Modulo Calculator

What This Calculator Does

Modulo is just the remainder after division. $17 \bmod 5$ asks “divide 17 by 5 - what is left over?” Since 5 goes into 17 three times (15), with 2 to spare, $17 \bmod 5 = 2$.

It is how clocks work: 15 o’clock is 3 PM because $15 \bmod 12 = 3$. Programmers reach for it constantly - to check if a number is even ($n \bmod 2$), to wrap a value around, or to sort things into a fixed number of buckets.

How It Works

$$a \bmod b = a - b \left\lfloor \frac{a}{b} \right\rfloor$$

How to Use It

1. Enter the dividend a and the divisor b.
2. Read the remainder.

Worked Examples

a	b	a mod b
17	5	2
100	7	2
24	8	0
9	4	1

FAQ

What is the modulo operation?

It returns the remainder of a division. $17 \bmod 5 = 2$, because 5 goes into 17 three times with 2 left over.

What is modulo used for?

Clock and cyclic arithmetic, checking whether a number is even or odd ($n \bmod 2$), and looping through a fixed set of items.

How are negative numbers handled?

The result follows the sign of the dividend a, as it does in most programming languages.