24-Hour Clock Calculator: Convert Time & Calculate Duration
A 24-hour clock calculator is an essential time conversion tool that accurately converts between 12-hour format (AM/PM) and 24-hour format (military time), calculates time duration between two times, performs time arithmetic operations (add or subtract hours and minutes), and handles international time notation. By using mathematical modulo operations and time conversion formulas, this calculator helps students, travelers, military personnel, healthcare workers, and international business professionals understand and work with 24-hour time notation, schedule conversions, shift planning, and precise time calculations across different time formats used globally.
🕐 Interactive 24-Hour Clock Calculator
Convert time formats and calculate durations
Convert 12-Hour to 24-Hour Format
Convert AM/PM time to military/24-hour format
Convert 24-Hour to 12-Hour Format
Convert military/24-hour time to AM/PM format
Calculate Time Duration
Calculate elapsed time between two times (24-hour format)
Add or Subtract Time
Add or subtract hours and minutes from a time
Understanding 24-Hour Time Format
The 24-hour clock, also known as military time, uses hours from 00:00 (midnight) to 23:59 (one minute before midnight) without AM or PM designations. This system eliminates confusion and is used internationally.
12-Hour to 24-Hour Conversion Formula
AM Hours Conversion
12-Hour AM to 24-Hour:
\[ H_{24} = \begin{cases} 0 & \text{if } H_{12} = 12 \text{ (midnight)} \\ H_{12} & \text{if } 1 \leq H_{12} \leq 11 \end{cases} \]
Examples:
12:00 AM → 00:00 (midnight)
1:00 AM → 01:00
11:59 AM → 11:59
PM Hours Conversion
12-Hour PM to 24-Hour:
\[ H_{24} = \begin{cases} 12 & \text{if } H_{12} = 12 \text{ (noon)} \\ H_{12} + 12 & \text{if } 1 \leq H_{12} \leq 11 \end{cases} \]
Examples:
12:00 PM → 12:00 (noon)
1:00 PM → 13:00
11:59 PM → 23:59
24-Hour to 12-Hour Conversion Formula
24-Hour to 12-Hour:
\[ H_{12} = \begin{cases} 12 & \text{if } H_{24} = 0 \text{ or } H_{24} = 12 \\ H_{24} \bmod 12 & \text{otherwise} \end{cases} \]
Period determination:
\[ \text{Period} = \begin{cases} \text{AM} & \text{if } 0 \leq H_{24} < 12 \\ \text{PM} & \text{if } 12 \leq H_{24} \leq 23 \end{cases} \]
Complete Conversion Examples
Example 1: 3:45 PM to 24-Hour
Given: 3:45 PM
Step 1: Hour = 3, Period = PM
Step 2: Since PM and hour ≠ 12: \( H_{24} = 3 + 12 = 15 \)
Step 3: Minutes remain the same: 45
Result: 15:45
Example 2: 17:30 to 12-Hour
Given: 17:30
Step 1: Hour = 17
Step 2: Since 17 ≥ 12, period = PM
Step 3: \( H_{12} = 17 \bmod 12 = 5 \)
Step 4: Minutes remain the same: 30
Result: 5:30 PM
Time Duration Calculation Formula
Duration Between Two Times:
\[ D_{\text{minutes}} = (H_{\text{end}} \times 60 + M_{\text{end}}) - (H_{\text{start}} \times 60 + M_{\text{start}}) \]
Convert to hours and minutes:
\[ H_{\text{duration}} = \lfloor D_{\text{minutes}} / 60 \rfloor \]
\[ M_{\text{duration}} = D_{\text{minutes}} \bmod 60 \]
Duration Calculation Example
Calculate duration from 09:30 to 17:15
Step 1: Convert start to minutes: \( 9 \times 60 + 30 = 570 \) minutes
Step 2: Convert end to minutes: \( 17 \times 60 + 15 = 1035 \) minutes
Step 3: Duration: \( 1035 - 570 = 465 \) minutes
Step 4: Convert to hours: \( \lfloor 465 / 60 \rfloor = 7 \) hours
Step 5: Remaining minutes: \( 465 \bmod 60 = 45 \) minutes
Result: 7 hours 45 minutes
Complete 24-Hour Conversion Chart
| 12-Hour Format | 24-Hour Format | Description |
|---|---|---|
| 12:00 AM | 00:00 | Midnight (start of day) |
| 1:00 AM | 01:00 | Early morning |
| 6:00 AM | 06:00 | Dawn |
| 12:00 PM | 12:00 | Noon (midday) |
| 1:00 PM | 13:00 | Afternoon |
| 3:00 PM | 15:00 | Mid-afternoon |
| 6:00 PM | 18:00 | Evening |
| 9:00 PM | 21:00 | Night |
| 11:59 PM | 23:59 | End of day |
Quick Reference: Common Times
| Event/Time | 12-Hour | 24-Hour |
|---|---|---|
| Midnight | 12:00 AM | 00:00 |
| Breakfast | 8:00 AM | 08:00 |
| Noon | 12:00 PM | 12:00 |
| Lunch | 1:00 PM | 13:00 |
| End of work | 5:00 PM | 17:00 |
| Dinner | 7:00 PM | 19:00 |
| Bedtime | 10:00 PM | 22:00 |
Military Time Usage
How to Read Military Time
Military Time Pronunciation:
- 00:00 - 00:59: "Zero hundred" to "Zero fifty-nine"
- 01:00: "Zero one hundred hours" or "Oh one hundred"
- 09:30: "Zero nine thirty hours"
- 12:00: "Twelve hundred hours"
- 13:00: "Thirteen hundred hours" or "One-three hundred"
- 18:45: "Eighteen forty-five hours"
- 23:59: "Twenty-three fifty-nine hours"
Where 24-Hour Time is Used
- Military operations: All branches worldwide use 24-hour format
- Aviation: Flight schedules, air traffic control
- Healthcare: Hospitals, medical records, prescriptions
- Emergency services: Police, fire, ambulance dispatch
- Transportation: Railways, buses, international travel
- Computing: System logs, timestamps, programming
- International business: Scheduling across time zones
- Most countries: Standard in Europe, Asia, Latin America
Time Arithmetic Operations
Adding Time
Add Hours and Minutes:
\[ M_{\text{total}} = M_{\text{base}} + M_{\text{add}} \]
\[ H_{\text{total}} = H_{\text{base}} + H_{\text{add}} + \lfloor M_{\text{total}} / 60 \rfloor \]
\[ M_{\text{final}} = M_{\text{total}} \bmod 60 \]
\[ H_{\text{final}} = H_{\text{total}} \bmod 24 \]
Example: Add 5 hours 45 minutes to 18:30
Start time: 18:30
Add: 5 hours 45 minutes
Step 1: Minutes: \( 30 + 45 = 75 \) minutes
Step 2: Carry hour: \( \lfloor 75 / 60 \rfloor = 1 \) hour, remainder \( 75 \bmod 60 = 15 \) minutes
Step 3: Hours: \( 18 + 5 + 1 = 24 \)
Step 4: Adjust for 24-hour: \( 24 \bmod 24 = 0 \) (next day)
Result: 00:15 (next day)
Common Misconceptions
⚠️ Avoid These Mistakes
- 12:00 AM confusion: 12:00 AM is midnight (00:00), NOT noon
- 12:00 PM confusion: 12:00 PM is noon (12:00), NOT midnight
- 24:00 doesn't exist: Day ends at 23:59, next second is 00:00
- Leading zeros matter: 09:00 not 9:00 in 24-hour format
- No "o'clock": Say "fourteen hundred" not "fourteen o'clock"
- Colon placement: Always HH:MM format (15:30 not 15.30)
- PM ≠ add 12 always: 12:30 PM stays 12:30, doesn't become 24:30
International Time Notation
ISO 8601 Standard
- Format: HH:MM:SS (hours:minutes:seconds)
- Example: 15:30:00 for 3:30:00 PM
- Date-time combined: 2025-10-18T15:30:00
- UTC notation: 15:30:00Z (Z indicates UTC/GMT)
- Time zone offset: 15:30:00+04:00 (4 hours ahead of UTC)
Practical Applications
Shift Work Scheduling
Example: Night Shift Duration
Shift: 22:00 to 06:00
Calculation:
Start: 22:00 (10:00 PM)
End: 06:00 (6:00 AM next day)
Duration: From 22:00 to 24:00 = 2 hours
Plus: From 00:00 to 06:00 = 6 hours
Total: 8 hours
Flight Schedule Example
International Flight Timing
Departure: Dubai 14:30 (2:30 PM)
Arrival: London 18:45 (6:45 PM local time)
Flight duration: Calculate using UTC conversion
Dubai: UTC+4, London: UTC+0
Departure UTC: 10:30
Arrival UTC: 18:45
Flight time: 8 hours 15 minutes
Frequently Asked Questions
What is 3:45 PM in 24-hour time?
3:45 PM = 15:45 in 24-hour format. Formula: Add 12 to PM hours except for 12 PM. 3 + 12 = 15, minutes stay same (45). All PM times from 1:00-11:59 PM add 12 to the hour. Example: 7:30 PM = 19:30, 10:15 PM = 22:15.
Is 12:00 AM midnight or noon?
12:00 AM is midnight (00:00 in 24-hour format), the start of a new day. 12:00 PM is noon (12:00 in 24-hour format), the middle of the day. This is the most common confusion in 12-hour time. To avoid confusion, use 00:00 for midnight and 12:00 for noon in 24-hour format.
How do you convert 17:30 to 12-hour time?
17:30 = 5:30 PM. Formula: If hour ≥ 12, subtract 12 and add PM. 17 - 12 = 5, so 5:30 PM. Hours 00-11 are AM, hours 12-23 are PM. Examples: 14:00 = 2:00 PM, 20:45 = 8:45 PM, 23:30 = 11:30 PM. Only exception: 12:00-12:59 stays 12:xx PM.
How do you calculate time duration in 24-hour format?
Convert both times to total minutes (hours × 60 + minutes), subtract, convert back. Example: 09:30 to 17:15. Start: 9×60+30 = 570 min. End: 17×60+15 = 1035 min. Duration: 1035-570 = 465 min = 7 hours 45 minutes. For times crossing midnight, add 1440 minutes (24 hours) to end time first.
Why is 24-hour time called military time?
Military time refers to the 24-hour clock system used by armed forces worldwide to avoid AM/PM confusion in critical operations. Precise timing is essential in military, aviation, and emergency services. While called "military time" in the US, it's standard civilian time in most countries. The 24-hour system eliminates ambiguity in scheduling and coordination.
How do you add hours to 24-hour time?
Add hours directly, if result ≥ 24, subtract 24 (next day). Example: 18:30 + 7 hours = 25:30, subtract 24 = 01:30 (next day). When adding minutes that exceed 60, carry over to hours: 18:30 + 45 minutes = 18:75 = 19:15. For 18:30 + 5h 45m: first 18:30 + 5h = 23:30, then + 45m = 24:15 = 00:15 next day.
Key Takeaways
Understanding 24-hour time format requires mastering conversion formulas, modular arithmetic for hour calculations, and proper handling of midnight and noon transitions. The system eliminates AM/PM ambiguity and is essential for international communication.
Essential principles to remember:
- 24-hour format uses 00:00 to 23:59 (no 24:00)
- 12:00 AM (midnight) = 00:00 in 24-hour format
- 12:00 PM (noon) = 12:00 in 24-hour format
- AM hours (1-11): use as-is with leading zero (01:00-11:59)
- PM hours (1-11): add 12 to hour (13:00-23:59)
- Duration = (end time in minutes) - (start time in minutes)
- Hour addition uses modulo 24 operation
- Leading zeros required: 09:00 not 9:00
- Format is always HH:MM (colon separator)
- Used globally in military, aviation, healthcare, transportation
Getting Started: Use the interactive 24-hour clock calculator at the top of this page to convert between 12-hour and 24-hour formats, calculate time duration between two times, and perform time arithmetic (add or subtract hours and minutes). Select your calculation type, enter the time values, and receive instant accurate conversions with step-by-step explanations.