Education
Mod Calculator
Last updated: June 19, 2026
A mod calculator computes the modulo operation, which returns the remainder after dividing one integer by another. Using the mathematical Euclidean division definition, the remainder is always non-negative and strictly smaller than the absolute value of the divisor. Modulo arithmetic is essential in programming, calendar math, index wrapping, and cryptography.
Compute the modulo (mod) operation of two integers. Get the remainder and division quotient instantly.
Quick Answer
Calculate the modulo (mod) of two integers. Input the dividend and divisor to get the remainder and quotient instantly.
Whole number to divide. · e.g. 17
Cannot be 0. · e.g. 5
Returns the quotient and a non-negative remainder. Dividend = divisor × quotient + remainder.
Quotient and remainder
3 R 2
17 ÷ 5
The calculator returns a non-negative remainder (Euclidean division), so 0 ≤ remainder < |divisor|. The JavaScript % operator gives a different sign for negative dividends.
Examples
17 mod 5
Quotient = 3, Remainder (Mod) = 2
100 mod 7
Quotient = 14, Remainder (Mod) = 2
-7 mod 3 (Euclidean)
Quotient = -3, Remainder (Mod) = 2
How it works
Modulo Arithmetic Rules
The modulo operation computes the remainder from Euclidean integer division. For any integers $a$ and $b$ (where $b \neq 0$):
a mod b = r
where $a = b \times q + r$ and the remainder $r$ satisfies the constraint $0 \le r < |b|$.
To compute standard fractional or long divisions, you can visit our general remainder calculator or use our GCF calculator to find common denominators using Euclidean algorithms.
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Frequently asked questions
In mathematics and computing, the modulo operation returns the remainder or signed remainder of a division, after one number is divided by another. It is written as 'a mod n'. For example, 17 mod 5 is 2.
Modulo division divides a dividend 'a' by a divisor 'n', finds the integer quotient, and returns the leftover remainder. Formally, a = n × q + r, where 0 ≤ r < |n|. The value 'r' is the modulo result.
Yes, for positive numbers. For negative numbers, standard computer programming languages handle the sign differently. In pure math, the modulo operation always yields a non-negative remainder, which is the convention this calculator uses.
Modulo is widely used in computer science for tasks like wrapping indices (circular arrays), checking if a number is even or odd (n mod 2), calculating calendar dates, and cryptographic algorithms.
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