Modulo Calculator
Instantly compute the remainder of a division operation (A mod B). Analyze the quotient step-by-step and safely handle standard programming modular arithmetic.
[Divisor × Quotient + Remainder] proofThe number being divided.
Cannot be 0.
How Modulo is Used in Programming
The most common use case for modulo. If you modulo any integer by 2 (n % 2) and the remainder is 0, the number is even. If the remainder is 1, it's odd.
return 'Even';
}
When iterating infinitely through a fixed array (like an image carousel), modulo ensures the index loops back to 0 cleanly instead of crashing.
Modulo is essential for stripping hours from minutes, or converting total seconds into a standard digital clock format by finding the remainder.
minutes = Math.floor(total_seconds / 60);
The Negative Modulo Trap
A major gotcha for new developers involves using modulo with negative numbers across different programming ecosystems. Mathematics relies on Euclidean division where remainders are strictly non-negative. However, processor architectures led many compiled languages to use Truncated division instead.
Truncated Division
Javascript, Java, C++, C#
The remainder takes the sign of the Dividend.
Floored Division
Python, Ruby, pure Math
The remainder takes the sign of the Divisor.
Fixing Javascript's Modulo for Negatives
If you are writing JavaScript or C# and need mathematical "wrap-around" behavior (like going backwards in an array), you must write a safe modulo function:
function safeMod(n, m) {
// Solves the negative dividend bug
return ((n % m) + m) % m;
}Frequently Asked Questions
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Help new developers understand the modulo operator and avoid the negative remainder trap in JavaScript.
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