Algebra Calculators
Free algebra calculators: linear, quadratic and cubic equations; two-variable systems; the polynomial engine behind adding, dividing and factoring; inequalities drawn on a number line; direct and inverse variation; and exponential and logarithmic equations. Every page shows the substitution, not just the answer.
Most popular
- algebraQuadratic Equation● ready
Enter a, b and c to get both roots — real or complex — plus the discriminant, the vertex of the parabola and the sum and product of the roots.
- algebraLinear Equation● ready
Enter the three coefficients of ax + b = c to get x, with the subtraction and division written out and the no-solution cases explained.
- algebraFactor Polynomial● ready
Enter a polynomial with integer coefficients to get its factored form, its rational roots and the working — or an honest note when a factor is irreducible.
- algebraInequality● ready
Enter a linear inequality like 2x + 1 > 5 to get the solution set, drawn on a number line with the correct open or closed endpoints.
- algebraComplete the Square● ready
Enter a, b and c to get the quadratic in vertex form a(x − h)² + k, the vertex (h, k) and each substitution in the working.
Equations
- algebraLinear Equation● ready
Enter the three coefficients of ax + b = c to get x, with the subtraction and division written out and the no-solution cases explained.
- algebraTwo-Variable System● ready
Enter two equations as ax + by = c to get the crossing point (x, y), or a clear report that the lines are parallel or the same.
- algebraQuadratic Equation● ready
Enter a, b and c to get both roots — real or complex — plus the discriminant, the vertex of the parabola and the sum and product of the roots.
- algebraCubic Equation● ready
Enter the four coefficients to get every root of the cubic — three real roots, or one real root plus a complex conjugate pair.
Polynomials
- algebraPolynomial● ready
Enter two polynomials like 2x^3 - 5x + 1 and x^2 + 4, pick an operation, and get the combined, simplified polynomial with its degree.
- algebraPolynomial Degree● ready
Enter a polynomial like 2x^3 - 5x + 1 to get its simplified form, degree, leading coefficient and, optionally, its value at a chosen x.
- algebraPolynomial Remainder● ready
Enter a polynomial and a value a to divide by (x − a), returning the quotient and the remainder — which equals P(a).
- algebraFactor Polynomial● ready
Enter a polynomial with integer coefficients to get its factored form, its rational roots and the working — or an honest note when a factor is irreducible.
Factoring & Rewriting
- algebraDifference of Squares● ready
Enter two terms — like 3x and 4 — to get a² − b² written as (a + b)(a − b), with both squares and the substitution shown.
- algebraComplete the Square● ready
Enter a, b and c to get the quadratic in vertex form a(x − h)² + k, the vertex (h, k) and each substitution in the working.
Inequalities
- algebraInequality● ready
Enter a linear inequality like 2x + 1 > 5 to get the solution set, drawn on a number line with the correct open or closed endpoints.
- algebraCompound Inequality● ready
Enter two linear inequalities, choose AND (intersection) or OR (union), and get the combined solution drawn on a number line.
- algebraAbsolute Value Inequality● ready
Enter a centre and a distance with an inequality sign to get the solution set — a single interval for < and ≤, two rays for > and ≥.
Variation & Logarithms
- algebraDirect Variation● ready
Enter any two of x, y and the constant k to get the third, with the equation y = kx spelled out.
- algebraInverse Variation● ready
Enter any two of x, y and the constant k to get the third, with the relationship y = k ÷ x written out.
- algebraExponential Equation● ready
Enter a positive base and a result to get the exponent x via logarithms, with the change-of-base step shown.
- algebraLogarithm Equation● ready
Fill in any two of base, argument and result in log_b(x) = y and the third is computed — for any base, not just 10 or e.
All tools
- algebraLinear Equation● ready
Enter the three coefficients of ax + b = c to get x, with the subtraction and division written out and the no-solution cases explained.
- algebraTwo-Variable System● ready
Enter two equations as ax + by = c to get the crossing point (x, y), or a clear report that the lines are parallel or the same.
- algebraQuadratic Equation● ready
Enter a, b and c to get both roots — real or complex — plus the discriminant, the vertex of the parabola and the sum and product of the roots.
- algebraCubic Equation● ready
Enter the four coefficients to get every root of the cubic — three real roots, or one real root plus a complex conjugate pair.
- algebraComplete the Square● ready
Enter a, b and c to get the quadratic in vertex form a(x − h)² + k, the vertex (h, k) and each substitution in the working.
- algebraDifference of Squares● ready
Enter two terms — like 3x and 4 — to get a² − b² written as (a + b)(a − b), with both squares and the substitution shown.
- algebraPolynomial● ready
Enter two polynomials like 2x^3 - 5x + 1 and x^2 + 4, pick an operation, and get the combined, simplified polynomial with its degree.
- algebraPolynomial Degree● ready
Enter a polynomial like 2x^3 - 5x + 1 to get its simplified form, degree, leading coefficient and, optionally, its value at a chosen x.
- algebraPolynomial Remainder● ready
Enter a polynomial and a value a to divide by (x − a), returning the quotient and the remainder — which equals P(a).
- algebraFactor Polynomial● ready
Enter a polynomial with integer coefficients to get its factored form, its rational roots and the working — or an honest note when a factor is irreducible.
- algebraInequality● ready
Enter a linear inequality like 2x + 1 > 5 to get the solution set, drawn on a number line with the correct open or closed endpoints.
- algebraCompound Inequality● ready
Enter two linear inequalities, choose AND (intersection) or OR (union), and get the combined solution drawn on a number line.
- algebraAbsolute Value Inequality● ready
Enter a centre and a distance with an inequality sign to get the solution set — a single interval for < and ≤, two rays for > and ≥.
- algebraDirect Variation● ready
Enter any two of x, y and the constant k to get the third, with the equation y = kx spelled out.
- algebraInverse Variation● ready
Enter any two of x, y and the constant k to get the third, with the relationship y = k ÷ x written out.
- algebraExponential Equation● ready
Enter a positive base and a result to get the exponent x via logarithms, with the change-of-base step shown.
- algebraLogarithm Equation● ready
Fill in any two of base, argument and result in log_b(x) = y and the third is computed — for any base, not just 10 or e.
About Algebra Calculators
Algebra questions are rarely about the final number — they are about the step that goes wrong. Each page here shows the working: the quadratic discriminant before the roots, the synthetic division before the remainder, the sign flip when an inequality divides by a negative, the change of base before the logarithm. The cases that break a naive calculator are answered as cases rather than as NaN: a negative discriminant gives complex roots written a ± bi, a two-equation system with a zero determinant is reported as parallel or identical rather than as a division by zero, a polynomial with no rational roots keeps an irreducible residual factor and says so, and |x − a| < 0 has no solution because nothing is a negative distance. A single polynomial parser and a single root-finder back the whole category, so the factored form and the roots can never disagree. Nothing is uploaded, there is no sign-up, and the pages keep working offline once loaded.
Related categories
- Number Theory & Statistics Calculators
Mean, median, mode, spread, percentiles, primes, divisors and sequences — one calculator per question.
- Coordinate Geometry Calculators
Plot points and lines, and find slope, intercepts, distances and equations.
- Geometry & Measurement Calculators
Area, perimeter, volume and coordinate geometry calculators with live diagrams.
- Math & Statistics Tools
Scientific calculator, prime numbers, matrices, statistics, and more.
Frequently asked questions
What happens when a quadratic has no real roots?
You get the complex roots written as a ± bi with the discriminant shown as negative, rather than an error. The quadratic formula still applies — the square root of a negative number is imaginary — and students are usually asked for exactly this answer, so the tool reports it instead of refusing.
Why does the polynomial factorization sometimes leave a bracket I cannot break down?
Because that residual factor has no rational roots. The tool factors over the rationals, which is what school algebra means by factoring, and honestly states that the remaining quadratic or cubic is irreducible in that sense rather than inventing a general symbolic factorisation it cannot do.
Why did the inequality sign change direction?
Because the tool divided by a negative number. Multiplying or dividing both sides of an inequality by a negative value reverses the inequality — so 3 − 2x > 7 becomes x < −2, not x > −2. The result panel tells you when the flip happened.
Do these tools support bases other than 10 and e?
Yes. The logarithm equation tool solves log_b(x) = y for any base: the general form is what it computes, using the change-of-base identity, so a base of 2 or 5 works as well as 10 or e.
Do these tools upload my equations?
No. Every calculation is plain TypeScript running in the page — there is no API call, no account and no telemetry. The pages keep working offline once loaded.