Modulo Calculator
Find the remainder after division
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📚 Examples, Rules & Help
⚡Quick Examples - Try These Calculations
🔍How Modulo Works
What is Modulo?
Modulo (mod) finds the remainder after division.
• The result is always between 0 and |b|-1
• Used in programming, cryptography, and mathematics
Step-by-Step Process
Step 1: Divide a by b using floor division
Step 2: Multiply the quotient by b
Step 3: Subtract from a to get the remainder
Negative Numbers
With negative numbers: Result follows the sign of the divisor
• Different programming languages may handle this differently
• This calculator uses mathematical definition
🌍Real-World Applications
❓Frequently Asked Questions
What's the difference between modulo and remainder?
Mathematically: Modulo and remainder are often the same for positive numbers.
With negatives: They can differ depending on the definition used.
This calculator: Uses the mathematical definition where result has the same sign as the divisor.
Example: -17 mod 5 = 3 (mathematical) vs -2 (some programming languages)
Why can't I divide by zero in modulo?
Modulo is based on division, so dividing by zero is undefined.
There's no meaningful way to find a remainder when you can't divide in the first place.
This is a fundamental mathematical restriction, not just a calculator limitation.
When is the modulo result zero?
The modulo result is zero when the dividend is perfectly divisible by the divisor.
Examples: 15 mod 5 = 0, 100 mod 10 = 0, 64 mod 8 = 0
This means there's no remainder - the division is exact.
How is modulo used in programming?
Common uses in programming:
- Checking if a number is even/odd: n mod 2
- Wrapping array indices: index mod arrayLength
- Creating repeating patterns: frame mod cycleLength
- Hash table bucket selection: hash mod bucketCount
- Time calculations: seconds mod 60 for minutes
What's the range of modulo results?
For positive divisor b, the result is always between 0 and b-1 (inclusive).
Example: n mod 5 can only be 0, 1, 2, 3, or 4
For negative divisor: The result is between b+1 and 0 (inclusive).
This predictable range makes modulo useful for constraining values.
🎯Common Use Cases
💻 Software Development
- • Array circular indexing and bounds checking
- • Hash table bucket calculations
- • Random number generation within ranges
- • Implementing circular buffers and queues
🔐 Security & Cryptography
- • RSA encryption key generation
- • Hash function implementations
- • Digital signature algorithms
- • Cryptographic protocol design
🎮 Game Development
- • Turn-based game rotation
- • Animation frame cycling
- • Random event generation
- • Tile-based world wrapping
📊 Mathematics & Science
- • Number theory research
- • Statistical distribution calculations
- • Physics simulation constraints
- • Mathematical proof verification