Modulo Calculator

Calculate the remainder of division (modulo operation). Modulo calculator with explanations for modular arithmetic.

Last revised 25 August 2026

By Team GlobalCalqulate · About our editorial standards

Inputs

Dividend (a)

The number being divided.

Divisor (b)

The number you're dividing by (cannot be 0).

Remainder (a mod b)

17 mod 5 = 2

Dividend (a)

Divisor (b)

Quotient (floor)

Truncated Quotient

Verification

3 × 5 + 2 = 17

Methodology

Formula:: Euclidean remainder
Content last updated:: August 2026
Scheduled re-verification:: August 2027

Calculation type: Exact calculation.

How to Use This Calculator

Enter Numbers

Input the dividend (a) and divisor (b).

See Remainder

The modulo operation returns the remainder after division.

Formula & methodology

Formula used

Euclidean remainder

r = ((a mod |b|) + |b|) mod |b|

The remainder is always non-negative and smaller than the divisor's absolute value, whatever the signs of a and b.

Quotient

q = (a − r) ÷ b

Derived from the remainder so that q × b + r equals a exactly for every combination of signs.

Variable definitions

Symbol	Meaning	Unit
a	Dividend. the number being divided	number
b	Divisor. the number to divide by; cannot be zero	number

Step-by-step calculation

1. Enter the dividend and divisor
Both may be negative.
2. Check the verification line
It restates quotient × divisor + remainder so you can confirm the identity holds.

Limitations

Uses the Euclidean convention, in which the remainder is never negative. JavaScript's own % operator does not: it gives −7 % 3 = −1 where this returns 2.
Division by zero is undefined and is reported as an error.
Operates on values held as double-precision numbers, so very large integers lose precision.

This page is educational. It applies the formula described above to the figures you enter and shows the arithmetic behind the result. The output is only as good as the inputs and the assumptions listed here, and it is general information rather than advice about your particular situation.

Help & FAQs

Frequently Asked Questions

Clear answers to common questions to help you use this calculator confidently.

What does modulo mean?

Tap to view the answer

Modulo (a mod b) returns the remainder when a is divided by b. 17 mod 5 = 2 because 17 = 3 × 5 + 2. The result is always between 0 and b−1 for positive b.

What is modulo used for?

Tap to view the answer

Modulo checks divisibility (even/odd), wraps numbers in ranges (clock arithmetic), powers checksums, cryptography (RSA), and cyclic operations in programming.

What happens with a negative dividend, like -7 mod 5?

Tap to view the answer

This calculator always returns a non-negative remainder for a positive divisor: -7 mod 5 = 3, because -7 = -2 × 5 + 3. The quotient shown (-2) is the floor of -7/5, so quotient × divisor + remainder always equals the original dividend.

Can the divisor be zero?

Tap to view the answer

No — division by zero is mathematically undefined, so the calculator returns an error instead of a result when the divisor is 0.

How is modulo different from regular division?

Tap to view the answer

Regular division gives a quotient (how many times b fits into a) and possibly a decimal. Modulo gives only the leftover remainder as a whole number — the part that doesn't divide evenly.

Need more help? Contact support or email globalcalqulate@gmail.com

We typically reply within 24–48 hours.

More everyday calculators

All everyday calculators

Understanding Your Results

What is Modulo?
a mod b returns the remainder when a is divided by b. Example: 17 mod 5 = 2 because 17 = 3 × 5 + 2. The remainder is always non-negative when the divisor is positive. In programming, % is the modulo operator: 17 % 5 = 2.
Uses of Modulo
Modular arithmetic is used in: clock math (14:00 mod 12 = 2 PM), check-digit algorithms (ISBN, credit card numbers), cryptography (RSA encryption), hash functions, cyclic patterns, and determining even/odd (n mod 2 = 0 means even).

Understanding Modular Arithmetic

What Is Modular Arithmetic?

Modular arithmetic is a system where numbers 'wrap around' after reaching a certain value — the modulus. Think of a 12-hour clock: 14:00 is 2 PM because 14 mod 12 = 2. This wrap-around behavior makes modular arithmetic essential for cryptography (RSA, Diffie-Hellman), hash functions, checksums (ISBN-10, credit card Luhn algorithm), and pseudo-random number generation.

Properties of Modulo

Key properties: (a + b) mod m = ((a mod m) + (b mod m)) mod m. (a × b) mod m = ((a mod m) × (b mod m)) mod m. These properties are crucial for efficient computation in cryptography where numbers can have hundreds of digits. The result a mod b is always in the range [0, b−1] for positive b.

Formula & methodology

Formula used

Euclidean remainder

r = ((a mod |b|) + |b|) mod |b|

The remainder is always non-negative and smaller than the divisor's absolute value, whatever the signs of a and b.

Quotient

q = (a − r) ÷ b

Derived from the remainder so that q × b + r equals a exactly for every combination of signs.

Variable definitions

Symbol	Meaning	Unit
a	Dividend. the number being divided	number
b	Divisor. the number to divide by; cannot be zero	number

Step-by-step calculation

1. Enter the dividend and divisor
Both may be negative.
2. Check the verification line
It restates quotient × divisor + remainder so you can confirm the identity holds.

Limitations

Uses the Euclidean convention, in which the remainder is never negative. JavaScript's own % operator does not: it gives −7 % 3 = −1 where this returns 2.
Division by zero is undefined and is reported as an error.
Operates on values held as double-precision numbers, so very large integers lose precision.

Modulo Calculator

Inputs

Methodology

How to Use This Calculator

Formula & methodology

Formula used

Euclidean remainder

Quotient

Variable definitions

Step-by-step calculation

Limitations

Frequently Asked Questions

What does modulo mean?

What is modulo used for?

What happens with a negative dividend, like -7 mod 5?

Can the divisor be zero?

How is modulo different from regular division?

More everyday calculators

Inputs

Methodology

How to Use This Calculator

Example: 17 mod 5

Understanding Your Results

Key Tips

Understanding Modular Arithmetic

What Is Modular Arithmetic?

Properties of Modulo

Formula & methodology

Formula used

Euclidean remainder

Quotient

Variable definitions

Step-by-step calculation

Limitations

Example: 17 mod 5

Understanding Your Results

Key Tips

Understanding Modular Arithmetic

What Is Modular Arithmetic?

Properties of Modulo

Calculator inputs

Inputs

Your results

Methodology

How to Use This Calculator

Formula & methodology

Formula used

Euclidean remainder

Quotient

Variable definitions

Step-by-step calculation

Limitations

What does modulo mean?

What is modulo used for?

What happens with a negative dividend, like -7 mod 5?

Can the divisor be zero?

How is modulo different from regular division?

Related calculators

More everyday calculators

Calculator inputs

Inputs

Your results

Methodology

How to Use This Calculator

Example: 17 mod 5

Understanding Your Results

Key Tips

Understanding Modular Arithmetic

What Is Modular Arithmetic?

Properties of Modulo

Formula & methodology

Formula used

Euclidean remainder

Quotient

Variable definitions

Step-by-step calculation

Limitations

Example: 17 mod 5

Understanding Your Results

Key Tips

Understanding Modular Arithmetic

What Is Modular Arithmetic?

Properties of Modulo