Linear algebra just got more manageable. This collection brings together the RREF Matrix Calculator, 3×3 Matrix Inverse Calculator, and Dot Product Calculator for everyday coursework, alongside the QR Factorization Calculator and System of Equations Calculator for deeper problem-solving.
Browse the most-popular list or open the Trending tab to see what students and engineers are reaching for. Everything is free, requires no account, and runs on any device.
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Linear System of 3 Unknowns SolverSolve a system of 3 linear equations in 3 unknowns (x, y, z) by Gauss-Jordan elimination. Shows the unique solution and the reduced row echelon form.
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Reduced Row Echelon Form (RREF) CalculatorFree RREF calculator. Reduce any matrix (up to 6x6) to reduced row echelon form using Gauss-Jordan elimination and find the matrix rank instantly.
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3D Vector Cross Product CalculatorCompute the cross product of two 3D vectors a × b instantly. Get each component (x, y, z) plus the magnitude of the resulting perpendicular vector.
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2x2 Matrix Eigenvalue CalculatorFind the eigenvalues of any 2x2 matrix instantly. Computes real or complex conjugate eigenvalues from the trace and determinant using the characteristic equation.
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2x2 Eigenvalue CalculatorFind the eigenvalues of any 2x2 matrix instantly. Computes trace, determinant, discriminant, and real or complex eigenvalues with full steps.
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Euclidean Distance Between Vectors CalculatorCompute the Euclidean (straight-line) distance between two vectors of any dimension using d = sqrt(Σ(aᵢ − bᵢ)²). Fast, free, accurate.
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3x3 System of Equations CalculatorSolve a 3x3 system of linear equations using Cramer's Rule. Enter coefficients to find x, y, z plus all determinants instantly.
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4×4 Matrix Determinant CalculatorCompute the determinant of any 4×4 matrix instantly using cofactor (Laplace) expansion. Enter all 16 entries and get det(A) with full precision.
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Cosine Similarity CalculatorCalculate cosine similarity between two vectors, plus their dot product, magnitudes, and the angle between them in degrees and radians.
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2×2 Matrix Multiplication CalculatorMultiply two 2×2 matrices instantly. Enter the 8 entries of matrices A and B to get the product C = A·B with full step-by-step results.
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3×3 Matrix Eigenvalue CalculatorFind the eigenvalues of any 3×3 matrix instantly. Solves the characteristic cubic det(A−λI)=0 with Cardano's method and lists λ₁, λ₂, λ₃.
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Characteristic Polynomial CalculatorFind the characteristic polynomial of a 2×2 or 3×3 matrix. Computes coefficients, trace and determinant from det(A − λI) instantly.
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Adding & Subtracting Vectors CalculatorAdd or subtract two 2D vectors to find the resultant magnitude and direction (angle). Computes Rx, Ry, magnitude √(Rx²+Ry²) and θ via atan2.
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2x2 Matrix Inverse CalculatorCompute the inverse of a 2x2 matrix instantly. Enter a, b, c, d to get the determinant and each element of A⁻¹, with a singular-matrix check.
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2x2 Eigenvalue CalculatorFind the eigenvalues of any 2x2 matrix instantly. Handles real and complex conjugate eigenvalues using the trace and determinant formula.
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3×3 System of Equations CalculatorSolve a 3×3 system of linear equations in x, y, z using Cramer's rule. Enter all 12 coefficients and get the exact solution and determinant instantly.
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2×2 Matrix Determinant CalculatorCompute the determinant of a 2×2 matrix instantly using det = ad − bc. Enter the four entries a, b, c, d and get the result with steps.
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2x2 Eigenvalue CalculatorFind the eigenvalues of any 2x2 matrix instantly. Computes real or complex conjugate eigenvalues from the trace and determinant using the characteristic equation.
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3×3 Matrix Multiplication CalculatorMultiply two 3×3 matrices instantly. Enter all 18 entries to get the product matrix C = A × B using the row-by-column dot-product rule.
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2×2 Eigenvector CalculatorFind the eigenvalues and eigenvectors of any 2×2 matrix instantly. Enter a, b, c, d and get λ₁, λ₂ and their eigenvectors with full working.
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Angle Between Two Vectors CalculatorFind the angle between two 2D or 3D vectors using the dot product formula. Get the result in degrees and radians, plus magnitudes and cos θ.
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Matrix Determinant CalculatorFree matrix determinant calculator for 2×2 and 3×3 matrices. Enter your matrix entries to instantly compute det A via cofactor expansion.
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Matrix Inverse CalculatorFind the inverse of a 2×2 or 3×3 matrix instantly. Computes the determinant and the inverse A⁻¹ = adj(A)/det(A) with step-by-step results.
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Matrix Power (Aⁿ) CalculatorCompute the n-th power of a square matrix A (Aⁿ = A·A·…·A) for 2x2, 3x3 or 4x4 matrices. Supports n = 0 (identity) and negative powers via the inverse.
Frequently asked questions
What matrix and linear algebra operations can I find here?
The collection covers matrix inversion (3×3 and n×n via LU decomposition), row reduction to RREF, QR factorization, dot products, matrix transposition, and full system-of-equations solving for both small and larger n-by-n systems. It handles most undergraduate linear algebra coursework in one place.
How accurate are the matrix results?
Calculations use standard numerical algorithms — LU decomposition, Gaussian elimination, and Gram-Schmidt orthogonalization among others — tested against reference solutions. For engineering or safety-critical applications, verify against the governing standard and have a qualified engineer review the work.
Is there a cost to use these calculators?
Every matrix calculator on this site is completely free, with no registration, no subscription, and no time limits. Enter your values, select the operation, and get your result immediately.
Are my matrix entries stored or transmitted?
No. Everything runs in your browser — your matrix data is never sent to our servers, logged, or shared with any third party. Close the tab and all inputs disappear.
Which tools in this collection are the most popular?
The default list is ranked by actual visitor usage, with the most-used tools at the top. Flip to the Trending tab to see what is currently most active, or check Recently Added for the newest tools in the collection.
