Algebra Calculator — Step-by-Step Algebra Solutions
The Algebra Calculator is your gateway to a complete suite of free algebra tools. Whether you need to solve quadratic equations, find x in a linear equation, work through a system of equations, or factorise a polynomial, our specialised calculators handle it all with step-by-step solutions.
Choose a calculator below to get started. Each tool provides instant results, detailed working, and clear mathematical notation so you can understand every step of the solution process.
Algebra Calculators
Quadratic Formula Calculator
Solve quadratic equations using the quadratic formula. Find roots, discriminant, and vertex. Free online quadratic formula calculator.
Solve For X Calculator
Solve algebraic equations for x. Handles linear, quadratic, polynomial, and simple equations. Free online equation solver.
System of Equations Calculator
Solve systems of linear equations with 2 or 3 unknowns. Step-by-step solutions using substitution, elimination, and Cramer's rule. Free online tool.
Factor Calculator
Find all factors, prime factorisation, factor pairs, GCD, and LCM. Free online factor calculator with instant results.
Quadratic Grapher
Graph quadratic functions instantly. Plot parabolas, find vertex, axis of symmetry, and roots. Free online quadratic graphing tool.
Slope Calculator
Calculate slope from two points, find slope-intercept and point-slope form. Free online slope calculator with graphing.
What is Algebra?
Algebra is the branch of mathematics that uses letters and symbols to represent numbers and quantities in formulas and equations. It provides a framework for generalising arithmetic operations and for solving problems where one or more values are unknown.
At its core, algebra involves finding the values of variables that make equations true. A simple example is solving x + 3 = 7, where x = 4. More advanced algebra deals with polynomials, systems of equations, matrices, and abstract structures.
Algebra is essential in science, engineering, economics, computer science, and countless other fields. The calculators on this page cover the most common algebra tasks students and professionals encounter.
Key Algebra Concepts
Linear Equations
Equations of the form ax + b = c, where the variable has an exponent of 1. These produce straight lines when graphed. Use our Solve For X Calculator to find solutions instantly.
Quadratic Equations
Equations of the form ax² + bx + c = 0. These have up to two solutions, found using the quadratic formula. The discriminant (b² - 4ac) determines whether solutions are real or complex. Our Quadratic Formula Calculator handles all cases.
Systems of Equations
Two or more equations with shared variables, solved simultaneously. Methods include substitution, elimination, and matrix operations. Our System of Equations Calculator supports 2-variable and 3-variable systems.
Factorisation
Breaking down numbers or expressions into their component factors. For integers, this means prime factorisation. For polynomials, it means expressing them as products of simpler polynomials. Use the Factor Calculator for instant results.
How to Use the Algebra Calculator
- Start from the type of problem. For an equation with one unknown like 2x + 3 = 11, open the Solve For X Calculator. For ax^2 + bx + c = 0, use the Quadratic Formula Calculator.
- For two or three equations that share unknowns, open the System of Equations Calculator. To break an expression or integer into factors, use the Factor Calculator.
- To see the shape of a quadratic, including its vertex and intercepts, use the Quadratic Grapher. To find the steepness and equation of a line through two points, use the Slope Calculator.
- Each tool shows its working step by step, so you can follow the method and check your own answers.