Calculate modular arithmetic operations: a mod n, modular addition, subtraction, multiplication, and exponentiation. Free online modulo calculator.
The Modular Arithmetic Calculator computes a mod n (the remainder when a is divided by n) and performs modular addition, subtraction, and multiplication. Modular arithmetic is "clock arithmetic" — numbers wrap around after reaching the modulus.
Modular arithmetic is foundational in number theory, cryptography (RSA, Diffie-Hellman), computer science (hash functions, checksums), and everyday life (12-hour clocks, days of the week).
This tool handles positive and negative numbers, always returning a non-negative result. It also performs modular exponentiation (a^b mod n), which is crucial in public-key cryptography.
Integrating this calculation into regular planning habits ensures that work priorities reflect actual data about where time and energy produce the greatest results each week. Precise measurement of this value supports better personal and professional planning, helping you make informed decisions about how to prioritize tasks and manage competing demands.
Integrating this calculation into regular planning habits ensures that work priorities reflect actual data about where time and energy produce the greatest results each week.
Modular arithmetic with large numbers, especially exponentiation, is computationally intensive. This calculator handles all operations including modular exponentiation. This quantitative approach replaces vague time estimates with concrete data, enabling professionals to plan realistic schedules and avoid the pattern of chronic overcommitment. Precise quantification supports meaningful goal-setting and accountability, ensuring that improvement efforts are focused on areas with the greatest potential impact on output.
a mod n = a − n × floor(a/n) Properties: (a + b) mod n = ((a mod n) + (b mod n)) mod n (a × b) mod n = ((a mod n) × (b mod n)) mod n
Result: 2
17 mod 5: 17 = 3 × 5 + 2. The remainder is 2. Equivalently, 17 and 2 are congruent modulo 5.
RSA encryption computes c = m^e mod n for encryption and m = c^d mod n for decryption. The security relies on the difficulty of factoring n into its prime components.
A 12-hour clock is mod 12: 10 o'clock + 5 hours = 3 o'clock. Days of the week cycle with mod 7. Calendar calculations routinely use modular arithmetic.
a has a modular inverse mod n if gcd(a, n) = 1. The inverse a⁻¹ satisfies a × a⁻¹ ≡ 1 (mod n). Extended Euclidean algorithm computes it.
Professionals in data science, engineering, and finance apply these calculations daily to model complex systems and test analytical hypotheses.
Modular arithmetic is a system where numbers "wrap around" after reaching a certain value (the modulus). It is like clock arithmetic: 10 + 5 = 3 on a 12-hour clock.
a mod n gives the remainder when a is divided by n. For example, 17 mod 5 = 2 because 17 = 3×5 + 2.
This calculator always returns a non-negative result. For −7 mod 5, the answer is 3 (not −2), because −7 = (−2)×5 + 3.
Computing a^b mod n efficiently, even for very large a, b, and n. It is the core operation in RSA encryption and can be computed using the square-and-multiply algorithm.
a ≡ b (mod n) means a and b have the same remainder when divided by n. For example, 17 ≡ 2 (mod 5).
Hash tables, checksums, circular buffers, random number generators, and cryptographic algorithms all rely on modular arithmetic. Sharing these results with team members or stakeholders promotes alignment and supports more informed decision-making across the organization.