Modulo Calculator (a mod n)

a mod n: remainder of a divided by n. Always non-negative for positive n.

Inputs

Result

Loading calculator…
—

General calculation reads

Amazon affiliate
How Not to Be Wrong
Jordan Ellenberg - math thinking
Shop on Amazon
The Joy of X
Steven Strogatz - accessible math
Shop on Amazon
Scientific calculator (Casio fx-991EX)
Shop on Amazon

As an Amazon Associate we may earn from qualifying purchases. This does not add cost for you.

How to use this calculator

  • Enter a and n.
  • Read mathematical mod (always 0..n−1) and JS-style mod (signed).

About this calculator

Modulo (a mod n) returns the remainder when a is divided by n. For positive operands: 17 mod 5 = 2 (since 17 = 3 × 5 + 2). For negative dividends, conventions differ: math mod is always non-negative (−7 mod 5 = 3); programmer's remainder follows sign of dividend (-7 % 5 = -2 in JS/C/Java). Used in cryptography, hashing, cyclic structures (clocks, calendars), and array indexing.

Frequently asked

Why two answers?+
Math mod follows Euclidean division (always non-negative). C/Java/JS "remainder" follows sign of dividend. Python's % matches math mod.
When does the difference matter?+
Only with negative dividends. -7 mod 5: math = 3 (clock-wraps), JS % = -2.
Modular arithmetic use?+
Hashing, cryptography (RSA, ECC), random number generators, cyclic schedules ("every 7th day").
a mod 0?+
Undefined — division by zero. Calc returns "undefined".
Modular inverse?+
Exists if gcd(a, n) = 1. Computed via extended Euclidean algorithm.

Related calculators

GCD (Greatest Common Divisor) Calculator
Euclidean algorithm: gcd(a,b) = gcd(b, a mod b). Supports 2-6 integers.
LCM (Least Common Multiple) Calculator
lcm(a,b) = |a × b| / gcd(a,b). Smallest number that both a and b divide evenly.
Prime Number Checker
Is n prime? Trial division up to √n; identifies smallest divisor and nearest primes if composite.
Base Converter (Bin/Oct/Dec/Hex)
Convert any integer between binary (2), octal (8), decimal (10), and hexadecimal (16).
Big-O Time Complexity Calculator
Operations vs. n for common Big-O classes: O(1), O(log n), O(n), O(n log n), O(n²), O(2ⁿ).
Scientific Notation Converter
Convert decimal ↔ scientific notation. Standard form a × 10^b with 1 ≤ |a| < 10.

More tools you might like

Hand-picked tools that pair well with this one — same audience, same intent.

GCD (Greatest Common Divisor) Calculator
Calc

Euclidean algorithm: gcd(a,b) = gcd(b, a mod b). Supports 2-6 integers.

LCM (Least Common Multiple) Calculator
Calc

lcm(a,b) = |a × b| / gcd(a,b). Smallest number that both a and b divide evenly.

Prime Number Checker
Calc

Is n prime? Trial division up to √n; identifies smallest divisor and nearest primes if composite.

Scientific Notation Converter
Calc

Convert decimal ↔ scientific notation. Standard form a × 10^b with 1 ≤ |a| < 10.

Base Converter (Bin/Oct/Dec/Hex)
Calc

Convert any integer between binary (2), octal (8), decimal (10), and hexadecimal (16).

NRI FD Calculator (NRE/NRO/FCNR)
Finance

Fixed Deposit calculator for Non-Resident Indians — NRE (tax-free, repatriable), NRO (taxable, restricted repatriation), FCNR (foreign currency). India bank rates + tax handling.