Modulo Calculator (Division Remainder)
Fast, accurate and free online modulo reszta from dzielenia calculator tool running directly in your browser.
-
1Enter data
Enter content, paste text or load a file from disk. -
2Click the button
The tool will immediately process your data in the browser. -
3Get the result
Copy the finished text or save the file to your device.
return "Result ready in 0.1s";
}
Rate this tool:
Related tools
Other tools you may find usefulModulo calculator - remainder of division with explanation
The modulo (%) operation returns the remainder of division. 17 mod 5 = 2 because 17 = 3 × 5 + 2. The calculator calculates the remainder of division for integers and real numbers, explaining step by step - useful in mathematics, programming and number theory.
Definition of modulo operation
a mod n = r, where a = q × n + r, 0 ≤ r < n. a: dividend, n: divisor (modulus), q: total quotient, r: remainder. Examples: 17 mod 5 = 2 (17 = 3×5+2). 20 mod 4 = 0 (20 = 5×4+0). 7 mod 10 = 7. 100 mod 7 = 2. Sign of the remainder: always non-negative in mathematics. In programming: depends on the language (Python vs C++).
Modulo in programming
Python: % operator. 17 % 5 = 2. Negative: -7 % 3 = 2 (Python rounds down). JavaScript: % is remainder (not modulo!). -7 % 3 = -1 (JS). True modulo in JS: ((a % n) + n) % n. Java: % as C (sign matches dividend). C/C++: % (sign matches dividend). PHP: fmod() for floating point. SQL: MOD(a,n) or a%n (MySQL).
Uses modulo
Cyclicity: (i+1) % n – wrap around in an array. Even/Odd: if(n%2==0). Last digit: n%10. Sum of digits: loop with %10 and /10. Hashing: index = hash%tableSize. Time: 26 hours → 26%24=2. Day of the week. Caesar Cipher: (c+shift)%26. RSA: a^e mod n. Checksums (ISBN, IBAN): verification by modulo.
Modulo for floating-point numbers
Python: 7.5 % 2.5 = 0.0. math.fmod(7.5, 2.5) = 0.0. PHP: fmod(7.5,2.5). C/C++: fmod(). JavaScript: 7.5% 2.5 = 0.0. Note: floating point inaccuracies: 1.5% 0.1 may give 0.0999... instead of 0.0. For finance: use whole numbers (cents instead of dollars). Pure math: modulo for reals defined by a - floor(a/n)*n.
FAQ
How to calculate modulo manually?
Step 1: calculate the total quotient: q = floor(a/n). Step 2: remainder = a - q×n. Example: 23 mod 7. q = floor(23/7) = floor(3.28...) = 3. Remainder = 23 - 3×7 = 23 - 21 = 2. Check: 3×7+2 = 23. ✓ Negative: -13 mod 5. q = floor(-13/5) = floor(-2.6) = -3. Remainder = -13 - (-3)×5 = -13+15 = 2.
How does modulo help check divisibility?
If a mod n = 0, then a is divisible by n. Divisibility by 2: n%2==0. By 3: sum of digits divisible by 3 (or n%3==0). By 9: sum of digits divisible by 9. By 10: last digit = 0. By 5: last digit 0 or 5. Algorithm: for(int i=2; i<=sqrt(n); i++) { if(n%i==0) { isPrime=false; break; } }
What is modular arithmetic?
Modular arithmetic: number operations modulo n. 12-hour clock: mod 12. Addition: (a+b) mod n. Multiplication: (a×b) mod n. Subtraction: (a-b+n) mod n. Caesar cipher: encrypt(c) = (c-'a'+shift)%26+'a'. Fermat: a^(p-1) ≡ 1 (mod p) for the first p. RSA: encryption = M^e mod n. Cryptography is modulo difficulty based.
What is the difference between modulo and remainder?
Mathematical modulo: the result is always non-negative (0 ≤ r < |n|). Remainder: a character that matches the dividend or divisor (language dependent). Difference with negative: Python: -7 % 3 = 2 (modulo). C/Java/JS: -7 % 3 = -1 (remainder). When it matters: When you're working with negative numbers. For non-negatives: identical. For cryptography you always want true modulo.
How does the modulo hash function work?
Hashing by modulo: index = hash(key) % tableSize. Example: hash("hello") = 99162322, tableSize = 10 → index = 2. Collision problem: two keys → same index. Solution: chaining (list in buffer) or open addressing. Good array size: first larger than the data. Example: 100 elements → tableSize = 127 (first). Python dict: automatically manages.
Related tools: division calculator, GCD and NWW calculator and prime number calculator.