What Is the 24-Hour to 12-Hour Time Converter?
This tool converts military time (a 24-hour clock running from 00:00 to 23:59) into the everyday 12-hour AM/PM format. Military time is used worldwide by armed forces, aviation, hospitals, and emergency services because it removes any ambiguity between morning and evening hours. If you have ever wondered what "18:30" or "0045" means on a standard clock, this converter gives you the answer instantly.
How to Use It
Enter the hour as a number from 0 to 23 and the minute from 0 to 59. For example, type 18 in the hour box and 30 in the minute box to convert 18:30. Press calculate and the converter shows the equivalent 12-hour time, such as 6:30 PM. Leading zeros are optional.
The Formula Explained
The 12-hour hour is found with \(\text{hour12} = ((H + 11) \bmod 12) + 1\), where \(H\) is the 24-hour input.
$$\text{Standard} = \left(\left(\text{Hour} + 11\right) \bmod 12 + 1\right) : \text{Minute}\ \begin{cases} \text{AM} & \text{Hour} < 12 \\ \text{PM} & \text{Hour} \ge 12 \end{cases}$$This neatly maps \(0 \to 12\), \(12 \to 12\), \(13 \to 1\), and \(23 \to 11\). The period is AM when \(H\) is less than 12 and PM when \(H\) is 12 or greater. Midnight (00:xx) becomes 12:xx AM, and noon (12:xx) becomes 12:xx PM.
Worked Example
Convert 13:45. Compute
$$\text{hour12} = ((13 + 11) \bmod 12) + 1 = (24 \bmod 12) + 1 = 0 + 1 = 1.$$Since \(13 \ge 12\), the period is PM. So 13:45 in 24-hour time equals 1:45 PM on a standard clock.
FAQ
What is 00:00 in 12-hour time? Midnight, written 12:00 AM.
What is 12:00 in 12-hour time? Noon, written 12:00 PM.
Why does the military write times without a colon? Military time is often written as four digits (e.g., 1830) and spoken as "eighteen thirty hours" to avoid confusion in radio communication.
