24 hours = 1 day

This means carrying and borrowing happen at 60, not 10:

• Addition: If seconds ≥ 60, convert to minutes.
• Subtraction: If seconds below 0, borrow 60 from minutes.

Step-by-Step: Adding Time Durations

Problem: Add 2 hours 47 minutes + 1 hour 38 minutes.

1. Add minutes: 47 + 38 = 85 minutes
2. Convert excess minutes: 85 ÷ 60 = 1 hour 25 minutes
3. Add hours: 2 + 1 + 1 = 4 hours
4. Final result: 4 hours 25 minutes

Step-by-Step: Subtracting Time Durations

Problem: Subtract 1 hour 20 minutes from 3 hours 10 minutes.

1. Minutes: 10 – 20 → can’t do → borrow 1 hour (60 minutes)
   → Hours: 3 – 1 = 2
   → Minutes: 10 + 60 = 70
2. Now subtract:
   • Minutes: 70 – 20 = 50
   • Hours: 2 – 1 = 1
3. Result: 1 hour 50 minutes

Calculating Time Differences (Clock Times)

To find how long something lasted: Formula: End Time – Start Time = Duration

But always convert to 24-hour format first to avoid AM/PM confusion.

Example: Start = 2:45 PM, End = 5:20 PM

• 24-hour: 14:45 to 17:20
• Minutes: 20 – 45 → borrow → 80 – 45 = 35
• Hours: 16 – 14 = 2
• Duration = 2 hours 35 minutes

Handling Cross-Midnight Scenarios

If end time < start time (e.g., night shift), add 24 hours to the end time.

Example: Start = 10:30 PM, End = 6:15 AM

• 24-hour: 22:30 to 06:15 → add 24 → 30:15
• Duration = 30:15 – 22:30 = 7 hours 45 minutes

Converting to Decimal Hours (Critical for Payroll)

Payroll systems use decimal hours, not HH:MM.

Formula:
Decimal Hours = Hours + (Minutes ÷ 60)

Examples:

• 8:30 → 8 + (30/60) = 8.5 hours
• 7:45 → 7 + (45/60) = 7.75 hours
• 9:20 → 9 + (20/60) ≈ 9.333 hours

To convert back:

• 0.75 hours × 60 = 45 minutes → 7.75 = 7:45

Multiplying and Dividing Time

Time durations can be scaled:

• Multiplication: 2 × (1:30) = 3:00
• Division: (4:00) ÷ 2 = 2:00

Real-world use:

• If one task takes 1:15, 8 tasks take 8 × 1:15 = 10:00.

Pro Tips & Common Mistakes

✅ Always use 24-hour time for differences—eliminates AM/PM errors.
✅ Convert to total seconds for complex calculations:

• Total Seconds = (H × 3600) + (M × 60) + S
• Do math, then convert back.
  ✅ Round consistently for payroll (e.g., nearest 0.25 or 0.1 hours).
  ❌ Don’t mix time of day and duration—they’re different data types.
  ❌ Don’t forget to borrow/carry at 60—not 100!
  ❌ Don’t ignore cross-day scenarios—verify if duration spans midnight.

Practical Applications

• Payroll: Convert clock-in/out times to decimal hours.
• Project Management: Track task durations and total effort.
• Travel: Calculate flight or drive times across time zones.
• Cooking: Add prep, cook, and rest times accurately.
• Fitness: Log workout durations for training logs.