Algebra calculators
50 free algebra calculators with step-by-step solutions.
Equations
- Equation solver— Solve linear, quadratic, cubic, radical, exponential equations
- Quadratic formula— Solve ax² + bx + c = 0 using the quadratic formula
- Inequality solver— Solve linear and polynomial inequalities
- Systems of equations— Solve 2 and 3 variable systems
- Discriminant— Calculate Δ = b²−4ac to determine roots
- Word problems— Age, rate, mixture, coin, and other word problems
- Literal equation— Solve a formula for any variable
- Trig equation— Solve sin(x)=½, cos(2x)=0, etc.
- Test a solution— Verify if a value satisfies an equation
Expressions
- Factoring— Factor polynomials and trinomials completely
- Expand— Expand and distribute algebraic expressions
- Simplify— Simplify algebraic expressions and radicals
- Partial fractions— Decompose rational expressions
- Complete the square— Rewrite quadratics in vertex form
- Rationalize denominator— Remove radicals from denominators
Polynomials
- Find roots— All real and complex roots
- Polynomial division— Long and synthetic division
- Remainder theorem— Find remainder when dividing by (x−c)
- Vertex calculator— Find vertex and vertex form
- Add polynomials— Add two polynomials, combine like terms
- Multiply polynomials— FOIL and distribution
- Polynomial degree— Find degree and leading coefficient
- Rational zeros— Find rational roots using p/q theorem
- Sum of roots (Vieta's)— Sum from coefficients: −b/a
- Product of roots (Vieta's)— Product from coefficients: c/a
- End behavior— Behavior at x→±∞ from degree and leading coefficient
Functions
- Domain & range— Find domain and range of any function
- Inverse function— Find the inverse f⁻¹(x)
- Composition (f∘g)— Find f(g(x))
- Evaluate f(a)— Substitute a value and simplify
- Even/odd function— Check symmetry: f(−x) = f(x) or −f(x)?
- Asymptotes— Vertical, horizontal, oblique asymptotes
- X & Y intercepts— Where the graph crosses the axes
- Transformations— Shifts, stretches, reflections
- Logarithm— Evaluate log, ln, and log base n
- Complex arithmetic— Add, multiply, divide complex numbers
Lines
- Line from two points— Find equation from (x₁,y₁) and (x₂,y₂)
- Point-slope form— y−y₁ = m(x−x₁) from point and slope
- Standard form— Convert to Ax + By = C
- Parallel line— Line parallel through a given point
- Perpendicular line— Line perpendicular through a given point
Complex numbers
- Conjugate— Find z̄ = a − bi
- Modulus |z|— Distance from origin: √(a²+b²)
- Polar form— Convert a+bi to r∠θ
Sequences & series
- Sequence calculator— Detect patterns, find nth term
- Summation (Σ)— Evaluate sigma notation
- Arithmetic series sum— Sum of arithmetic sequence
Coordinate conversions
- Cartesian → Polar— (x,y) to (r,θ)
- Polar → Cartesian— (r,θ) to (x,y)
- Modular inverse— Find a⁻¹ mod m
What is algebra?
Algebra uses symbols and letters to represent numbers and relationships. It's essential for solving equations, modeling real-world problems, and building the foundation for calculus, statistics, and beyond.
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