Modulo Calculator

Dividend (a)

The number to be divided

Divisor (n)

The number to divide by

Negative Handling

Number to Check

Check Range

Mode

Divisor (n)

Dividends (one per line or comma separated)

Divisor (n)

Start Value

End Value

Highlight Remainder

Common Applications

Clock arithmetic (12-hour) → mod 12

Day of week → mod 7

Even/Odd check → mod 2

Last digit of number → mod 10

Byte overflow (8-bit) → mod 256

Leap year check → mod 4, 100, 400

Divisible by 2 Last digit is even (0,2,4,6,8)

Divisible by 3 Sum of digits divisible by 3

Divisible by 4 Last 2 digits divisible by 4

Divisible by 5 Last digit is 0 or 5

Divisible by 6 Divisible by both 2 and 3

Divisible by 9 Sum of digits divisible by 9

Divisible by 10 Last digit is 0

Addition: (a + b) mod n = ((a mod n) + (b mod n)) mod n

Subtraction: (a - b) mod n = ((a mod n) - (b mod n)) mod n

Multiplication: (a × b) mod n = ((a mod n) × (b mod n)) mod n

Identity: a mod n = a, if 0 ≤ a < n

Periodicity: (a + n) mod n = a mod n

JavaScript / Java / C++ a % n

Python a % n

Excel / Sheets =MOD(a, n)

SQL a MOD n or a % n

Ruby a % n or a.modulo(n)

Understanding Modulo

What Is Modulo?

The modulo operation finds the remainder after division of one number by another.

Written as: a mod n or a % n
Result is always 0 to n-1
17 mod 5 = 2 (17 = 5×3 + 2)
Used extensively in programming

Division Relationship

Modulo is related to integer division through the formula:

a = n × q + r
q = quotient (integer part)
r = remainder (modulo result)
0 ≤ r < n (for positive n)

Negative Numbers

Different conventions exist for negative numbers:

Truncated: sign matches dividend
Floored: sign matches divisor
Euclidean: always non-negative
Languages differ in behavior