Modulo Calculator
Instantly calculate the remainder and quotient of any division operation. Perfect for modular arithmetic, programming logic, and mathematical problem-solving.
Division Parameters
Enter the dividend and divisor to calculate the modulo
The numerator or the total amount you want to divide (a)
The denominator or the amount you are dividing by (b)
Modulo Analysis
Quotient and remainder breakdown
Enter a dividend and divisor, then click Calculate Modulo to see the step-by-step mathematical breakdown.
Operation Examples
Common examples of the modulo operator (%) used in mathematics and computer science.
| Expression | Dividend | Divisor | Quotient | Remainder |
|---|---|---|---|---|
| 10 % 3 | 10 | 3 | 3 | 1 |
| 25 % 5 | 25 | 5 | 5 | 0 |
| 14 % 4 | 14 | 4 | 3 | 2 |
| 7 % 2 | 7 | 2 | 3 | 1 |
| 100 % 9 | 100 | 9 | 11 | 1 |
Modulo FAQ
Learn more about the modulo operator, modular arithmetic, and its applications in programming.
The modulo operation (often abbreviated as ‘mod’) finds the remainder after division of one number by another. For example, 10 mod 3 equals 1, because 10 divided by 3 is 3 with a remainder of 1.
To calculate the modulo of ‘a’ divided by ‘b’, you perform integer division to find the quotient, multiply the quotient by the divisor, and subtract that result from the original dividend. The formula is: Remainder = a – (b × Quotient).
In many programming languages, the ‘%’ symbol calculates the remainder, which can be negative if the dividend is negative. True mathematical modulo (Euclidean division) always yields a positive remainder. For positive numbers, both operations yield the exact same result.
The modulo operator is widely used in computer science and mathematics. Common applications include determining if a number is even or odd (n % 2), wrapping around arrays (circular buffers), converting units (e.g., seconds to minutes), and generating cyclic patterns or cryptographic algorithms.
Yes, but the result depends on the definition used. In standard programming (like JavaScript or C), the result takes the sign of the dividend (e.g., -10 % 3 = -1). In mathematical modulo (Euclidean), the remainder is always positive and takes the sign of the divisor (e.g., -10 mod 3 = 2). This calculator provides the standard programming remainder.