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Decimal Clock

Watch a live decimal clock beside ordinary clock time, or use Set time to convert a time of day. Choose a time zone and switch between the ten-hour French Republican scale and ordinary decimal hours; both readings stay labelled.

DECIMAL TIME--:--:--Starting from the clock on your device
Decimal
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Local
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Day done
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Scale
Clock
Time zone

The ten-hour day of the French Republic: 10 decimal hours of 100 decimal minutes of 100 decimal seconds. Noon is 5:00:00 and one decimal hour is 2 hours 24 minutes.

Two things are called decimal time. The ten-hour day of the French Republic cuts the day into 10 hours of 100 minutes of 100 seconds, so noon is 5:00:00 and one decimal hour lasts 2 hours 24 minutes. A timesheet's decimal hours are the ordinary 24-hour clock written as a fraction, so the same noon is 12.000 hours. The Scale control decides which one the clock shows large, and the line under the readout always gives the other, because the two readings for one moment are 2.4 times apart and look alike on the page.

Clock time to decimal conversion chart

Clock is ordinary time since midnight. The 10 h column is French Republican time; the 24 h column is ordinary decimal hours rounded to three places. First-hour rows give every whole minute's fractional hour, followed by each whole hour of the day. These are time-of-day values, not elapsed hours worked.

Clock10 h24 h
00:000:00:000.000
00:010:00:690.017
00:020:01:380.033
00:030:02:080.050
00:040:02:770.067
00:050:03:470.083
00:060:04:160.100
00:070:04:860.117
00:080:05:550.133
00:090:06:250.150
00:100:06:940.167
00:110:07:630.183
00:120:08:330.200
00:130:09:020.217
00:140:09:720.233
00:150:10:410.250
00:160:11:110.267
00:170:11:800.283
00:180:12:500.300
00:190:13:190.317
00:200:13:880.333
00:210:14:580.350
00:220:15:270.367
00:230:15:970.383
00:240:16:660.400
00:250:17:360.417
00:260:18:050.433
00:270:18:750.450
00:280:19:440.467
00:290:20:130.483
00:300:20:830.500
00:310:21:520.517
00:320:22:220.533
00:330:22:910.550
00:340:23:610.567
00:350:24:300.583
00:360:25:000.600
00:370:25:690.617
00:380:26:380.633
00:390:27:080.650
00:400:27:770.667
00:410:28:470.683
00:420:29:160.700
00:430:29:860.717
00:440:30:550.733
00:450:31:250.750
00:460:31:940.767
00:470:32:630.783
00:480:33:330.800
00:490:34:020.817
00:500:34:720.833
00:510:35:410.850
00:520:36:110.867
00:530:36:800.883
00:540:37:500.900
00:550:38:190.917
00:560:38:880.933
00:570:39:580.950
00:580:40:270.967
00:590:40:970.983
01:000:41:661.000
02:000:83:332.000
03:001:25:003.000
04:001:66:664.000
05:002:08:335.000
06:002:50:006.000
07:002:91:667.000
08:003:33:338.000
09:003:75:009.000
10:004:16:6610.000
11:004:58:3311.000
12:005:00:0012.000
13:005:41:6613.000
14:005:83:3314.000
15:006:25:0015.000
16:006:66:6616.000
17:007:08:3317.000
18:007:50:0018.000
19:007:91:6619.000
20:008:33:3320.000
21:008:75:0021.000
22:009:16:6622.000
23:009:58:3323.000
23:59:599:99:9824.000

Common questions

What is decimal time?
French Republican decimal time, associated with the French Revolution, splits a day into 10 hours, each with 100 minutes of 100 seconds. That is 100,000 decimal seconds instead of 86,400 ordinary seconds. One decimal second is exactly 0.864 of an ordinary second, and one decimal hour lasts 2 hours 24 minutes. This clock demonstrates that scale alongside ordinary decimal hours.
Why does a decimal clock show 5:00:00 at noon?
Noon is halfway through the day, so it is halfway through ten decimal hours. Midnight starts at 0:00:00, 06:00 reads 2:50:00, and 18:00 reads 7:50:00. At 23:59:59 the reading is 9:99:98; the clock returns to zero at midnight. The landmark rows show midnight and noon on the scale you select.
How do you convert clock time to decimal time?
For the ten-hour scale, count ordinary seconds since midnight and divide by 0.864. At 18:00 there are 64,800 ordinary seconds, giving 75,000 decimal seconds, or 7:50:00. The ten-hour reading truncates to a whole decimal second. Ordinary decimal hours instead use hours + minutes/60 + seconds/3600, rounded here to three decimal places; one step in that display is 3.6 ordinary seconds.
Is 18.5 hours the same as 18:50?
No. The fraction in 18.5 is half an ordinary hour, so it means 18:30. That time is shown as 18.500 h on the 24 h scale and 7:70:83 on the ten-hour scale. The Scale control changes which reading is large.
Does it use my time zone, and what happens when the clocks change?
The live reading starts from your device clock and uses your browser's time zone database for the selected zone and date. Decimal time follows the wall clock, so it jumps or repeats when that clock changes. A day with a one-hour change lasts 23 or 25 elapsed hours; a half-hour change lasts 23.5 or 24.5. The note identifies the change for the date shown and flags a typed time within a skipped or repeated period.
Can I convert a particular time rather than watch the clock?
Yes. Choose Set time and enter an ordinary time such as 18:31:40, 18:31, 1831, 183140, 6:31:40 pm, noon or midnight. The box accepts a time of day from 00:00:00 through 23:59:59, not a duration or an hours-worked total. It rejects invalid hours, minutes and seconds with a specific message. The date used for time zone rules remains the current date in the chosen zone.
Can I enter decimal hours or ten-hour decimal time?
The input takes ordinary clock time. It does not accept a decimal-hour number or a French decimal reading as input. For example, entering 18.5 produces an explanation instead of a converted result. The conversion chart is a lookup reference; the clock does not calculate shifts, subtract start and end times, or total a timesheet.
How do time-clock minutes become decimal hours?
Divide the minute part by 60, then add the whole hours. Fifteen minutes is 0.250 hours, thirty is 0.500, and forty-five is 0.750. The chart includes every whole minute from 00 through 59 in its first-hour rows. For 08:45, adding 8 to 0.750 gives 8.750 hours. These fractions use ordinary 60-minute hours.
Are my entries uploaded?
The time conversion runs in this page without uploading your typed time or chosen zone. The clock remembers its settings in this browser after you change a control. Copy places a labelled reading on your clipboard if the browser permits it; it does not download a file.

Exact conversion: the day is divided into 10 decimal hours of 100 minutes of 100 seconds, so one decimal second is exactly 0.864 of an ordinary second. It converts the clock on your device, or a time you type, in the time zone you choose, and daylight saving comes from that zone's own rules for the civil day shown. The arithmetic is exact; the reading is only as right as the clock it reads, and decimal time is a curiosity rather than a timekeeping standard.