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Master Mathematics
with Every Step
Free mathematical calculators, detailed solutions, and powerful learning tools for students worldwide.
Linear algebra, number theory, cryptography and discrete mathematics, with exact arithmetic and every intermediate step. No sign-up; your inputs never leave your browser.
Popular calculators
Matrix Operations & Rank Calculator
Add, subtract, multiply, scale and transpose any-size matrices, then find rank, REF and RREF — every row operation explained, with PDF export.
RSA Calculator
Generate an RSA key pair from two primes and encrypt or decrypt an integer, with every calculation shown.
Extended Euclid & Modular Inverse
Find gcd(a, b), Bézout coefficients and modular inverses, with the full quotient / remainder table.
GCD & LCM Calculator
Greatest common divisor and least common multiple of up to eight integers, with Euclid's algorithm and prime factorization.
Linear Equations Solver
Solve a system of linear equations by Gauss–Jordan elimination: unique, infinite or no solution, with every row operation.
Square & Multiply
Fast modular exponentiation a^b mod n with the binary breakdown of b and a step table.
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Null Space & Column Space Calculator
Find a basis and the dimension of the column space, row space, null space and left null space of a matrix, with exact verification.
Gram-Schmidt Calculator
Orthogonalize and normalize vectors with the Gram–Schmidt process using exact fractions and radicals, with every projection shown.
Matrix Diagonalization Calculator
Diagonalize a 2×2 or 3×3 matrix as A = P D P⁻¹ with exact eigenvalues and vectors, and compute powers Aᵏ.
Permutation & Combination Calculator
Compute nPr, nCr, factorials, counts with repetition and multiset arrangements exactly, even for huge numbers.
Complex Number Calculator
Add, subtract, multiply, divide and raise complex numbers to powers exactly, plus modulus, argument, polar form and n-th roots.
Inverse Matrix Calculator
Find the inverse of a 2×2 up to 5×5 matrix by Gauss–Jordan elimination, with exact fractions and a verification.
Mathematics categories
Featured tutorials
All tutorialsGaussian Elimination and RREF: A Step-by-Step Guide
Learn Gaussian elimination, row echelon form and reduced row echelon form with a fully solved example, the rank connection and practice questions.
The Extended Euclidean Algorithm Explained
Understand the Euclidean algorithm, Bezout coefficients and modular inverses with a full back-substitution example, formulas and practice questions.
How RSA Works: A Step-by-Step Worked Example
A clear walk-through of RSA key generation, encryption and decryption with small numbers, the maths behind why it works, and practice questions.
All calculators
Linear Algebra
All linear algebra toolsMatrix Operations & Rank Calculator
Add, subtract, multiply, scale and transpose any-size matrices, then find rank, REF and RREF — every row operation explained, with PDF export.
Inverse Matrix Calculator
Find the inverse of a 2×2 up to 5×5 matrix by Gauss–Jordan elimination, with exact fractions and a verification.
Linear Equations Solver
Solve a system of linear equations by Gauss–Jordan elimination: unique, infinite or no solution, with every row operation.
Null Space & Column Space Calculator
Find a basis and the dimension of the column space, row space, null space and left null space of a matrix, with exact verification.
Gram-Schmidt Calculator
Orthogonalize and normalize vectors with the Gram–Schmidt process using exact fractions and radicals, with every projection shown.
Matrix Diagonalization Calculator
Diagonalize a 2×2 or 3×3 matrix as A = P D P⁻¹ with exact eigenvalues and vectors, and compute powers Aᵏ.
Eigenvalues & Eigenvectors Calculator
Characteristic polynomial, eigenvalues and eigenvectors of 2×2 and 3×3 matrices, exact where possible, with every step.
Matrix Determinant & Inverse
Exact determinant and inverse for 2×2 and 3×3 matrices, with cofactor / adjugate steps and a verification check.
Number Theory
All number theory toolsGCD & LCM Calculator
Greatest common divisor and least common multiple of up to eight integers, with Euclid's algorithm and prime factorization.
Prime Factorization Calculator
Factor any integer into primes, with the divisors, divisor count, divisor sum and Euler totient.
Euler Totient Calculator
Compute Euler's totient φ(n), the count of integers up to n that are coprime to n, with the product formula.
Chinese Remainder Theorem Solver
Solve a system of congruences x ≡ a (mod m), including moduli that are not coprime, with every merge step shown.
Primitive Root Calculator
Find the smallest primitive root modulo n, count them, list them and test whether a given g generates the group.
Modular Arithmetic Calculator
Add, subtract, multiply, divide and exponentiate modulo m, find modular inverses and solve ax ≡ b (mod m).
Extended Euclid & Modular Inverse
Find gcd(a, b), Bézout coefficients and modular inverses, with the full quotient / remainder table.
Discrete Mathematics
All discrete mathematics toolsPermutation & Combination Calculator
Compute nPr, nCr, factorials, counts with repetition and multiset arrangements exactly, even for huge numbers.
Base Number Converter
Live conversion between binary, octal, decimal and hexadecimal (plus any base 2–36) for integers of any size.
Mathematics
Cryptography
All cryptography toolsSquare & Multiply
Fast modular exponentiation a^b mod n with the binary breakdown of b and a step table.
Caesar Cipher
Encrypt or decrypt with a shift of 0–25, or brute-force all 25 shifts when the key is unknown. Every letter is shown.
Vigenère Cipher
Encrypt or decrypt with a keyword. Shows the repeated key and the shift applied to every letter.
Affine Cipher
Encrypt or decrypt with E(x) = (ax + b) mod 26. Shows the modular inverse of a and every letter step.
Hill Cipher
Encrypt or decrypt with a 2×2 or 3×3 key matrix. Shows the determinant, the key inverse mod 26 and every block.
RSA Calculator
Generate an RSA key pair from two primes and encrypt or decrypt an integer, with every calculation shown.
Diffie-Hellman Key Exchange
Walk through a Diffie–Hellman key exchange: public values, shared secret and a check that both sides agree.
ElGamal Encryption Calculator
Generate ElGamal keys and encrypt or decrypt a number modulo a prime, with every calculation shown.
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Why students use CipherMatrix
Every step is shown. Each calculator displays the formula, the intermediate values and a final check, so you learn the method instead of just copying an answer.
Exact results. Integers use arbitrary-precision arithmetic and matrices use exact fractions, so an RREF, a rank or a modular inverse is never distorted by rounding error.
Private and free. Everything runs in your browser. Your inputs are never uploaded. Read more about the project or see the disclaimer on educational use.
Frequently asked questions
Are the calculators free to use?
Yes. Every calculator, tutorial and worked example is free, with no sign-up.
How accurate are the results?
Integers use arbitrary-precision arithmetic and matrices use exact fractions, so results are not distorted by rounding. Every algorithm is tested against independent reference implementations and textbook examples. Approximate values, such as some complex roots, are clearly labelled.
Do you store the numbers I enter?
No. All calculations run in your browser and nothing you type is sent to a server. Some tools keep a short history in your own browser storage, which you can clear at any time.
Can I use CipherMatrix for homework and exams?
It is designed for learning and for checking your own working. Follow your institution's rules on calculators and online tools for assessed work.
Why do some answers appear as fractions or radicals?
Exact forms such as 7/3 or √2 carry full precision. Where a decimal helps, an approximation is shown next to the exact value.
Are the cryptography calculators secure?
No. RSA, Diffie–Hellman, ElGamal and the classical ciphers are teaching demonstrations with tiny parameters and no padding. Never use them to protect real data.