Type a function or equation – y = x² − 4, a circle like x² + y² = 25, an inequality, a polar curve or a list of points – and it is drawn at once, with intersections, zeros, maxima and minima marked in exact form such as √2 and π/2. Sliders animate constants, and a table of values and full-screen mode are a click away.
What you can graph
Select any example to draw it in the calculator above.
| Type | Examples | Notes |
|---|---|---|
| Functions of x | y = 2x + 1 f(x) = x^3 - 3x sin(x) | A line without y = is read as y = … |
| Functions of y | x = y^2 - 3 | Sideways parabolas and other curves that are functions of y |
| Equations in x and y | x^2 + y^2 = 25 x^2/16 + y^2/9 = 1 xy = 4 | Circles, ellipses, hyperbolas and any other curve |
| Inequalities | y > x^2 - 4 x + y <= 3 | The region is shaded; a dashed edge means the edge is not included (< or >) |
| Polar curves | r = 2 + 2cos(θ) r = 3sin(2θ) | θ goes once around, from 0 to 2π |
| Points | (1, 2), (3, -1) | One or more points in brackets |
| Part of a graph | y = x^2 {0 <= x <= 3} x^2 + y^2 = 4 {y > 0} | A restriction in curly brackets at the end draws only that part |
| Your own functions | f(x) = x^3 - 3x, then y = f(x - 2) + 1 | Define a function on one line and use it on the others – handy for transformations |
| Sliders | y = a x^2 + b with a = 2, b = -1 | Any letter except x, y, r and e can be a slider; it can be used in every line, points included |
Functions you can use: sqrt, abs, sin, cos, tan, sec, csc, cot, asin, acos, atan, ln, log, exp and floor, with the constants pi and e. Write powers with ^ and multiplication with * or by putting things next to each other: 2x, 3sin(x), (x + 1)(x - 2). Angles are in radians unless you choose degrees in the settings.
How the graphs are drawn
A graph that only joins up dots can draw a line straight down an asymptote, miss a hole or skip a narrow spike. This calculator checks every piece of a curve with interval arithmetic: instead of a single value of x it works out the whole range of values a function can take over a small stretch of x. That tells it where a function is undefined, where it jumps and where it shoots off to infinity, so
y = 1/(x - 2)is drawn as two separate branches, with the asymptote x = 2 marked,y = (x^2 - 1)/(x - 1)is drawn as a line with an open circle (a hole) at (1, 2),y = sqrt(x)stops exactly at x = 0 andy = tan(x)breaks at every asymptote,- curves like
x^2 + y^2 = 25are traced by dividing the screen into squares and following the curve through the squares where it can pass.
Key points are found the same way and then made exact where possible: a maximum at x = 1.5707963… is shown as \tfrac{\pi}{2}, and a zero at 1.4142… as \sqrt{2}.
Reading key points
| Key point | What it means |
|---|---|
| Zero (x-intercept) | Where the graph crosses or touches the x-axis: the solutions of f(x) = 0 |
| y-intercept | Where the graph crosses the y-axis: the value f(0) |
| Maximum and minimum | The highest or lowest point in its neighbourhood (a turning point) |
| Intersection | Where two graphs meet – any two kinds, such as a line and a circle or two ellipses. For two functions these are the solutions of f(x) = g(x) |
| Hole | A single missing point, usually from a factor that cancels in a fraction |
| Vertical asymptote | A line x = a that the graph approaches but never reaches |
To solve an equation such as x^2 - 2x - 3 = x + 1 by graphing, draw both sides as separate lines and read the x-coordinates of the intersections. For the full worked solution use the equation solver or the algebra calculator.
Coming from Desmos, GeoGebra or a TI calculator?
You type graphs the same way: y = 2x + 1, x^2 + y^2 = 9, r = 2sin(3θ) or y < x^2. Letters such as a in y = ax^2 become sliders, and f(x) = … defines a function you can reuse. Graphs are saved in the page link, so copying the link shares exactly what you see – no account needed.
Frequently asked questions
Is this graphing calculator free?
Yes. It runs in your browser, with no sign-up, and works on phones, tablets and computers.
How do I graph a circle?
Type the equation in x and y, for example x^2 + y^2 = 25 for a circle of radius 5 centred at the origin, or (x - 2)^2 + (y + 1)^2 = 9 for a circle of radius 3 centred at (2, −1).
How do I graph an inequality?
Type it with <, >, <= or >=, such as y > x^2 - 4. The region where it is true is shaded. A dashed edge means the edge itself is not part of the region.
How do I share a graph?
Press Copy link. The link holds every line and the current view, so it opens exactly what you see. Save as image downloads a PNG of the graph.
Why is there an open circle on my graph?
That is a hole: a single x where the function is undefined although the graph around it is not broken – for example (x^2 − 1)/(x − 1) at x = 1, because the factor x − 1 cancels.
Does it use degrees or radians?
Radians by default: sin(x) has period 2π, about 6.28. Switch to degrees in the graph settings (the sliders button on the graph); then y = sin(x) has period 360. The x-axis can also be marked in multiples of π.