Modulo Calculator

What Is a Modulo Calculator?

A modulo calculator determines the remainder left after one number is divided by another. The modulo operation is commonly written as a mod b or a % b. For example, 17 divided by 5 is 3 with a remainder of 2, so 17 mod 5 equals 2.

Modulo calculations are useful in mathematics, programming, computer science, number theory and everyday calculations involving repeating cycles or remainders. This calculator provides a quick way to calculate the result without performing the division manually.

Why Use Modulo Calculator?

This free modulo calculator makes it simple to find the remainder between two numbers while clearly displaying the calculation used to produce the result.

How to Use Modulo Calculator

Enter the two numbers involved in the division and calculate the remainder directly in your browser.

1. Enter a Dividend — Enter the number you want to divide.
2. Enter a Divisor — Enter the number by which the dividend should be divided. The divisor must not be zero.
3. Calculate the Result — Click Calculate Modulo or press Enter from either input field.
4. Review the Result — View the remainder, calculation and division quotient.

How to Calculate Modulo

The modulo operation finds the remainder after division. It is commonly written as a mod b = r, where a is the dividend, b is the divisor and r is the remainder. For example, 23 mod 7 equals 2 because 23 divided by 7 gives a quotient of 3 with 2 left over.

The relationship between division and modulo can be expressed as a = bq + r, where q is the quotient and r is the remainder. For example, 29 = 6 × 4 + 5, so 29 mod 6 equals 5.

Modulo Examples

Some simple modulo examples include 10 mod 3 = 1, 20 mod 4 = 0, 15 mod 7 = 1 and 100 mod 9 = 1. When the dividend divides evenly by the divisor, the modulo result is zero because there is no remainder.

Modulo in Mathematics and Programming

Modulo is widely used in programming and computer science for operations involving repeating patterns, cycles and divisibility. It can be used to determine whether a number is even or odd, rotate through a fixed range of values, or identify the remainder when distributing items into equal groups.

Understanding Modulo Results

The modulo result represents the remainder after the division operation. If the dividend divides exactly by the divisor, the result is zero. For example, 24 mod 6 equals 0 because 24 is evenly divisible by 6.

The divisor cannot be zero because division and modulo by zero are undefined. This calculator accepts finite numeric values, including decimals and scientific notation, and performs the calculation directly in the browser using JavaScript numeric arithmetic.

Frequently Asked Questions