Admissions Open for 2025-26

Mod Calculator - a powerful tool designed for calculating the modulus operation. Whether you're a student studying mathematics or a programmer working with modular arithmetic, our Mod Calculator simplifies the process of finding remainders after division.

The Mod Calculator is a specialized tool for performing modular arithmetic, commonly denoted as *'a mod n'* It calculates the remainder when an integer 'a' is divided by another integer 'n', providing a crucial operation in various mathematical and programming contexts.

Mod Calculators help to find remainders easily when dividing numbers, crucial in programming for tasks like looping through elements or handling periodic events. It simplifies modular arithmetic calculations and is handy for various applications in math and computer science.

To use a Mod Calculator, enter two numbers and select the *'mod'* or *'%'* function. The result will show the remainder when the first number is divided by the second, useful for tasks like programming or solving modular arithmetic problems.

The calculator employs the following formula for modular arithmetic:

`a mod n = a − n ⋅ ⌊a/n⌋`

This formula ensures an efficient and accurate calculation of the modulus operation.

**Note** : The convention of using "." for multiplication in mathematics, rather than "x," ensures clarity and avoids confusion with the variable "x."

Example 1:

a: 17

n: 15

Calculation:

17 mod 5 = 17- 5 ⋅ ⌊17/5⌋

17 mod 5 = 17 - 5 ⋅ 3

17 mod 5 = 2

Example 2:

a: 28

n: 6

Calculation:

28 mod 6 = 28 - 6 ⋅ ⌊28/6⌋

28 mod 6 = 28 - 6 ⋅ 4

28 mod 6 = 4

Example 3:

a: 10

n: 3

Calculation:

10 mod 3 = 10 - 3 ⋅ ⌊10/3⌋

10 mod 3 = 10 - 3 ⋅ 3

10 mod 3 =1

Modular arithmetic is commonly used in programming for tasks such as hashing, cryptography, and handling periodic phenomena like days of the week.

Yes, the calculator accommodates negative integers, providing accurate results for the modulus operation.

Yes, in many cases, the modulus operation is equivalent to finding the remainder in standard division. However, the key difference lies in the treatment of negative numbers.