Find the modulo result for two whole numbers and see how the quotient and remainder produce the answer.
29 mod 5 = 4 because 29 = 5 × 5 + 4. The modulo result is the remainder after whole-number division.
Using the Euclidean convention, the remainder is always from 0 to 4.
- Divide 29 by 5.
- Use the whole quotient 5.
- Write 29 = 5 × 5 + 4.
- The modulo result is the remainder, so 29 mod 5 = 4.
Embed Modulo Calculator
Copy this iframe code into a page that permits embeds.
All calculations run locally in your browser. Your number input is not sent to an external service.
How to Use the Modulo Calculator
Enter the dividend and a positive modulus. The calculator divides the dividend by the modulus, keeps the whole quotient, and returns the remainder.
- Enter the dividend.
- Enter a positive modulus.
- Read the remainder as the modulo result.
Modulo Formula
The modulo operation uses the remainder from division.
Euclidean Remainder Convention
This calculator returns a nonnegative remainder for a positive modulus. That is the common math convention and is useful for cycles, clocks, and number patterns.
Modulo Examples
29 mod 5
29 = 5 × 5 + 4, so 29 mod 5 = 4.
42 mod 7
42 = 7 × 6 + 0, so 42 mod 7 = 0.
-13 mod 5
-13 = 5 × -3 + 2, so the Euclidean modulo result is 2.
Common Modulo Mistakes
Using a zero modulus
The modulus cannot be zero because division by zero is undefined.
Mixing math and programming conventions
Some programming languages handle negative numbers differently. This calculator states its Euclidean convention clearly.
Confusing quotient and remainder
The modulo answer is the remainder, not the whole-number quotient.
Modulo Calculator FAQs
What does mod mean?
Mod means the remainder after dividing one number by another.
What is 29 mod 5?
29 mod 5 is 4 because 29 = 5 × 5 + 4.
Why is 42 mod 7 equal to 0?
42 divides evenly by 7, so the remainder is 0.
Related SolverCalc tools
Reviewer
This educational math content is reviewed under the SolverCalc reviewer rule by Prof. Dr. Khalil Mudassar. WordPress adds the author bio automatically, so this page does not include a duplicate author box.
Keep solving with SolverCalc
Use number theory tools to move from remainders to divisibility, factors, and prime checks.
Sources
View mathematical references
Disclaimer
This calculator is intended for general educational and practical use. Check class, textbook, or programming-language rules when an assignment defines a different convention.