Algebra Calculators 2026 - Equations, Factoring, Matrix
What makes the algebra category useful
This category groups calculators that solve closely related real-world tasks, so you can move from a quick estimate to a more specific planning tool without restarting the process.
Solve linear, quadratic, and systems of equations with the working shown line by line
Factor polynomials, complete the square, and find roots without graphing manually
Calculate determinants, inverses, eigenvalues, and matrix products up to 4 by 4
Convert logarithm bases and expand or condense logarithmic expressions in one step
Graph algebraic functions and inequalities to visualize the solution set
Homework and exam prep
Check your working and follow the algebraic steps so you can rework similar problems on a test.
Linear algebra and matrices
Solve determinant, inverse, and eigenvalue problems for engineering and computer science coursework.
Function analysis
Transform, factor, and graph functions to understand their behavior before applying calculus.
All Algebra Calculators
Algebra Graphing Calculator
Plot 2D functions and algebraic equations.
Inequality Graphing Calculator
Graph and shade mathematical inequalities.
Function Transformation Calculator
Visualize and calculate function transformations.
Completing the Square Calculator
Convert quadratics to vertex form step by step.
Logarithm Change of Base Calculator
Convert logarithms between any bases.
System of Equations Solver
Solve 2x2 systems by elimination or substitution.
Polynomial Factoring Calculator
Factor quadratic polynomials step by step.
Geometric Sum Calculator
Find the sum of a geometric series.
2x2 Determinant Calculator
Find the determinant of a 2x2 matrix instantly.
3x3 Determinant Calculator
3x3 matrix determinant with invertibility.
4x4 Determinant Calculator
Compute a 4x4 determinant.
Matrix Determinant Calculator
Determinant for 2x2 to 4x4 matrices.
Inverse Matrix Calculator
Inverse matrix for 2x2 and 3x3.
Matrix Multiplication Calculator
Multiply two 2x2 matrices.
Matrix Rank Calculator
Rank calculator for 3x3 matrices.
Matrix Transpose Calculator
Transpose calculator for 3x3.
Adjoint Matrix Calculator
Adjoint matrix for 2x2 and 3x3.
Cofactor Matrix Calculator
Cofactor matrix for 3x3.
Eigenvalue Calculator
Find eigenvalues of a 2x2 matrix instantly.
Eigenvector Calculator
Find eigenvectors of a 2x2 matrix for a given eigenvalue.
Eigenbasis Calculator
Test if a 2x2 matrix has a real eigenbasis.
Diagonalization Calculator
Diagonalize a 2x2 matrix as A = PDP inverse.
Characteristic Polynomial Calculator
Find the characteristic polynomial of a 2x2 matrix.
Matrix Decomposition Calculator
Decompose a 2x2 matrix using LU, QR, or eigendecomposition.
Linear Transformation Calculator
Apply a 2x2 matrix transformation to a vector.
Vector Projection Calculator
Project one 2D vector onto another using dot products.
Null Space Calculator
Find the null space and kernel of a 2x2 matrix.
Column Space Calculator
Find the column space and rank of a 2x2 matrix.
Determinant Calculator
Matrix determinant for 2x2 through 4x4.
Determinant Calculator with Steps
3x3 determinant with step breakdown.
Eigenvalues and Eigenvectors Calculator
Eigenvalues and eigenvectors for 2x2.
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How do I solve a system of two equations?
Use substitution or elimination to remove one variable. For x + y = 5 and x - y = 1, adding both gives 2x = 6, so x = 3 and y = 2. The system of equations solver shows each step automatically.
How do I complete the square for x squared plus 6x plus 5?
Take half the x coefficient, square it, then add and subtract: (x + 3) squared minus 9 plus 5 equals (x + 3) squared minus 4. Solving gives x = -1 or x = -5.
How do I factor a polynomial?
Look for a greatest common factor first, then check for special patterns like difference of squares or sum of cubes. For x squared minus 9, the factored form is (x + 3)(x - 3).
What is an eigenvalue?
An eigenvalue is a scalar lambda for which a square matrix A satisfies A times v equals lambda times v for some non-zero vector v. Eigenvalues come from solving det(A minus lambda I) = 0.
How do I change the base of a logarithm?
Use the change of base formula: log base b of x equals log(x) divided by log(b). To find log base 2 of 8 using natural log, calculate ln(8) divided by ln(2), which equals 3.
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