A Clock (Modular) Arithmetic Renaming Calculator

Here is a calculator for finding different "names" of a whole number on a clock with a given number of hours. (In mathematical terminology, it finds congruent integers for a given modulus.) If this doesn't make any sense to you, here's an explanation of what clock arithmetic is, with an interactive clock that shows the different names for a number on a clock in another way.

If you don't have a java-enabled browser, you won't be able to see this applet.


  1. Type the number you want another name for in the first box.
  2. Type the number of hours on the clock you want to use in the second box (after "mod").
  3. Click the "=" button to get the smallest nonnegative "name" for the first number on the clock.
  4. If you want a bigger name, click the "up" button. If you want a smaller name, click the "down" button.

Problems? Got an "E"?

Technical Comments

Original Web Site by Susan Addington