Clock Arithmetic: 12-Hour Clock

It's 9 o'clock. What time is it in seven hours?

Strong Mind Rare & Unusual Maths Maths Games for Kids (6-10) Maths Games for Juniors (11-14)

12-Hour Clock 24-Hour Clock Days of the Week Pure Modulo

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How Clock Arithmetic: 12-Hour Clock works

Clock arithmetic is modular arithmetic wearing a friendly face. On a twelve-hour clock, 9 + 7 is 4, because the numbers wrap around. That is not a quirk of clocks — it is a whole branch of number theory, and it underpins everything from calendars to cryptography.

The days-of-the-week variant is the practical one. Working out what day a date falls on is the same wrap-around calculation, just with a modulus of seven instead of twelve.

This version: The classic wrap-around. Your best score is saved in this browser, so you can come back and try to beat it. Nothing is uploaded and no sign-up is needed.

Frequently asked questions

What does 'modulo' actually mean?

The remainder after division. 16 modulo 12 is 4, which is exactly why four hours after twelve o'clock the clock reads four.

Where is this used outside clocks?

Calendars, musical scales, check digits on card numbers and barcodes, and most modern cryptography. Wrap-around arithmetic is everywhere once you notice it.

Is the 24-hour version harder?

Slightly, because the wrap point is less familiar, but the method is identical.

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