Hexadecimal Time
Time in Base-16
What is Hexadecimal Time?
Hexadecimal time is an alternative way of representing time using base-16 (hexadecimal) notation. Instead of the traditional 24-hour system, the entire day is represented as a fraction between 0 and 1.
Key Points:
- .0000 = Midnight (00:00:00)
- .8000 = Noon (12:00:00)
- .FFFF = One second before midnight (23:59:59)
The day is divided into 65,536 parts (16⁴), providing accuracy of about 1.3 seconds per unit.
This system was proposed by John W. Nystrom in 1863 and later popularized by Mark Vincent Rogers in 1997 with his JavaScript implementation.
Why use hexadecimal time?
It provides a consistent base-16 system throughout the day, making calculations more elegant for programmers and mathematicians who work with hexadecimal numbers.
How to Read Hexadecimal Time
The four digits after the point are a fraction of the day written in base 16. Read them as a hexadecimal number between 0000 and FFFF, then divide by 65,536 to get the share of the day that has passed. At .4000 a quarter of the day is gone, which is 06:00. At .C000 three quarters are gone, which is 18:00.
| Hexadecimal | Standard | Day elapsed |
|---|---|---|
| .0000 | 00:00:00 | 0% |
| .1000 | 01:30:00 | 6.25% |
| .4000 | 06:00:00 | 25% |
| .8000 | 12:00:00 | 50% |
| .C000 | 18:00:00 | 75% |
| .F000 | 22:30:00 | 93.75% |
| .FFFF | 23:59:58.7 | 99.998% |
The clock above reads your device's local time, so it shifts with your time zone the same way an ordinary clock does.
Converting between the two
To go from standard time to hexadecimal, count the seconds since midnight, divide by 86,400, multiply by 65,536, and write the result as four hexadecimal digits. 14:30:00 is 52,200 seconds into the day. Divided by 86,400 that gives 0.60417, multiplied by 65,536 it gives 39,594, and 39,594 written in base 16 is 9AAA. The clock reads .9AAA.
Going the other way is the same arithmetic reversed: read the four digits as a decimal number, divide by 65,536, then multiply by 86,400 to get seconds since midnight.
Hexadecimal hours, minutes and seconds
The day splits into 16 hexadecimal hours rather than 24, each lasting an hour and a half. A hexadecimal hour holds 256 hexadecimal minutes of about 21.1 seconds, and a hexadecimal minute holds 16 hexadecimal seconds of about 1.32 seconds. Those divisions map onto the digits on screen: the first is the hour, the middle two are the minute, the last is the second. Some implementations add separators to make the split visible, writing .F000 as F_00_0.
Where it came from
John William Nystrom was a Swedish-born engineer who settled in Philadelphia and served as a chief engineer in the United States Navy during the Civil War. In 1859 he proposed replacing base 10 with base 16 across arithmetic, weights, measures and coinage, and published the scheme in 1862 as the Tonal System. Time was one piece of it. So was a calendar of sixteen months, and a set of names for the sixteen digits: an, de, ti, go, su, by, ra, me, ni, ko, hu, vy, la, po, fy and ton. His argument for the base was that 16 can be halved again and again without remainder, where 10 and 12 cannot. None of it was adopted.
The version this clock runs on is more recent. In 1997 Mark Vincent Rogers of Intuitor described a similar scheme and implemented it in JavaScript as the Hexclock.
Common questions
Is hexadecimal time used for anything?
No standards body has adopted it. Nystrom's proposal went nowhere in the 1860s, and the modern form survives as a curiosity.
How precise is it?
One hexadecimal second covers about 1.32 standard seconds, so the smallest unit on screen is slightly coarser than a normal second.
Is this the same as decimal time?
No. Decimal time divides the day into 10 hours of 100 minutes each and comes out of the French Revolution. Hexadecimal time divides it into 16 and comes from Nystrom.