Compute a mod n — negatives handled correctly, every convention shown
Inputs
Convention
Result
-13 mod 5 =
2
All conventions at a glance
| Convention | Quotient (q) | Remainder (r) |
|---|---|---|
| Floored | -3 | 2 |
| Truncated | -2 | -3 |
| Euclidean | — | 2 |
Verify: a = q × n + r
Floored: -3 × 5 + 2 = -13✓
Truncated: -2 × 5 + -3 = -13✓
Quick Examples
The modulo operation finds the remainder after dividing one number by another, but the result differs depending on how negative numbers are handled. This free modulo calculator computes a mod n using three conventions: floored (Python, Ruby), truncated (JavaScript, C, Java), and Euclidean (always non-negative). Enter any integers — positive or negative — and get instant, verified results across all conventions.
Python uses floored division, so the remainder always has the same sign as the divisor (n). JavaScript uses truncated division, so the remainder takes the sign of the dividend (a). For −13 mod 5: Python gives 2, while JavaScript gives −3.
Use floored (Python-style) for most mathematical work and clock/cyclic arithmetic since the result is always in [0, n−1] when n > 0. Use truncated when matching JavaScript, C, or Java behavior. Use Euclidean when you need a guaranteed non-negative result regardless of the signs of both inputs.
Yes — the same conventions apply to decimal numbers. For example, 5.5 mod 2.5 gives 0.5. This calculator supports any finite real number for both the dividend and modulus.
The Euclidean remainder is always non-negative. It is computed as a % |n|, then if the result is negative, |n| is added. This ensures the result lies in the range [0, |n|) regardless of the signs of a or n, satisfying the property that a = q × |n| + r with r ≥ 0.