Last updated: August 1, 2026
Modulo Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
The Modulo Calculator divides a dividend by a divisor and returns the remainder using the truncated (JavaScript-style) convention along with the truncated integer quotient.
Enter a dividend and a divisor, and the calculator returns the remainder and quotient of that division.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
remainder = dividend mod divisor; quotient = trunc(dividend / divisor)
Where:
- a=Dividend
- n=Divisor
Worked Examples
Simple remainder
Divide 17 by 5.
- 15 fits into 17 three times (15)
- 217 - 15 leaves a remainder of 2
- 3Quotient is 3
Exact division
Divide 20 by 4.
- 14 fits into 20 exactly five times
- 2No remainder is left
- 3Quotient is 5
Negative dividend
Divide -17 by 5.
- 1JavaScript-style modulo keeps the sign of the dividend
- 2-17 mod 5 = -2
- 3Quotient truncates toward zero to -3
Divisor larger than dividend
Divide 3 by 8.
- 18 does not fit into 3 at all
- 2The remainder is the dividend itself
- 3Quotient is 0
Introduction
The Modulo Calculator finds the remainder left over after dividing one number by another, along with the whole-number quotient, making it useful for everything from clock arithmetic to programming.
What Is the Modulo Operation?
Modulo (often written mod or %) returns the remainder after division. For example, 17 mod 5 equals 2, because 5 fits into 17 three times with 2 left over.
The remainder is always smaller in magnitude than the divisor
Modulo is written as a mod n or a % n in most programming languages
This calculator uses the truncated (JavaScript-style) convention
How the Calculator Works
The calculator computes the remainder with the % operator and the quotient by truncating the division result toward zero, matching how most programming languages handle modulo.
Both dividend and divisor must be finite numbers
The divisor cannot be zero
The remainder keeps the same sign as the dividend
Input Guide
Enter the dividend (the number being divided) and the divisor (the number dividing it).
- 1
dividend: the number being divided, e.g. 17
- 2
divisor: the number dividing the dividend, e.g. 5
Output Guide
The calculator returns both the remainder and the whole-number quotient.
- 1
remainder: what is left over after division
- 2
quotient: how many whole times the divisor fits into the dividend
How to Use This Calculator
Enter the dividend and divisor, then read the remainder and quotient.
Type any numeric dividend
Type any nonzero numeric divisor
Review both the remainder and quotient outputs
Common Mistakes
The most common issue is entering a zero divisor or expecting a different sign convention.
Entering a zero divisor, which is undefined
Assuming the remainder is always positive with negative dividends
Confusing the remainder with the quotient
Practical Uses
Modulo arithmetic is used in scheduling, cryptography, and everyday programming tasks.
Determining if a number is even or odd (mod 2)
Wrapping values around a fixed range, like clock hours
Distributing items evenly with a remainder left over
FAQs
What does the Modulo Calculator compute?
It computes the remainder and quotient when the dividend is divided by the divisor.
What is the modulo operation?
Modulo returns what is left over after dividing one number by another; for example 17 mod 5 equals 2.
What happens with a negative dividend?
This calculator uses the truncated convention, so the remainder keeps the same sign as the dividend, matching JavaScript's % operator.
Can the divisor be zero?
No, division and modulo by zero are undefined, so the calculator returns a validation error.
Is modulo the same as division?
No, division finds how many times one number fits into another, while modulo finds the remainder left over.
How do I check if a number is even?
Compute the number mod 2; a remainder of 0 means the number is even, and 1 means it is odd.
Does the quotient round up or down?
The quotient is truncated toward zero, matching standard integer division in most programming languages.