Modulo Calculator

Below is a modulo calculator, which will return the remainder as the result of division, or the modulo or mod number.

Modulo Calculator

What is a Remainder? How does it relate to Modular Arithmetic?

A remainder is the extra amount when you do division and the divisor doesn't divide a divisor equally. If the division is equal, the remainder is 0.

Here's an illustration of division with remainders:

\frac{x}{y}=q+r

And in the equation:

• x: the divisor or number we will divide by y
• y: the dividend, the number of times to divide x
• q: the quotient, or the whole number times y could divide b
• r: the remainder or left over number from dividing x by y

In modular arithmetic, you "wrap around" a number, so the remainder is the final answer and you discard the quotient.

For example, if you divide 14 by 5, you get 2 plus a remainder of 4. But we would say:

14\ mod\ 5=4

Sometimes modulo operations are written like this:

14\ \%\ 5=4

Using the Modulo Calculator

To use the module calculator, enter a Dividend and a Divisor. Then, hit the Compute Remainder button.

You'll next see the Quotient and Remainder box fill with the results of the division. The result of the mod math is the Remainder.

Afterwards, see our other tools. Or, see the closely related remainder calculator.