Modulo Calculator
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About Modulo Calculator
A free modulo calculator for calculating the modulo of a divided by n. It supports integers, decimals, negative numbers, and scientific notation, and displays all modulo steps.
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Frequently Asked Questions
What is the modulo operation?
The modulo operation traditionally refers to the non-negative remainder after dividing an integer a by a positive integer n. However, in computer science and advanced mathematics, this range is extended to any real number (including decimals and negative numbers), with the only rule being that the modulus n can never be 0.
a mod n = a - n × ⌊a/n⌋, where ⌊a/n⌋ represents the largest integer less than or equal to a/n.
For example:
- 5.5 mod 2 = 5.5 − 2 × ⌊2.75⌋ = 5.5 − 2 × 2 = 1.5
- -7 mod 3 = -7 - 3 × ⌊-2.333... ⌋ = -7 - 3 × (-3) = 2
How to use the modulo calculator?
Enter the modulo operator (% or mod) in the input box to calculate your modulo problem. For example, 17 mod 5. Click "Solve" for an explanation of the modulo steps.
What is the difference between modulo and remainder?
For positive numbers, modulo and remainder are the same. For negative numbers, there are different rules. For example, -7 divided by 3: the remainder is -1, and the modulo result is 2. For positive numbers, such as 7 divided by 3, both results are 1.
What is the remainder when 7 is divided by 5?
The remainder when 7 is divided by 5 is 2.
What is the remainder when 3 is divided by 4?
The remainder when 3 is divided by 4 is 3.
