31 Precision Tools

Algebra Calculators 2026 - Equations, Factoring, Matrix

Free algebra calculators for systems of equations, polynomial factoring, completing the square, logarithms, matrices, and eigenvalues. Each tool walks through every step of the solution so you learn the method, not just the answer.

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Why use these tools

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.

Category FAQ

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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