Grafolyn

Tools

Everything here is free, needs no account, and runs entirely in your browser. Nothing you type is sent to a server, so your work stays on your own device.

What each one is for

Graphing calculator

Plot functions, equations, inequalities and implicit curves. Add sliders to any parameter and watch the curve respond. Find roots, turning points and intersections to full precision rather than reading them off a pixel. Fit regression models to your own data. Export a graph as a vector SVG that prints cleanly, or share it as a link that carries the whole state.

Statistics calculator

One- and two-variable summary statistics with histograms and box plots. Probabilities from the normal, t, chi-square, binomial and Poisson distributions, with the region shaded so you can see you asked the right question. Confidence intervals and hypothesis tests that show the working — standard error, critical value, degrees of freedom — and list the conditions each procedure assumes.

Derivative calculator

Differentiate an expression and see which rule was applied at each step rather than only the final answer. The same expression is integrated, both symbolically where a standard antiderivative exists and numerically over any interval, including improper integrals to infinity. Turning points, inflections and limits come from the same input, and every result is drawn against the original curve so a sign error is visible rather than hidden in the algebra.

Matrix calculator

Every value is an exact fraction from start to finish, so a determinant that should be zero is zero rather than 4.4 × 10⁻¹⁶. Multiply, invert and row reduce with each row operation written in the notation a textbook uses, solve Ax = b with the complete solution set including the infinite families, and read off rank, nullity and all four fundamental subspaces. Eigenvalues come with the characteristic polynomial and eigenvectors scaled to whole numbers.

Equation solver

Solve one equation in one unknown, exactly where an exact answer exists. Linear equations stay in fractions, quadratics come back as surds like (3 ± √5)/2 with the discriminant explained, and higher polynomials have their rational roots found and divided out before anything is approximated. Where no closed form exists — sin x = x/2, or a quintic — it searches for sign changes and says plainly that the answer is numeric.

Asymptote calculator

Vertical, horizontal and slant asymptotes of any rational function, found exactly by factoring and cancelling rather than by looking at a graph, so a hole is reported as a hole and never as an asymptote. It says which way the curve goes on each side of every vertical asymptote, whether and where the graph crosses its horizontal one, and which side it approaches from at each end. For eˣ, ln x, tan x and arctan x it works numerically, handles a different asymptote at each end, and says so.

X and y intercept calculator

Both intercepts of a function or an equation — y = x² − 5x + 6, 2x + 3y = 6 or a circle — exact wherever an exact answer exists, including surds such as ±√2 from a quartic with no rational root. It marks which roots the graph crosses and which it only touches, and lists every value that looks like an intercept but is not, with the reason: a hole, a pole, or a hole sitting exactly on the axis.

Fraction calculator

Add, subtract, multiply and divide fractions and mixed numbers with the lowest common denominator and every rewritten fraction shown, because that working is what the question is marking. Order a list of fractions over a common denominator, and convert between fractions, decimals and percentages exactly — including repeating decimals, written as 0.(3) rather than rounded off and quietly changed into a different number.

Conic sections calculator

Type any second-degree equation in x and y and it identifies the curve rather than asking you which one you have. It completes the square to standard form and gives the centre, vertices, foci, asymptotes, directrices and eccentricity as exact surds, with the curve drawn. The degenerate cases — a single point, a pair of crossing lines, an equation with no real solutions at all — are named rather than forced into a shape they are not.

Riemann sum calculator

Five rules for approximating an integral, with the panels drawn as the shapes each one actually uses: rectangles for the endpoint and midpoint rules, trapezia with slanted tops for the trapezoidal rule, parabolic arcs for Simpson’s. The error is measured against a high-accuracy value from a different method, and the order of convergence is measured from the errors rather than quoted from a textbook.

Vector calculator

Dot and cross products, magnitudes, angles and projections in two or three dimensions. The organising idea is which quantities are exactly rational — the dot product, the cross product, the vector projection — and which are irrational and given as exact surds, like a magnitude of √14. The angle is the only genuinely transcendental one, so its cosine is exact and the angle itself is labelled a decimal. A 2D pair is drawn with its projection and rejection, which is the whole picture of resolving a vector into components.

Sequence and series calculator

Paste the terms and it works out the rule rather than asking you which kind of sequence you have: constant differences mean arithmetic, constant ratios mean geometric, and a constant second difference means quadratic — the case most calculators skip. Building a sequence from its parameters gives the nth term, the partial sums and, for a geometric series, the sum to infinity with the convergence test explained. The terms and the running total are plotted together, because whether a series settles is far easier to see than to read.

3D graphing calculator

Plot z = f(x, y) as a surface and turn it with a finger or a mouse, then look at the same function as a contour map or slice it at any fixed x or y. What no other 3D grapher does is the fourth tab: it differentiates the function symbolically, solves ∇f = 0 by Newton’s method from a grid of seeds, and classifies every critical point it finds by the sign of D = fₓₓ·fₔₔ − fₓₔ² — reporting “the test is inconclusive” when D = 0 rather than guessing. And because the surface is drawn with the same primitives as every other chart here, it downloads as a true vector SVG, which a WebGL grapher cannot do.

Factoring calculator

Factor a polynomial completely over the rationals, with the common factor, the rational roots and what is left over all written out, and the answer multiplied back out to prove it. The difference from every other factoring tool is that it does not factor by finding roots: x⁴ + 3x² + 2 has no root at all and still factors as (x² + 1)(x² + 2), and a root-finder calls that irreducible. The search here is exhaustive, so “irreducible” means no factor exists rather than none was found — and it names the identity, from difference of squares to the four-term case that factors by grouping.

Chart maker

Venn diagrams, tally charts, dot plots and box-and-whisker plots, all built from the data rather than from the answers. Every other Venn maker asks how many things are in each region, which is the part the question was about; this one takes the members and works the regions out, lists what is in each of them, and keeps the empty ones visible with a zero. Tally charts are counted from the raw observations and the marks are drawn as proper five-bar gates rather than faked with text characters. The box plot draws up to four groups on one shared axis, because comparing is what a box plot is for, and it reports all three quartile conventions whenever they disagree — which is the real answer to “my calculator says 1.5 and the book says 2”.

Still to come

These are planned. They are listed here so it is clear what does not exist yet rather than implied by omission.

Learn how to use them

The guides work through the topics these tools are for, with worked examples and graphs you can open and change.

All guides →