Decimal Time Converter (French Revolutionary 10-hour clock ↔ standard time)

Understanding the decimal time converter — concept and principle

This converter turns ordinary clock time into French Republican decimal time, with 10 hours in a day, and back again. It is used by history fans, puzzle and game designers, writers of alternate-history fiction and anyone curious about how a metric clock would read.

How it is calculated

Both clocks measure the same fraction of the day, f:

• Standard time: f = (h × 3,600 + m × 60 + s) ÷ 86,400
• Decimal time: f = (H × 10,000 + M × 100 + S) ÷ 100,000

To convert, find f from one clock and express it in the other. Decimal seconds since midnight = f × 100,000; standard seconds = f × 86,400. Results are rounded to the nearest whole second.

The principle

In 1793 the French Republic decreed that the day, from midnight to midnight, would be divided into 10 hours, each of 100 minutes, each of 100 seconds: 100,000 decimal seconds instead of 86,400. Because both systems divide the same day, converting is a matter of proportion. One decimal hour is 2 h 24 min, one decimal minute is 1 min 26.4 s and one decimal second is 0.864 s. Decimal midday is 5:00:00. The scheme was officially used only briefly, but it shows how a base-10 clock would work.

Worked example

Default input: standard time 15:00:00 converted to decimal time.

1. Seconds since midnight = 15 × 3,600 = 54,000.
2. f = 54,000 ÷ 86,400 = 0.625 of the day.
3. Decimal seconds = 0.625 × 100,000 = 62,500.
4. 62,500 = 6 × 10,000 + 25 × 100 + 0, so decimal time = 6:25:00.

How to read the result

Read decimal time like a fraction of the day: 6:25 means 62.5% of the day has passed. Midnight is 0:00:00, 6 a.m. is 2:50:00, noon is 5:00:00 and 6 p.m. is 7:50:00. Decimal minutes and seconds run from 00 to 99, so 6:99:99 is followed by 7:00:00.

Common mistakes

• Confusing decimal time with decimal hours for timesheets, where 1:30 is 1.5 hours.
• Entering decimal minutes above 99 or standard minutes above 59.
• Assuming a decimal hour is 60 minutes long.
• Forgetting that the day starts at midnight in both systems.

Frequently asked questions

What time is noon in decimal time?

5:00:00, half of the 10-hour day.

How long is a decimal hour?

2 hours 24 minutes of standard time.

Was decimal time ever really used?

France made it official in 1793, but it was dropped within a couple of years and never caught on.

Sources: Decree of the National Convention on the Republican Calendar (4 Frimaire, Year II / 1793), Article XI