Real-Time Modulo Calculator

Calculate modulo operations instantly

Calculate modulo (mod) operations in real-time as you type. Supports negative numbers and decimals. Perfect for programming, mathematics, and cryptography learning.

How to Use

Calculate modulo operations in just 3 steps:

Enter Dividend
Enter the number to be divided (dividend) in the left input field. You can enter negative numbers and decimals.
Enter Divisor
Enter the divisor in the right input field. You can specify any non-zero number.
View Result
The remainder is automatically calculated and displayed in the result section as you type.

All calculations are performed in your browser. No data is sent to our servers.

Modulo Calculator

mod

Result (Remainder)

Practical Uses of Modulo Operations

Modulo operations are used in various programming and mathematical scenarios:

1. Even/Odd Number Detection

If a number modulo 2 equals 0, it's even; if 1, it's odd. Example: 8 mod 2 = 0 (even), 7 mod 2 = 1 (odd). Frequently used for conditional branching in programs.

2. Circular Processing (Round-Robin)

Used to cyclically reference array or list elements. Example: When applying index 5 to a 3-element array, 5 mod 3 = 2, so element at index 2 is referenced.

3. Hash Table Index Calculation

The remainder of dividing a hash function's value by the array size determines where to store data. Example: hash("key") mod 100 distributes data across indices 0-99.

4. Cryptography Applications

Public-key cryptography like RSA uses modulo operations with large prime numbers at its core. Example: C = M^e mod n generates ciphertext C.

5. Time Calculations

Used for 12-hour and 24-hour time format calculations. Example: 8 hours from 15:00 is (15 + 8) mod 24 = 23:00 (11 PM).

What is Modulo Operation

Modulo operation (modulo operation) is an arithmetic operation that finds the remainder when one number is divided by another. In mathematics, it's written as 'a mod n', meaning the remainder when a is divided by n.

Notation

Mathematical notation: a mod n Programming: a % n (in most languages) Example: 17 mod 5 = 2 (remainder when 17 is divided by 5 is 2)

Examples

10 mod 3 = 1 (10 ÷ 3 = 3 remainder 1)
15 mod 4 = 3 (15 ÷ 4 = 3 remainder 3)
20 mod 5 = 0 (20 ÷ 5 = 4 remainder 0, evenly divisible)
7.5 mod 2 = 1.5 (can calculate with decimals)

Mathematical Definition

Modulo operation is defined as follows:

a mod n = a - n × ⌊a ÷ n⌋ ⌊ ⌋ represents the floor function (round down). Example: 17 mod 5 = 17 - 5 × ⌊17 ÷ 5⌋ = 17 - 5 × 3 = 2

Modulo Operations in Programming Languages

In major programming languages, modulo operations can be performed using the % operator or mod function:

JavaScript

// Modulo operation in JavaScript
const result1 = 10 % 3;  // 1
const result2 = -10 % 3; // -1 (be careful with negative numbers)
const result3 = 7.5 % 2; // 1.5

console.log(result1); // Output: 1

Python

# Modulo operation in Python
result1 = 10 % 3  # 1
result2 = -10 % 3 # 2 (Python always returns positive remainder)
result3 = 7.5 % 2 # 1.5

print(result1)  # Output: 1

PHP

<?php
// Modulo operation in PHP
$result1 = 10 % 3;  // 1
$result2 = -10 % 3; // -1
$result3 = fmod(7.5, 2); // 1.5 (use fmod for decimals)

echo $result1; // Output: 1
?>

Java

// Modulo operation in Java
int result1 = 10 % 3;    // 1
int result2 = -10 % 3;   // -1
double result3 = 7.5 % 2; // 1.5

System.out.println(result1); // Output: 1

Modulo Operations with Negative Numbers

Modulo operations involving negative numbers may produce different results depending on the programming language:

Warning: Behavior of modulo with negative numbers varies by language

Behavior by Language

JavaScript, Java, C++: Result follows the sign of the dividend (e.g., -10 % 3 = -1)
Python, Ruby: Result follows the sign of the divisor (e.g., -10 % 3 = 2)
Mathematical definition: Generally returns a value from 0 to n-1

Examples with Negative Numbers

-10 mod 3:
JavaScript: -1
Python: 2
Mathematics: 2

10 mod -3:
JavaScript: 1
Python: -2
Mathematics: 1

Frequently Asked Questions

Is modulo operation the same as division remainder?

Yes, they are fundamentally the same. Modulo operation finds the remainder of a division. However, when dealing with negative numbers, results may differ depending on the programming language.

What happens when dividing by zero?

Mathematically, division by zero is undefined. This tool displays an error message. In programming, it causes an error or exception.

Can I perform modulo operations with decimals?

Yes, this tool supports modulo operations with decimal numbers. Example: 7.5 mod 2 = 1.5. However, some programming languages only support integers.

What is modulo operation used for?

It's used for even/odd detection, circular processing, hash table index calculation, cryptography, time calculations, and many other programming and mathematical scenarios.

How is modulo calculated with negative numbers?

It varies by programming language. JavaScript and Java follow the dividend's sign, while Python follows the divisor's sign. Mathematically, it typically returns a positive value from 0 to n-1.

What's the difference between modulo and division?

Division finds the quotient (how many times it divides), while modulo finds the remainder (the indivisible part). Example: 17 ÷ 5 = 3 (quotient), 17 mod 5 = 2 (remainder).

How precise is this tool's calculation?

This tool uses a high-precision calculation library (Decimal.js), providing higher accuracy than standard floating-point arithmetic. You get accurate results even with large numbers or decimals.

Is my input data saved?

No, all calculations are performed in your browser and no data is sent to servers. Your input numbers are never stored, ensuring complete privacy protection.