Symbolic Algebra Engine
Manipulate algebra symbolically, not numerically: expand, factor, simplify, solve equations, rearrange formulas (solve for a variable), partial-fraction decomposition, and an expression-tree viewer. Exact rational arithmetic, all in your browser.
How to Use
- Type an algebraic expression — use <code>^</code> for powers, <code>*</code> or just juxtaposition for multiplication (<code>2x</code>, <code>(x+1)(x-2)</code> both work), and letters for variables.
- Pick an operation: <strong>Expand</strong>, <strong>Simplify</strong>, <strong>Factor</strong>, <strong>Solve</strong>, <strong>Solve for…</strong>, <strong>Partial fractions</strong>, or <strong>Tree</strong>.
- For <strong>Solve</strong> you can write an equation with <code>=</code> (e.g. <code>x^2 - 5x + 6 = 0</code>); without an <code>=</code> the expression is set equal to 0.
- For <strong>Solve for…</strong> (rearranging a formula), enter the target variable in the small box — e.g. <code>V = I*R</code>, solve for <code>R</code>, gives <code>R = V / I</code>.
- Everything is computed with exact rational (fraction) arithmetic — answers like <code>1/2</code>, <code>√2</code> or <code>i</code> appear exactly, never as rounded decimals.
What each operation does
About the Symbolic Algebra Engine
The Symbolic Algebra Engine is a simple, free helper for everyday maths and number work that runs entirely on your own device. Manipulate algebra symbolically, not numerically: expand, factor, simplify, solve equations, rearrange formulas (solve for a variable), partial-fraction decomposition, and an expression-tree viewer. Exact rational arithmetic, all in your browser.
How it works
Enter your figures and the result appears instantly, updating the moment you change anything. There is no submit button and nothing to wait for, so it is easy to try a few what-if numbers and compare the results. Just check each box holds the kind of value it expects.
Want the deeper story? The Knowledge Base explains the ideas behind the tools in more detail.
Frequently Asked Questions
What kinds of expressions can it handle?
Polynomials and rational functions (ratios of polynomials) in one or several variables, with exact rational coefficients. It expands products and powers, collects like terms, factors single-variable polynomials over the rationals (pulling out common factors, finding rational roots, recognising perfect squares and differences of squares), simplifies fractions by cancelling common factors, solves linear and quadratic equations exactly (including surd and complex answers), rearranges multi-variable formulas for any variable, and does partial-fraction decomposition over linear factors.
How is this different from a normal calculator?
A normal calculator works on <em>numbers</em> — you give it values and it returns a value. This works on <em>expressions</em>: it keeps the letters as symbols and transforms the algebra itself. <code>(x + 3)(x − 4)</code> becomes <code>x² − x − 12</code>; <code>V = I × R</code> becomes <code>R = V / I</code>. Nothing is plugged in or approximated.
Does it solve any equation?
Linear and quadratic equations are solved exactly — rational roots, irrational roots shown as surds (e.g. <code>√2</code>), and complex roots shown with <code>i</code>. Cubics and higher are solved for their rational roots and reduced; if an irreducible quadratic remains it is also solved, and anything left that isn't solvable by simple radicals is reported as a remaining factor rather than guessed at. It does not do trigonometric, exponential or transcendental equations.
What does "rearrange a formula" / "solve for a variable" mean?
Given a formula relating several quantities, it isolates the one you choose. Ohm's law <code>V = I*R</code> solved for <code>R</code> gives <code>R = V / I</code>; the area of a triangle <code>A = (1/2)*b*h</code> solved for <code>h</code> gives <code>h = 2A / b</code>. It handles formulas that are linear in the target variable (the common case for physics and engineering) and quadratic ones via the quadratic formula.
What is partial-fraction decomposition for?
It breaks a single complicated fraction into a sum of simpler ones — e.g. <code>1/(x² − 1)</code> becomes <code>(1/2)/(x − 1) − (1/2)/(x + 1)</code>. It's a standard step before integrating a rational function in calculus, and before doing an inverse Laplace transform in control theory and circuit analysis. This tool decomposes over linear factors (including repeated ones).
Is my input sent anywhere?
No. The entire engine — parser, exact-rational arithmetic, factoring and solving — runs locally in your browser with JavaScript. Nothing is uploaded; it works offline.
How do I use the Symbolic Algebra Engine?
Just type your numbers. The answer shows up right away — there is no button to press. Change anything and it updates by itself.
Does it cost anything or need an account?
No. The tool is completely free, there is no account to create, and it keeps working offline after the page first loads.
Is anything I type uploaded?
No. The tool works entirely on your device, so the values you enter never leave your browser.
Common Use Cases
Algebra & pre-calc students
Expand, factor and simplify to check homework, and watch the expression tree to understand operator precedence.
Electricians & physics
Rearrange formulas — Ohm's law, power, kinematics — to solve for whatever quantity you need.
Engineering math
Partial-fraction a transfer function before an inverse Laplace transform, or simplify a rational expression.
Solving equations
Get exact roots of linear and quadratic equations, including irrational (surd) and complex answers.
Calculus prep
Decompose rational functions into partial fractions ahead of integration.
Teaching
Show the same expression expanded and factored side by side, with exact fractions throughout.
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