Modulo Calculator – Find Remainder
Calculate the remainder of division (modulo operation).
Table of Contents
How to Use
- Enter the dividend (the number to be divided)
- Enter the divisor (the number to divide by)
- Click calculate to find the remainder
- View the quotient and formula breakdown
What is the Modulo Operation?
The modulo operation (often abbreviated as 'mod') finds the remainder after division of one number by another. For example, 17 mod 5 = 2 because 17 divided by 5 equals 3 with a remainder of 2.
The formula is: a mod b = a - b × floor(a/b), where floor() rounds down to the nearest integer.
Common Applications
The modulo operation has many practical applications:
- Determining if a number is even or odd (n mod 2)
- Wrapping values around (like clock arithmetic)
- Hash functions and data structures
- Cryptography and encryption algorithms
- Checking divisibility
- Cycling through arrays or lists
Modulo with Negative Numbers
When dealing with negative numbers, different programming languages may handle modulo differently. This calculator uses the mathematical definition where the result has the same sign as the divisor.
For example: -17 mod 5 = 3 (mathematical definition), but some languages return -2.
Frequently Asked Questions
- What is the difference between modulo and remainder?
- In mathematics, modulo and remainder are often used interchangeably. However, they can differ with negative numbers. The modulo result typically has the same sign as the divisor, while the remainder has the same sign as the dividend.
- Why can't I divide by zero?
- Division by zero is undefined in mathematics. The modulo operation requires division, so the divisor cannot be zero.
- How is modulo used in programming?
- Modulo is commonly used to check if numbers are even/odd, cycle through array indices, implement circular buffers, and in cryptographic algorithms. Most programming languages use the % operator for modulo.
- What is clock arithmetic?
- Clock arithmetic is a common example of modular arithmetic. On a 12-hour clock, 14:00 becomes 2:00 because 14 mod 12 = 2. This wrapping behavior is the essence of modular arithmetic.