algebra Calculators
Quadratic Formula Calculator
Finds all real solutions to any quadratic equation of the form ax² + bx + c = 0. Use it when factoring is difficult or impossible and you need exact roots fast.
Slope Calculator
Calculates the slope (steepness) of a straight line passing through any two coordinate points. Useful in algebra, physics, and data analysis whenever you need the rate of change between two values.
Linear Equation Solver
Solves a linear equation of the form ax + b = 0 for the unknown x in one step. Ideal for students and professionals who need the root of a first-degree equation quickly.
Distance Formula Calculator
Finds the straight-line distance between two points (x₁, y₁) and (x₂, y₂) on a coordinate plane. Use it for geometry homework, mapping, or any problem involving Euclidean distance.
Midpoint Calculator
Finds the exact midpoint coordinates between two points on a plane by averaging their x- and y-values. Use it in geometry, construction, and design whenever you need to bisect a line segment.
2x2 System of Equations Solver
Solve a pair of two-variable linear equations instantly using Cramer's rule. Enter coefficients for both equations to find the unique x and y values that satisfy the system simultaneously.
Vertex Form Calculator
Find the vertex of any quadratic function in standard form ax² + bx + c. Use this when graphing a parabola or solving optimization problems that require the minimum or maximum value.
Exponential Growth Calculator
Calculate how an initial value grows over time at a constant percentage rate using A = P(1 + r)ᵗ. Useful for population growth, investment returns, and any quantity that compounds over discrete periods.
Polynomial Evaluator
Evaluate a cubic polynomial ax³ + bx² + cx + d at any value of x. Useful for quickly checking polynomial outputs in algebra, calculus, and engineering curve analysis without manual arithmetic.
Logarithm Calculator
Compute the logarithm of any positive number to any base you choose. Handy for solving exponential equations, working with decibels, pH calculations, and information theory problems.
Quadratic Equation Solver
Finds real roots of any quadratic equation ax² + bx + c = 0 using the quadratic formula. Use it whenever you need to factor a parabola, find x-intercepts, or solve physics and engineering problems involving squared variables.
System of Linear Equations Solver (2×2)
Solves a 2×2 system of linear equations (a₁x + b₁y = c₁ and a₂x + b₂y = c₂) using Cramer's Rule. Use it to find the exact point where two straight lines intersect.
Polynomial Synthetic Division Calculator
Divides a polynomial by a linear factor (x − r) using synthetic division, returning the quotient coefficients and remainder. Use it to quickly test roots or factor higher-degree polynomials without long division.
Exponential Growth and Decay Calculator
Computes a final amount after exponential growth or decay using A = Pe^(rt). Use it for population projections, radioactive half-life problems, or continuously compounded investment calculations.
Matrix Determinant Calculator (2×2 and 3×3)
Calculates the determinant of a 2×2 or 3×3 matrix from its elements. Use it to check matrix invertibility, solve linear systems via Cramer's Rule, or compute areas and volumes in geometry.
Arithmetic and Geometric Sequence Calculator
Find the nth term or partial sum of arithmetic and geometric sequences instantly. Use it when solving series problems, verifying patterns, or preparing for algebra and precalculus exams.
Rational Expression Calculator
Simplify, add, subtract, multiply, or divide rational expressions (fractions with polynomial numerators and denominators) in one step. Ideal for algebra students checking homework or teachers preparing worked examples.
Linear Inequality Solver
Solve linear inequalities of the form ax + b < c (or ≤, >, ≥) and express the answer as an interval or number line. Use it when solving algebraic inequalities in coursework or real-world constraint problems.
Function Composition Calculator
Evaluate the composite function (f∘g)(x) = f(g(x)) for linear, quadratic, exponential, or logarithmic f and linear g at any x value. Use it to check composition homework or explore how nested functions behave.
System of Linear Equations Solver
Solve a system of two linear equations in two unknowns (x and y) using Cramer's Rule. Use it when you need exact solutions to simultaneous equations in algebra, physics, or engineering problems.
Polynomial Factoring Calculator
Factor any polynomial up to degree 3 and instantly find its roots and factored form. Ideal for students solving quadratics or cubics in algebra class or checking homework.
Function Composition Calculator
Compute the composite function (f∘g)(x) for two linear functions and evaluate it at any point x. Perfect for precalculus students learning how function composition works.
Rational Function Analyzer
Analyze a rational function of the form (num_a·x + num_b) / (den_a·x + den_b) to find its vertical asymptote, horizontal asymptote, domain, and intercepts. Useful for precalculus and calculus students.
Arithmetic & Geometric Series Calculator
Find the nth term and sum of arithmetic or geometric sequences instantly. Use it when solving textbook problems, modeling financial growth, or analyzing patterns in data.
2×2 Matrix Operations Calculator
Perform addition, multiplication, determinant, and inverse operations on 2×2 matrices. Ideal for linear algebra students and anyone solving systems of two equations.
Quadratic Formula Solver
Solve any quadratic equation of the form ax² + bx + c = 0 instantly. Use this when factoring is difficult or impossible and you need exact roots fast.
Polynomial Roots Calculator
Finds the real roots and factors of polynomials up to degree 4. Use it when solving quadratic, cubic, or quartic equations by entering the polynomial's coefficients.
Arithmetic Sequence Calculator
Calculate the nth term, sum of n terms, or position of a term in an arithmetic sequence. Ideal for students and professionals working with linearly changing data.
Geometric Sequence Calculator
Calculate the sum of a finite or infinite geometric series given a first term and common ratio. Useful in finance, physics, and any problem involving exponential growth or decay.
Arithmetic & Geometric Sequence Calculator
Find the nth term of either an arithmetic or geometric sequence side by side. Perfect for students comparing how linear and exponential growth differ over the same number of steps.
Quadratic Expression Factoring Calculator
Factors any quadratic expression ax² + bx + c into two linear factors. Use it when solving equations, simplifying fractions, or checking roots without manual trial and error.
Radical Expression Simplifier
Simplifies radical expressions of the form c·ⁿ√radicand by extracting perfect nth-power factors. Ideal for algebra homework, rationalising denominators, and pre-calculus problem sets.
Matrix Operations Calculator
Computes determinant, inverse, and multiplication for 2×2 and 3×3 matrices. Use it in linear algebra courses, systems of equations, and computer graphics transformations.
Function Domain & Range Calculator
Determines the domain and range of rational, radical, and logarithmic functions from their coefficients. Use it when analysing function behaviour or preparing graphs in algebra and precalculus.
Partial Fraction Decomposition Calculator
Decomposes a rational function with a factorable denominator into a sum of simpler partial fractions. Essential for evaluating integrals and performing inverse Laplace transforms.