Modulo Calculator
Calculate the remainder of a division — the modulo operation
Modulo Calculator
Calculate the remainder of a division
Find A mod B
A mod B = A - B x floor(A/B)What is a Modulo Calculator?
A Modulo Calculator is a math tool that finds the remainder of a division. The modulo operation is written as a mod b (or sometimes a % b in programming). It tells you what’s left over when a is divided by b.
For example, when you divide 17 by 5, you get 3 with a remainder of 2. So: 17 mod 5 = 2. The modulo operation returns that remainder.
Modulo is used in many practical situations:
- Determining if a number is even or odd (n mod 2)
- Working with time and cycles (like clocks, repeating patterns)
- Computer science tasks such as hashing, indexing, and cryptography
- Finding repeating patterns in math (modular arithmetic)
This calculator makes it easy to compute remainders quickly, especially with large numbers.
How to Use This Modulo Calculator
- Enter the dividend (A) -- the number you want to divide (example: 17)
- Enter the divisor (B) -- the number you divide by (example: 5)
- Click 'Calculate' -- to compute the modulo result
- Review the result -- the output shows both the remainder (A mod B) and the quotient (how many times B fits into A)
- Try other values -- explore patterns like mod 2, mod 10, or mod 60
Tips:
- The divisor B should not be 0 (division by zero is undefined)
- Modulo is commonly used to 'wrap around' within a range (like 0–59 for minutes)
- If you’re using negative numbers, different systems can handle modulo slightly differently—this calculator follows JavaScript’s convention consistently
Modulo Formulas
Division with Remainder
Any division can be expressed as:
a = b × q + r
a = dividend
b = divisor
q = quotient (whole number result)
r = remainder
Modulo Result
a mod b = r
The remainder from division
Remainder Range
0 ≤ r < |b|
Remainder is always less than the absolute value of b
Common Modulo Patterns
Even / Odd Check
n mod 2
0 → even, 1 → odd
Last Digit
n mod 10
Returns the last digit of n
Time Wrapping
minutes mod 60
Minute-hand position in a cycle
Example Calculations
Example 1: Basic Modulo
Compute: 17 mod 5
Division: 17 ÷ 5 = 3 remainder 2
Check: 5 × 3 = 15, and 17 − 15 = 2
Result: 17 mod 5 = 2
Example 2: Check Even or Odd
Compute: 29 mod 2
Division: 29 ÷ 2 = 14 remainder 1
Reasoning: Remainder is 1 → 29 is odd
Result: 29 mod 2 = 1
Example 3: Modulo 10 (Last Digit)
Compute: 347 mod 10
Division: 347 ÷ 10 = 34 remainder 7
Reasoning: The remainder matches the last digit
Result: 347 mod 10 = 7
Example 4: 'Wrap Around' Time
Problem: A digital clock uses a 12-hour cycle. It’s 9 o’clock now. What time is it in 8 hours?
Calculation: (9 + 8) = 17
Modulo: 17 mod 12 = 5
Result: 5 o’clock
Frequently Asked Questions
What does 'mod' mean?
'Mod' means modulo, which returns the remainder after division. For example, 10 mod 3 = 1 because 10 ÷ 3 leaves a remainder of 1.
Is modulo the same as division?
Not exactly. Division gives the quotient (how many times a number fits), while modulo gives the remainder. You often use them together when you need both the quotient and what’s left over.
Why is modulo useful?
Modulo is useful for repeating cycles (time, rotations, repeating patterns), checking even/odd, limiting values to a range (like 0–59), and many programming and math applications.
What happens if the divisor is 0?
Modulo by 0 is undefined, because division by 0 is undefined. The calculator will not return a result if you enter 0 as the divisor.
How does modulo work with negative numbers?
Different systems define negative modulo differently (some use the sign of the dividend, some the divisor). If you use negative numbers, make sure you understand the convention used by the calculator and keep it consistent in your work.
Want to add this modulo calculator to your website? Get a custom embed code that matches your site's design and keeps visitors engaged.
What Is the Modulo Operation?
The modulo operation finds the remainder when one number is divided by another. Written as a mod n (or a % n in programming), it returns what's left over after dividing a by n as many times as possible. For example, 17 mod 5 = 2 because 17 = 3×5 + 2. The result is always a non-negative whole number smaller than the divisor — so mod 5 always gives you something between 0 and 4.
Modulo is everywhere in programming: checking if a number is even (n % 2 == 0), rotating through a list of options (index % length), building hash functions, and clock arithmetic (time wraps around at 12 or 24). It's one of the most useful operations in computer science and mathematics. This calculator handles both positive and negative inputs and shows you the full calculation breakdown.
How to Use the Modulo Calculator
- Enter the dividend — the number being divided (a).
- Enter the divisor — the modulus (n).
- Click Calculate.
- Read the remainder — that is your modulo result.
Formula and Examples
a mod n = a − n × floor(a / n)
Examples:
17 mod 5 = 2 (17 = 3×5 + 2)
20 mod 4 = 0 (20 = 5×4 + 0, exact division)
7 mod 3 = 1 (7 = 2×3 + 1)
Even/odd check:
n mod 2 = 0 → even
n mod 2 = 1 → odd
Clock arithmetic (12-hour):
14 mod 12 = 2 → 2:00 PMThe result of a mod n always satisfies 0 ≤ result < n (for positive n). Negative number behavior varies by programming language — some languages use floored division (Python), others use truncated division (C, Java, JavaScript), which can produce negative remainders.
Real-World Examples
100 mod 7 = 2
100 = 14×7 + 2. Useful for distributing 100 items evenly across 7 bins — you'd have 14 full bins with 2 items left over.
256 mod 16 = 0
256 is an exact multiple of 16, so the remainder is 0. This comes up constantly in hexadecimal and binary math — powers of 2 divide cleanly into each other.
29 mod 12 = 5
Clock arithmetic: 29 hours after noon is 5:00 AM the next day. The modulo operation is what makes circular time calculations work.