17 mod 5 = 2. Dividing 17 by 5 gives a quotient of 3 with a remainder of 2, because 17 = 5 * 3 + 2.

How does modulo work with negative numbers?

It depends on the convention. Math modulo (floored division) always returns a non-negative result in [0, |b|), so -7 mod 3 = 2. C-style modulo (truncated division) follows the sign of the dividend, so -7 % 3 = -1. This calculator shows both.

How do I calculate modulo by hand?

To compute a mod b: (1) divide a by b, (2) take the integer quotient (floor for math, truncate for C-style), (3) multiply the quotient by b, (4) subtract from a. The result is the remainder.

What is the difference between mod and remainder?

In everyday use they are synonyms, but technically 'remainder' often refers to the C-style truncated result, while 'modulo' often refers to the math-style floored result. They agree for positive operands and only differ when exactly one operand is negative.

Can modulo be used with decimals?

Yes. a mod b is defined for real numbers as a - b * floor(a/b). For example, 5.5 mod 2 = 1.5. Floating-point modulo is common in angle wrapping (theta mod 360) and phase calculations.

What is modular arithmetic used for?

Modular arithmetic underpins cryptography (RSA, Diffie-Hellman), hashing, checksums, clock arithmetic, pseudo-random number generation, and cyclic data structures like ring buffers.

Modulo Calculator

The modulo operation returns the remainder of a division. For positive numbers everyone agrees: 17 mod 5 = 2. But for negative numbers, languages and mathematicians diverge. The mathematical convention defines a mod b so the result is always in the range [0, |b|) — so -7 mod 3 = 2. The C/Go/JavaScript convention uses truncated division, so the remainder takes the sign of the dividend — meaning -7 % 3 = -1. This calculator shows both so you can pick the one your domain expects. It also supports floating-point moduli (used in angle wrapping, clock arithmetic, and signal processing) and explains each step of the calculation.

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percent a mod b

Dividend (a)

The number being divided. Integers or decimals, positive or negative.

Divisor (b)

The modulus. Must be non-zero.

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Modulo (math, floored)

Always in range [0, |b|)

Remainder (C-style, truncated) 2

Sign follows dividend. Matches C, C++, Go, Java, JavaScript (%).

Quotient (floor)

Quotient (trunc)

Step by step

tips_and_updates Tips

• Use math modulo (floored) for modular arithmetic, hashing, and angle wrapping
• Use C-style modulo (truncated) when matching behavior of C, C++, Go, Java, or JavaScript
• For positive a and b the two conventions agree, so the distinction only matters with negatives
• Modulo by zero is undefined — the divisor must be non-zero
• Python's % operator uses math (floored) modulo: -7 % 3 = 2

The Formula

Math modulo uses floor division so the remainder is always 0 <= r < |b|. C-style modulo uses truncated division so the remainder has the same sign as the dividend.

r = a - b * q, where q = floor(a/b) (math) or trunc(a/b) (C-style)

lightbulb Variables Explained

a Dividend (the number being divided)
b Divisor (the modulus)
q Quotient (floored or truncated)
r Remainder / modulo result

tips_and_updates Pro Tips

Use math modulo (floored) for modular arithmetic, hashing, and angle wrapping

Use C-style modulo (truncated) when matching behavior of C, C++, Go, Java, or JavaScript

For positive a and b the two conventions agree, so the distinction only matters with negatives

Modulo by zero is undefined — the divisor must be non-zero

Python's % operator uses math (floored) modulo: -7 % 3 = 2

Frequently Asked Questions

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The Formula

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