Algebra Calculator: Solve, Simplify, Factor, and Expand Equations Online

From a quick homework check to working through a multi-step equation, this free online Algebra Calculator handles it all directly in your browser — no software to install, no account required, and nothing sent to a server. Here’s exactly what it can do, how to use every feature, and a set of example problems to try right now.

What This Algebra Calculator Can Do

The calculator runs on a lightweight algebra engine built directly into the page, which means every calculation happens locally in your browser rather than being sent off to a remote server — your equations and your work stay private. It’s organized around five core modes, selectable right above the input area:

• Solve — finds the value(s) of your variable that make an equation true, from simple linear equations to more complex expressions.
• Simplify — reduces an expression to its simplest equivalent form, combining like terms and canceling where possible.
• Factor — breaks an expression down into its multiplied components, such as turning a quadratic into two binomials.
• Expand — does the reverse of factoring, multiplying out bracketed expressions into a single polynomial.
• Graph — plots your expression visually, useful for seeing the shape of a function rather than just its algebraic form.

The On-Screen Math Keyboard

Rather than forcing you to type awkward plain-text math, the calculator includes a full on-screen keyboard organized into tabs so you can find what you need quickly:

• 123 tab — digits, basic operators (+, −, ×, ÷), parentheses, exponents (^), and square roots.
• ABC tab — variable letters (a through z) for multi-variable expressions and equations.
• Functions tab — fractions (a/b), powers (x²), roots (√, ⁿ√), absolute value (|x|), logarithms (ln, log, log_a), and trig functions (sin, cos, tan).
• Symbols tab — matrix notation, systems of equations, function notation f(x), Euler’s number e, scientific notation (×10ⁿ), set notation, intersections/unions (∩, ∪), piecewise functions, intervals, π, and infinity.

One honest note worth knowing: the matrix, system, piecewise, and set-notation keys currently insert the correct notation into your expression, but full computation for those advanced structures isn’t supported yet — they’re best used today for writing out matrices or systems clearly, with solving support planned as the engine develops.

How to Use the Algebra Calculator

1. Choose your mode. Tap Solve, Simplify, Factor, Expand, or Graph depending on what you need done with your expression.
2. Enter your expression or equation. Type directly if you’re comfortable with standard math notation, or use the on-screen keyboard for exponents, roots, fractions, and functions.
3. Use the Functions and Symbols tabs for anything beyond basic arithmetic — trig functions, logarithms, absolute value, or special constants like π and e.
4. Press Enter to run the calculation in whichever mode you selected.
5. Review your result. Depending on the mode, you’ll see the solved value, the simplified expression, the factored form, the expanded polynomial, or a graph of the function.
6. Adjust and recalculate as needed — edit your expression and press Enter again to see an updated result instantly.

Using the History for Reference and Review

Every calculation you run is kept in the History panel, accessible from the button at the top of the calculator. This is especially useful for:

• Homework and study sessions — work through several problems in a row and scroll back through History to review each one without having to redo the math.
• Double-checking your steps — if a later problem builds on an earlier result, History lets you confirm exactly what you calculated before.
• Keeping a reference copy — since everything runs in your browser, you can copy problems and results straight out of History into your own notes, or use your browser’s print option to keep a physical or PDF copy of a full session for later reference.

Because the calculator works entirely client-side, your History stays local to your own browser session — nothing is uploaded, which is part of why it’s fast and private, but also means it’s worth copying or printing anything you want to keep before closing the tab.

A Short History of Algebra

The word “algebra” comes from the Arabic al-jabr, meaning roughly “reunion of broken parts,” taken from the title of a 9th-century treatise by the Persian mathematician Muhammad ibn Musa al-Khwarizmi. His systematic methods for solving linear and quadratic equations — without yet using the symbolic notation we use today — laid the groundwork for algebra as a distinct branch of mathematics, and his name is also the origin of the word “algorithm.” For centuries afterward, algebra problems were written out almost entirely in words rather than symbols.

The symbolic algebra familiar today — using letters for unknowns and symbols for operations — developed gradually through the 16th and 17th centuries, with French mathematicians François Viète and René Descartes playing central roles in standardizing the notation. Descartes in particular popularized using letters from the end of the alphabet (x, y, z) for unknowns, which is exactly why “solve for x” is still the default algebra phrase nearly four hundred years later.

Algebra Examples to Try

Frequently Asked Questions

Whether you’re solving a single equation, simplifying a messy expression, factoring a quadratic, or graphing a function to see its shape, this Algebra Calculator brings a full symbolic math keyboard and a private, in-browser engine together in one straightforward tool — free to use as often as you need.