Starlight Tools

Starlight Tools directory

Algebra & Equation Calculators

27 free, browser-based tools. No account required.

Simplify expressions and solve equations, fractions, ratios, powers, logarithms, and number-form problems with step-by-step browser-based algebra tools. Start with the System of Equations Solver, Linear Equation Solver, or Completing the Square Calculator.

Yellow star mascot comparing arithmetic and geometric sequence patterns

Arithmetic and Geometric Sequence Calculator

Find the nth term, finite sum, explicit formula, generated terms, and worked steps for arithmetic and geometric sequences. v1.0

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Yellow star mascot evaluating one function inside another

Function Composition Calculator

Evaluate f(g(x)) with a composed rule, inner and outer substitution steps, domain checks, and a reverse-order comparison. v1.0

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Yellow star mascot demonstrating a function and its inverse

Inverse Function Calculator with Steps

Find inverse rules for linear, power, rational, exponential, and logarithmic functions with domain restrictions and verification. v1.0

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Yellow star mascot solving a rational equation with a domain restriction

Rational Equation Solver

Solve rational equations with original-domain restrictions, cleared-denominator steps, rejected candidates, and verification. v1.0

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Yellow star mascot solving a two-equation linear system

System of Equations Solver

Solve two linear equations exactly with substitution, elimination, graphing, determinant checks, and verification. v1.0

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Yellow star mascot solving a linear equation step by step

Linear Equation Solver

Solve ax + b = c with exact fractions, decimals, step-by-step inverse operations, and substitution checks. v1.0

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Yellow star mascot demonstrating how an expression expands and like terms combine

Equation Expander and Like-Terms Combiner

Expand polynomial expressions or both sides of an equation, then group and combine like powers with exact steps. v1.0

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Yellow star mascot solving an inequality on a number line

Inequality Solver

Solve linear inequalities with variables on either side using exact steps, interval notation, set-builder notation, and a number line. v1.0

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Yellow star mascot solving an absolute value equation with two solutions

Absolute Value Equation and Inequality Solver

Solve |ax + b| equations and inequalities exactly with steps, interval or set notation, checks, and a number line. v1.0

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Yellow star mascot finding real and complex polynomial roots

Polynomial Root Calculator

Find every real and complex zero of a degree 1โ€“10 polynomial with multiplicities, method steps, and numerical checks. v1.0

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Yellow star mascot splitting a cubic polynomial into three linear factors

Polynomial Factoring Calculator

Factor polynomials over the rational numbers with GCF, repeated-factor, synthetic-division, and exact verification steps. v1.0

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Yellow star mascot explaining an exact polynomial long division example

Polynomial Long Division Calculator

Divide polynomials exactly with quotient, remainder, worked divideโ€“multiplyโ€“subtract steps, and an identity check. v1.0

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Yellow star mascot completing polynomial synthetic division

Synthetic Division Calculator

Divide a polynomial by x โˆ’ c with exact coefficients, a synthetic table, quotient, remainder, and Remainder Theorem check. v1.0

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Yellow star mascot arranging algebra tiles to complete a square

Completing the Square Calculator

Convert a quadratic to completed-square and vertex form, then find exact roots with every algebra step. v1.0

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Yellow star mascot calculating a quadratic discriminant

Discriminant Calculator

Calculate ฮ” = bยฒ โˆ’ 4ac exactly, classify real or complex roots, and identify whether real roots are rational. v1.0

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Yellow star mascot cancelling common factors in a rational expression

Rational Expression Simplifier

Factor numerator and denominator polynomials, cancel common factors, and preserve every original restriction. v1.0

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Yellow star mascot decomposing an algebraic fraction into partial fractions

Partial Fractions Calculator with Steps

Decompose proper or improper rational functions with repeated factors, quadratic factors, exact coefficients, and verification. v1.0

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Yellow star mascot simplifying the square root of 72 to 6 square root 2

Radical Expression Simplifier

Extract perfect powers and combine like square, cube, and nth roots with exact coefficients and worked steps. v1.0

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Quadratic equation calculator solving ax squared plus bx plus c equals zero with steps

Quadratic Equation Calculator

Find exact and decimal roots, the discriminant, a graph, and steps using multiple solution methods. v1.0

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Ratio calculator solving and scaling proportional values

Ratio Calculator

Simplify, scale, compare, divide totals, and solve missing values in two- or three-part ratios. v1.0

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Fraction calculator adding and simplifying mixed numbers

Fraction Calculator

Add, subtract, multiply, and divide fractions and mixed numbers with simplification and worked steps. v1.0

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Comparing fractions calculator showing greater than less than and equal results

Comparing Fractions Calculator

Compare and order fractions, mixed numbers, decimals, or whole numbers with exact steps and visual bars. v1.0

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Proportion calculator solving a missing value in two equal ratios

Proportion Calculator

Solve a missing value or verify four values in an equality of ratios with exact steps. v1.0

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Yellow star mascot comparing direct and inverse variation

Direct and Inverse Variation Calculator

Solve or verify direct and inverse variation with two x-y pairs, the constant k, optional units, and worked steps. v1.0

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Exponent calculator with base and exponent fields

Exponent Calculator

Calculate powers or solve for the base or exponent, including negative, decimal, and fractional exponents. v1.0

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Logarithm calculator computing natural common binary and arbitrary-base logarithms

Logarithm Calculator

Compute logarithms and antilogarithms using natural, common, binary, or arbitrary bases. v1.0

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Scientific notation converter showing standard scientific engineering and E notation

Scientific Notation Converter

Convert between decimal, scientific, engineering, and E notation while preserving significant figures. v1.0

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About These Algebra Calculators

These tools cover foundational arithmetic and algebraic operations, equation solving, ratios, fractions, powers, and logarithms. Each calculator is designed for quick checks, learning, and step-by-step verification.