An online function grapher for Cartesian, parametric and polar curves
This function grapher plots up to six functions at once and lets you explore them the way you would on a graphing calculator: drag to pan, scroll or pinch to zoom, and move the pointer along a curve to read off x and y. Roots (where a curve crosses the x-axis) and intersections between curves are found numerically for the visible range and listed below the chart, so you can check a solution without squinting at gridlines.
It understands ordinary maths notation — x^2 - 4, 2x sin x, e^(-x^2), sqrt(1 - x^2) — including implicit multiplication and the usual functions and constants. Switch to parametric mode to draw curves defined by x(t) and y(t) such as Lissajous figures, or polar mode for r(θ) curves such as cardioids and roses. Export the picture as a vector SVG or a 1600×1000 PNG, or copy a link that reproduces exactly what you see.
Everything is computed in your browser; nothing is uploaded.
How to use the Function Grapher
- Choose the curve type: y = f(x), Parametric (x(t) and y(t)) or Polar r(θ).
- Type up to six expressions in the f1…f6 boxes. The graph updates as you type; an error line explains anything the parser cannot read.
- Drag the graph to pan, use the mouse wheel, pinch or the + / − buttons to zoom, and press Reset view to return to the default window.
- Hover or touch a curve to trace it: the nearest function and its x, y values appear under the chart.
- Read the roots and intersections found in the visible range in the results box; untick Mark roots or Mark intersections to hide the markers.
- Download the graph as PNG or SVG, or copy a share link that stores the functions and the view.
Function Grapher features
Natural maths input
Implicit multiplication (2x, x sin x), right-associative powers, factorials, unicode symbols such as × ÷ π √ ² and a long function list — the parser is built in, so the page loads no external library.
Three curve types
Cartesian y = f(x), parametric (x(t), y(t)) with an adjustable t range, and polar r(θ) curves, each with its own example set.
Numeric roots and intersections
Sign changes are located by scanning 2,000 points across the view and refined by bisection to about 1e-12. Asymptotes (as in tan x or 1/x) are detected and not reported as roots.
Pan, zoom, pinch and keyboard
Pointer drag, wheel zoom around the cursor, two-finger pinch on touch screens and arrow keys with + / − when the graph has focus.
Trace cursor
The nearest curve is highlighted with a dot and its exact values are printed as you move, which is handy for reading maxima, minima and crossing points.
Vector and raster export
The SVG keeps the curves as paths so it can be edited or printed at any size; the PNG is rendered at twice the on-screen resolution.
Input syntax reference
| Write | Meaning | Example |
|---|---|---|
^ | power (right-associative, so 2^3^2 = 2^9) | x^3 - 2x |
| juxtaposition | multiplication | 3x, x(x-1), 2 sin x |
sin cos tan sec csc cot | trigonometric functions in radians | sin(2x), sin 2x |
asin acos atan sinh cosh tanh | inverse and hyperbolic functions | atan(x) |
ln, log, log2 | natural log, base-10 log, base-2 log | ln(x), log(x) |
sqrt cbrt abs floor ceil round sign | roots, absolute value and rounding | sqrt(1-x^2) |
min max mod atan2 pow | two-argument functions | max(x, 0), mod(x, 2) |
pi, π, e, tau | constants | e^(-x^2/2)/sqrt(2pi) |
n! | factorial (gamma function for non-integers) | x! |
How roots and intersections are found
The visible x range is divided into 2,000 intervals. Wherever f(x) changes sign between neighbouring samples, the grapher narrows the interval by bisection sixty times, giving the crossing point to double precision. A crossing is accepted only if |f| is tiny at the result; this rejects vertical asymptotes, where tan x jumps from +∞ to −∞ without ever being zero. Intersections of two curves use the same procedure on the difference fi(x) − fj(x).
Two cases are not detected: a curve that touches the axis without crossing (such as x² at 0, which has a double root) and crossings that lie outside the current view — zoom out or pan to include them. For exact roots of a quadratic use the quadratic equation solver, which also shows the working.
Parametric and polar curves
In parametric mode each curve needs two expressions in the parameter t: for instance x = cos(3t), y = sin(2t) with t from 0 to 2π draws a Lissajous figure, and x = t − sin t, y = 1 − cos t with t from 0 to 4π draws a cycloid. In polar mode you give r as a function of θ (type θ, theta or t): r = 1 + cos θ is a cardioid, r = 2 sin 3θ a three-petal rose, and r = θ an Archimedean spiral. The parameter range box applies to both modes; expressions such as 2pi or -pi/2 are accepted there too.
When you have a fitted equation from the linear regression calculator, paste it here to compare it with the raw trend, and if you need the formula typeset for a report, the LaTeX equation editor will render it.
Function Grapher FAQ
How do I graph a function online with this tool?
Type the expression in terms of x into the f1 box — for example x^2 - 4 — and the curve appears immediately. Add more functions in f2 to f6 to compare them on the same axes.
Why does my expression show an error?
Common causes are an unbalanced parenthesis, an unknown function name, or using t or θ in y = f(x) mode. The error line names the position; the syntax table above lists everything the parser accepts.
Can it find where two graphs intersect?
Yes. With Mark intersections ticked, every pair of Cartesian curves is checked across the visible range and the crossing points are listed with six significant digits and marked with rings on the graph.
Are angles in degrees or radians?
Radians, as in all mathematical software. To plot with degrees, convert inside the expression: sin(x*pi/180).
How do I zoom on a phone?
Pinch with two fingers on the graph, or use the + and − buttons. Drag with one finger to pan; the page itself will not scroll while you touch the graph.
Can I save or share the graph?
Download PNG gives a 1600×1000 image, Download SVG gives an editable vector file, and Copy share link stores the functions, mode and view in the address so it can be re-opened or sent to someone.