Modulo Calculator
Calculate the remainder of a division (A mod B) instantly.
Recommended Books on Mathematics & Number Theory
Concrete Mathematics
Ronald L. Graham
Discrete Mathematics and Its Applications
Kenneth H. Rosen
Elementary Number Theory
David M. Burton
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How to Use the Modulo Calculator
Enter the Dividend
Type the number you want to divide (A) into the first field.
Enter the Divisor
Type the number to divide by (B) into the second field.
Read the Result
The remainder (A mod B) is calculated instantly and displayed below.
Use Cases
Check Even or Odd
"Use N mod 2. If the result is 0, the number is even; otherwise it's odd."
Clock Arithmetic
"Calculate what time it will be after a given number of hours: (current + hours) mod 12."
Cyclic Patterns
"Determine position in repeating cycles, like days of the week: dayNumber mod 7."
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Frequently Asked Questions
?What is the modulo operation?
The modulo operation finds the remainder after dividing one number by another. For example, 17 mod 5 = 2, because 17 ÷ 5 = 3 remainder 2.
?What happens when I divide by zero?
Division by zero is undefined. The calculator will show an error if you enter 0 as the divisor.
?Does this work with negative numbers?
Yes. This calculator always returns a non-negative remainder, following the mathematical convention.
?What is modulo used for in programming?
Modulo is used for checking divisibility, cycling through arrays, hashing, formatting output, and many algorithmic problems.
?What is the difference between mod and remainder?
In most contexts they are the same. However, for negative numbers, some languages define remainder differently from the mathematical modulo. This tool uses the mathematical definition.
?Is my data private?
Yes. Everything runs locally in your browser. No data is sent to any server.
?Is this tool free?
Yes. Completely free with no limits, no sign-up required.