What is a Modulo Calculator?
A modulo calculator is a mathematical tool that computes the remainder when one number (the dividend) is divided by another number (the divisor). The modulo operation, represented by the % symbol in many programming languages, finds the remainder after division.
When to Use a Modulo Calculator
The modulo operation has various practical applications:
- In computer programming for implementing cyclic behavior, such as generating random numbers within a range
- For checking if a number is odd or even (n % 2 = 0 for even numbers)
- In cryptography and hash functions to ensure values fall within specific ranges
How to Calculate Modulo
The modulo operation follows this formula:
a mod b = a - b × floor(a ÷ b)
Where:
- a is the dividend (the number being divided)
- b is the divisor (the number dividing a)
- floor(x) rounds x down to the nearest integer
For integers, the modulo is simply the remainder after division. For decimal numbers, we first calculate the quotient, round it down to the nearest integer, and then find the remainder.
Examples
Example 1: Basic Integer Modulo
Find the result of 17 mod 5
| Dividend (a) | Divisor (b) | Calculation | Result |
|---|---|---|---|
| 17 | 5 | 17 - 5 × floor(17 ÷ 5) = 17 - 5 × 3 = 17 - 15 | 2 |
Example 2: Negative Dividend
Find the result of -13 mod 4
| Dividend (a) | Divisor (b) | Calculation | Result |
|---|---|---|---|
| -13 | 4 | -13 - 4 × floor(-13 ÷ 4) = -13 - 4 × (-4) = -13 + 16 | 3 |
Example 3: Decimal Numbers
Find the result of 7.5 mod 2.2
| Dividend (a) | Divisor (b) | Calculation | Result |
|---|---|---|---|
| 7.5 | 2.2 | 7.5 - 2.2 × floor(7.5 ÷ 2.2) = 7.5 - 2.2 × 3 = 7.5 - 6.6 | 0.9 |
Related Calculators
Explore other mathematical calculators that might be useful for your calculations:
- Remainder Calculator - Find the remainder after division
- GCF Calculator - Calculate the greatest common factor of numbers
- LCM Calculator - Find the least common multiple of numbers