Modulo Calculator

Enter a dividend a and a divisor b. The calculator shows a mod b, the remainder left after dividing, and the floor quotient, how many whole times b fits into a, rounded down.

With the defaults, 17 mod 5 is 2 and the quotient is 3. The two always fit together as a = b × quotient + remainder: 5 × 3 + 2 = 17. That identity is a quick way to check any result, including the negative ones below.

There are two common conventions for the remainder of a negative number, and they give different answers. This calculator uses the mathematical one, sometimes called floored modulo. It computes ((a % b) + b) % b and rounds the quotient down. With a positive divisor, the result is always between 0 and b − 1.

JavaScript's % operator, and its equivalent in C and Java, truncates toward zero, so the remainder takes the sign of the dividend. Python's % gives the same results as this calculator. If you're checking code, make sure you compare against the convention your language uses.

The identity still holds either way: 5 × −4 + 3 = −17. If you type a negative divisor, the result takes the divisor's sign. 17 mod −5 is −3, with a quotient of −4.

• Clock time: 15 hours after 14:00 is (14 + 15) mod 24 = 5, so 05:00 the next day.
• Days of the week: 100 days after a Monday, 100 mod 7 = 2, so two days on: a Wednesday.
• Counting backwards: one hour before 12 on a 12-hour dial is −1 mod 12 = 11. This is where the floored convention earns its keep, since truncated modulo would give −1.
• Odd or even: n mod 2 is 0 for even numbers and 1 for odd ones, negatives included.
• Last digit: 1234567 mod 10 is 7, and the quotient, 123,456, is the number with that digit removed.

When a is smaller than b, the remainder is just a and the quotient 0: 5 mod 17 is 5.

Decimals work: 7.5 mod 2 is 1.5, with a quotient of 3. But numbers like 0.1 can't be stored exactly in binary, which leads to odd results. 0.3 mod 0.1 should be 0, yet the calculator shows 0.1, with a quotient of 2. The stored remainder is a hair under 0.1, and the two-decimal display rounds it up.

To avoid this, scale to whole numbers first. Instead of 0.3 mod 0.1, use 3 mod 1, which is 0. A divisor of 0 shows dashes, since dividing by zero has no remainder.