Equation Calculators
Browse our comprehensive collection of equation calculators for solving linear, quadratic, polynomial, rational, radical, exponential, logarithmic, differential equations, and more. Free online solvers with step-by-step solutions for students, teachers, and professionals.
Linear Equation Solver
Solve linear equations in one variable (ax + b = c) with step-by-step isolation and verification.
linearTwo-Point Linear Equation
Find the equation of a line from two points, including slope, intercept, and standard form.
linearSlope-Intercept Calculator
Find slope and y-intercept from linear equations, and convert between forms.
linearPoint-Slope Form Calculator
Convert between point-slope, slope-intercept, and standard forms of a line.
linearLinear Inequality Solver
Solve linear inequalities with interval notation and number line visualization.
linearParallel & Perpendicular Line
Find parallel and perpendicular lines to a given line through a point.
linearMidpoint & Distance Calculator
Calculate midpoint and distance between two points on a line.
linearLinear Equation from Intercepts
Find the equation of a line from x-intercept and y-intercept with formula.
linearQuadratic Equation Solver
Solve ax² + bx + c = 0 using the quadratic formula with discriminant analysis and step-by-step work.
quadraticCubic Equation Solver
Find real and complex roots of cubic equations using factoring, synthetic division, and Cardano's method.
quadraticQuartic Equation Solver
Solve quartic equations (degree 4) with step-by-step factorization and root extraction.
quadraticPolynomial Equation Solver
Solve polynomial equations of any degree with rational root theorem, synthetic division, and numerical methods.
quadraticDiscriminant Calculator
Calculate the discriminant (b² - 4ac) and determine the nature of roots.
quadraticQuadratic Inequality Solver
Solve quadratic inequalities using sign charts with interval notation.
quadraticCompleting the Square Calculator
Complete the square for quadratic expressions with step-by-step work.
quadraticVertex Form Calculator
Convert quadratic equations between standard, vertex, and factored forms.
quadraticSystem of Equations Solver (2x2)
Solve 2-variable linear systems using substitution, elimination, and Cramer's rule with detailed steps.
systemsSystem of Equations Solver (3x3)
Solve 3-variable linear systems using Gaussian elimination, matrix inverse, and Cramer's rule.
systemsNonlinear System Solver
Solve systems of nonlinear equations (quadratic, exponential, etc.) with substitution and graphing.
systemsAugmented Matrix Solver
Perform row reduction on augmented matrices and solve systems in reduced row echelon form (RREF).
systemsCramer's Rule Calculator
Solve systems using Cramer's rule with determinant calculation and step-by-step work.
systemsGaussian Elimination Solver
Solve systems using Gaussian elimination with row operations and back substitution.
systemsSystem of Inequalities Solver
Solve systems of linear inequalities with graphical region visualization.
systemsLinear Independence Checker
Check if vectors are linearly independent or dependent in a system.
systemsRational Equation Solver
Solve rational equations by clearing denominators with the LCD method, including domain checking.
rationalProportion Solver
Solve proportions and rational proportions with cross-multiplication and step-by-step simplification.
rationalPartial Fraction Decomposition
Decompose rational expressions into partial fractions for integration and simplification.
rationalRational Inequality Solver
Solve rational inequalities with sign analysis and interval notation.
rationalComplex Rational Expression
Simplify complex rational expressions with step-by-step LCD method.
rationalAsymptote Finder (Rational)
Find vertical, horizontal, and oblique asymptotes of rational functions.
rationalRational Expression Simplifier
Simplify rational expressions by factoring and canceling common factors.
rationalRemovable Discontinuity Finder
Identify and simplify removable discontinuities in rational functions.
rationalRadical Equation Solver
Solve equations with square roots, cube roots, and other radicals with extraneous solution checking.
radicalNested Radical Solver
Simplify and solve nested radical expressions with step-by-step simplification.
radicalSquare Root Equation Solver
Solve equations containing square roots with isolation and squaring method.
radicalCube Root Equation Solver
Solve equations containing cube roots with isolation and cubing method.
radicalRadical Inequality Solver
Solve radical inequalities with domain restrictions and interval notation.
radicalRadical Simplifier
Simplify radical expressions and rationalize denominators with step-by-step work.
radicalRationalize Denominator Calculator
Rationalize denominators with radicals using conjugate multiplication.
radicalRadical Equation Extraneous Check
Check for extraneous solutions in radical equations with verification.
radicalAbsolute Value Equation Solver
Solve absolute value equations with case-by-case analysis, interval testing, and solution verification.
absoluteAbsolute Value Inequality Solver
Solve absolute value inequalities and express solutions in interval notation with number line visualization.
absoluteAbsolute Value Function Graph
Graph absolute value functions with transformations and vertex identification.
absoluteCompound Absolute Value
Solve compound absolute value equations and inequalities with AND/OR logic.
absoluteAbsolute Value Table
Generate tables of values for absolute value functions with graphing.
absoluteAbsolute Value Piecewise Function
Convert absolute value functions to piecewise form with domain breakdown.
absoluteDistance on Number Line
Calculate distance between points using absolute value on the number line.
absoluteAbsolute Value in Context
Solve real-world problems involving absolute value (error, tolerance, distance).
absoluteExponential Equation Solver
Solve equations with exponential expressions using logarithms, with step-by-step isolation and evaluation.
exponentialLogarithmic Equation Solver
Solve logarithmic equations with properties of logarithms, including domain restrictions and checking.
exponentialLogarithm Properties Calculator
Expand, condense, and evaluate logarithmic expressions with step-by-step property application.
exponentialExponential Growth/Decay Solver
Solve exponential growth and decay problems with formula application and continuous compounding.
exponentialLogarithm Change of Base
Convert logarithms between different bases using the change of base formula.
exponentialExponential Function Graph
Graph exponential functions with transformations and asymptote identification.
exponentialLogarithmic Function Graph
Graph logarithmic functions with transformations and vertical asymptote identification.
exponentialExponential Inequality Solver
Solve exponential and logarithmic inequalities with domain restrictions and interval notation.
exponentialFirst-Order ODE Solver
Solve first-order ordinary differential equations using separation of variables, integrating factors, and more.
differentialSecond-Order ODE Solver
Solve second-order linear ODEs with constant coefficients, including characteristic equation and particular solutions.
differentialIVP Solver (Initial Value Problems)
Solve initial value problems for ODEs with given initial conditions and step-by-step integration.
differentialSlope Field Plotter
Visualize slope fields and solution curves for first-order differential equations.
differentialBernoulli Equation Solver
Solve Bernoulli differential equations using substitution and standard techniques.
differentialExact Differential Equation
Solve exact differential equations with potential function and step-by-step check.
differentialIntegrating Factor Calculator
Find integrating factors and solve first-order linear ODEs with step-by-step work.
differentialEuler Method (Numerical ODE)
Approximate solutions to ODEs using Euler's method with step-by-step iterations.
differentialNewton-Raphson Solver
Find real roots of equations using the Newton-Raphson iterative method with convergence tracking.
numericalBisection Method Solver
Find roots of continuous functions using the bisection method with step-by-step interval halving.
numericalSecant Method Solver
Approximate roots using the secant method with convergence analysis and iteration details.
numericalFixed-Point Iteration
Solve equations by converting to fixed-point form with iteration and convergence checks.
numericalRegula Falsi (False Position)
Find roots using the false position method with step-by-step interval updates.
numericalError Analysis Calculator
Calculate absolute error, relative error, and percentage error in numerical approximations.
numericalConvergence Test Tool
Analyze convergence of iterative methods with tolerance and iteration count.
numericalRoot Isolation Finder
Find intervals containing roots of equations using graphical and analytical methods.
numericalWhat Are Equation Calculators?
Our Equation Calculators collection brings together a powerful suite of tools designed to help students, educators, engineers, and researchers solve a wide variety of mathematical equations. From simple linear equations to complex differential equations, these calculators provide not only the final answer but also detailed step-by-step solutions to enhance understanding.
Whether you are working with quadratic equations, systems of linear equations, radical equations, exponential and logarithmic equations, or ordinary differential equations, our tools are built to deliver accurate results with transparent reasoning.
How to Use This Directory
- Search: Type a keyword into the search bar to find specific tools by name or description.
- Filter by Category: Use the dropdown to narrow down calculators by equation type — each option shows the number of tools available.
- Click to Use: Each calculator card links directly to the tool. Click on any card to start solving equations instantly.
- Explore More: Check the "Explore More Math Calculators" section for related calculators across other categories.
Why Use Our Equation Calculators?
- Comprehensive: Covers linear, quadratic, polynomial, rational, radical, absolute value, exponential, logarithmic, differential, and numerical methods.
- Step-by-Step: Each calculator shows detailed solution steps, helping you learn the underlying methods.
- Free & Accessible: No registration or fees — use any tool instantly on any device.
- Accuracy Guaranteed: Each calculator uses robust algorithms and is regularly tested for precision.
- Educational Focus: Designed to support learning and teaching, with clear notation and explanations.
❓ Equation Calculators FAQ
What types of equations can I solve with these calculators?
You can solve linear, quadratic, cubic, quartic, general polynomial, rational, radical, absolute value, exponential, logarithmic, and ordinary differential equations, as well as systems of equations and numerical roots.
How do I use the Quadratic Equation Solver?
Enter the coefficients a, b, and c from ax² + bx + c = 0. The solver will compute the discriminant, show the quadratic formula, and provide both real and complex roots with step-by-step arithmetic.
What is the difference between solving a linear and a quadratic equation?
A linear equation has the form ax + b = 0 and has one solution. A quadratic equation has the form ax² + bx + c = 0 and can have two real, one real, or two complex solutions. Our calculators handle both with appropriate methods.
How do I solve a system of equations?
Use our System of Equations Solvers. For 2x2 or 3x3 systems, you can choose between substitution, elimination, and matrix methods (Cramer's rule or Gaussian elimination). Each method is shown step by step.
What is a rational equation and how is it solved?
A rational equation contains fractions with variables in the denominator. Our Rational Equation Solver clears denominators using the least common denominator (LCD), then solves the resulting polynomial equation while checking for extraneous solutions.
How do I solve an exponential equation?
Exponential equations have variables in the exponent. Our Exponential Equation Solver uses logarithms to isolate the variable, showing step-by-step application of log properties and base conversion.
What is a differential equation solver?
A differential equation involves derivatives. Our ODE solvers handle first-order and second-order ordinary differential equations, using methods like separation of variables, integrating factors, and characteristic equations.
What are numerical methods for solving equations?
Numerical methods (like Newton-Raphson, bisection, secant) approximate roots of equations that are difficult to solve analytically. Our tools show each iteration step, helping you understand convergence and error analysis.
How do I check for extraneous solutions?
Our radical, rational, and logarithmic equation solvers automatically check solutions against domain restrictions and flag extraneous solutions, showing you why they are rejected.
Can I solve equations with absolute values?
Yes. Our Absolute Value Equation Solver uses case-by-case analysis (positive/negative inside the absolute value) and provides interval testing to verify solutions.
How accurate are the numerical solvers?
Our numerical solvers use high-precision arithmetic and allow you to set the tolerance (error margin) for convergence. The results are accurate to 10⁻⁶ or better by default.
How often are new equation solvers added?
We regularly add new tools based on user requests and curriculum updates. If you have a suggestion for a specific type of equation, please contact us through our contact page.