Graphing Calculator
Plot up to six functions at once. Drag to pan, scroll to zoom, hover to trace, and read the roots and intersections off the panel below.
Window
Points of interest
Found numerically inside the visible x range, so pan or zoom to search elsewhere.
Roots — where a curve crosses y = 0
Intersections — where two curves meet
Turning points
Table of values
How to use this calculator
Step by step
- Type a function of
xinto any of the six slots —x^2 - 3,sin(x),1/(x-2). The graph redraws as you type. - Click a coloured square to hide or show that curve without deleting it. Handy when two functions overlap and you want to check one on its own.
- Drag the graph to pan and scroll (or pinch) to zoom. The window boxes underneath always show where you are, and you can type exact bounds into them.
- Move the pointer across the plot to trace: the strip under the graph reports every visible curve at that x at once.
- Roots, intersections and turning points are found numerically for whatever is currently on screen — pan somewhere else to search a different range.
- The table of values at the bottom takes its own range and step, and copies out as tab-separated text that pastes straight into a spreadsheet.
Good to know
- Multiplication signs next to brackets and constants are optional:
3(x+1),2xand4sin(x)all parse. - For an asymptote-heavy function such as
tan(x), the stroke breaks at the poles rather than drawing a false vertical line. - Use Equal axes before judging a shape. On unequal axes a circle looks like an ellipse and a 45° line does not look like one.
- Fit to curves sets the y range from what is actually on screen — the fastest fix when a curve has shot off the top.
- Trig defaults to radians, which is what calculus expects. Tick the degrees box if your worksheet uses degrees, and note that the period of
sin(x)becomes 360 rather than 2π. - The root finder reports crossings, not touches. A curve such as
x^2that just kisses the axis has no sign change, so it is listed under turning points instead.
The maths behind it
- Slope of a line y = mx + c m is the rise per unit run; c is where it cuts the y-axis.
- Vertex of a parabola x = −b ÷ 2a Where the turning point of y = ax² + bx + c sits.
- Numerical derivative f′(x) ≈ ( f(x+h) − f(x−h) ) ÷ 2h The central difference used to locate turning points.
- Bisection sign change between a and b ⇒ a root between them How the roots and intersections below the graph are found.
- Degrees to radians rad = deg × π ÷ 180 What the degrees switch applies inside the trig functions.
Why is nothing drawn for my function?
Either it failed to parse — a red message appears under the box saying where — or the curve is outside the current window. Try Fit to curves, which sets the y range from the values actually present.
Can I plot an equation like x² + y² = 25?
Not directly: this page plots y as a function of x. Split it into sqrt(25-x^2) and -sqrt(25-x^2) in two slots and turn on Equal axes. For genuinely implicit or polar shapes, use the polar and parametric plotter.
How accurate are the roots?
Each bracket is halved 70 times, which is far past the precision of double-precision arithmetic — the limit is the function itself, not the search. Roots very close together may be missed if both fall inside one sampling interval; zoom in and they separate.
Does the saved image keep the dark background?
Yes. Save image exports exactly what is on the canvas at the resolution your screen is drawing it, which on a high-DPI display is twice the CSS size.