CAS Calculator

Free online CAS calculator (computer algebra system): solve equations, systems and inequalities with steps, find every real root of hard equations numerically, simplify, factor, expand, partial fractions, limits, series, sums and matrices.

Press Enter to run (Shift+Enter for a new line). Separate the equations of a system with commas, semicolons or new lines.

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Free online CAS calculator (computer algebra system)

A computer algebra system works with exact symbols instead of decimals: it solves x^2 - 5x + 6 = 0 as x = 2 or x = 3, keeps √2 and π exact, factors, expands and simplifies expressions, and finds limits, series and sums in closed form. This one runs SymPy right in your browser.

  • Solve equations, systems (separate them with commas, semicolons or new lines) and inequalities, with steps for linear and quadratic equations (factoring or the quadratic formula with the discriminant), polynomials (rational root theorem), equations with fractions, substitutions such as s = sin α, and linear systems.
  • Hard equations too: when there is no closed form, every real root in the search interval is found numerically (sign changes plus touching roots, refined to 30 digits), shown in radians and degrees for trigonometric equations, with the periodic general solution and a plot of the roots.
  • Simplify, factor, expand, partial fractions, combine fractions, trigonometric simplification and rationalizing denominators.
  • Limits (two-sided, left, right, at ±∞), Taylor and Maclaurin series, sums and products, matrices (determinant, inverse, eigenvalues, rank, row-reduced form) and exact or high-precision evaluation.

Example: the optimal launch angle equation

Type 0 = 2 - sin α · ln((1+sin α)/(1−sin α)) exactly like that. The calculator notices that α only appears through sin α, substitutes s = sin α (so the equation is 2 = 2s·artanh(s)), solves for s ≈ ±0.8336 and back-substitutes, giving α ≈ 0.98551 rad ≈ 56.47° and the other solutions in [0, 2π].

Tips

Typing maths
2x, x^2, sqrt x, sin x, e^x, ln, |x|, pi, and the symbols × ÷ − √ π · ≤ ≥ all work. Greek letters are variables.
Privacy
Everything is computed on your own device: the first run downloads Python and SymPy (about 10 MB, cached afterwards). Your history is kept in your browser only.
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