Modulo Calculator
Free online modulo calculator. No sign-up, no installation. Runs entirely in your browser.
Basic Modulo Operation
Modular Exponentiation (an mod m)
Calculate large powers efficiently using fast modular exponentiation. Useful for cryptography and number theory.
Clock Arithmetic Visualizer
Visualize modulo operations on a clock. The pointer shows where the result lands on a clock with b positions.
What is the Modulo Operation?
The modulo operation finds the remainder after division. When you divide one number by another, you get a quotient (how many times it divides evenly) and a remainder (what’s left over).
Formula: a mod b = r, where a = b × q + r, and 0 ≤ r < b
Example: 17 mod 5 = 2, because 17 = 5 × 3 + 2
The modulo operation is used extensively in:
- Cryptography (RSA, hash functions)
- Computer science (array indexing, hashing)
- Number theory (prime checking, GCD)
- Clock/calendar arithmetic
- Checksum calculations
How to Use This Calculator
Basic Modulo: Enter a dividend and divisor, then click Calculate. You’ll see the quotient, remainder, and divisibility status in large text.
Modular Exponentiation: Enter a base, exponent, and modulus to compute an mod m efficiently. This handles very large numbers without overflow.
Clock Arithmetic: Visualize modulo on a circular “clock” where numbers wrap around. Useful for understanding cyclic behavior and modular arithmetic visually.
Common Uses & Applications
Cryptography: Modular exponentiation is the core of RSA encryption. Large powers are computed modulo a public key.
Divisibility Testing: Check if a number is even (n mod 2 = 0), divisible by 3 (n mod 3 = 0), etc.
Array Indexing: Use modulo to wrap indices in circular buffers: nextIndex = (currentIndex + 1) mod arraySize
Checksums & Hashing: Distribute data into buckets using hash mod tableSize
Time/Date Arithmetic: 25 hours mod 24 = 1 hour (next day). 367 days mod 365 = 2 days (into next year).
Frequently Asked Questions
What’s the difference between remainder and modulo?
In most programming languages, “remainder” and “modulo” are the same for positive numbers. For negative numbers, they can differ. This calculator treats them as equivalent for clarity.
Can I use this calculator with negative numbers?
Yes! The calculator handles negative dividends and divisors. The mathematical definition a mod b = a – b × floor(a/b) ensures consistent results.
Why is modular exponentiation useful?
Computing 2^100 normally gives a huge number (over 30 digits). But 2^100 mod 13 can be computed efficiently without calculating the full power first, using the property: (a × b) mod m = ((a mod m) × (b mod m)) mod m
What does “divisible” mean in the results?
A number is divisible by another if the remainder is 0. For example, 15 mod 3 = 0, so 15 is divisible by 3. If the remainder is non-zero, it’s not divisible.
How does the clock visualizer work?
Imagine a clock with b numbers (0 to b-1). Starting at 0, move a positions clockwise. You’ll land on the position equal to a mod b. This visually shows how modulo “wraps around.”
Is my data private?
Yes! All calculations happen in your browser. Nothing is sent to a server. Your data never leaves your device.