Graphing Calculator
Plot equations, curves and regions, then trace them, slide them and share them.
Expressions
What can I type?
- y = x^2 − 3 or just x^2 − 3 — functions of x
- x = y^2 — x as a function of y
- r = 1 + cos(θ) — polar (type θ or theta)
- (cos(t), sin(2t)) — parametric, t from 0 to 2π (editable)
- x^2 + y^2 = 25 — any equation in x and y
- y < x + 1, x^2 + y^2 ≤ 9 — shaded regions (dashed edge = not included)
- (2, 3) or (1, 2), (3, 4) — points
- a = 2 — a slider; use it as y = a x^2
- f(x) = x^3 — define a function, then use y = f(x − 1)
- y = x < 0 ? −x : x^2 — piecewise (condition ? then : else)
Loading the graphing engine…
Click the graph or hold Ctrl (⌘ on Mac) to zoom with the scroll wheel.
Drag to move · pinch or Ctrl + scroll to zoom · hover or tap a curve to trace it.
Table of values
Key points in view
Zeros, turning points, intercepts and intersections of y = f(x) curves.No key points in the current view.
About the Graphing Calculator
Type an equation and see it drawn: functions such as y = x^2 − 2x − 3, x = y^2, polar curves r = cos(3θ), parametric curves (cos(t), sin(2t)), any equation in x and y such as x^2 + y^2 = 25, shaded inequalities, and points. Drag to move around, pinch or use Ctrl + scroll to zoom, and hover or tap a curve to read its coordinates.
Letters you have not defined become sliders — y = a sin(bx) offers sliders for a and b, and a slider can be played to animate the graph. The calculator marks key points in view (zeros, maxima and minima, the y-intercept and intersections between curves), builds a table of values, and saves the whole graph in a link you can share. Asymptotes are handled properly: tan x and 1/x break where they should instead of being joined by vertical lines.
How to use it
- Type an expression in the first box. Press Enter for a new line; Backspace on an empty line removes it.
- Use Add slider for any letter that is not defined yet, or type a line such as
a = 2. Drag the slider, or press play to animate it. - Drag the graph to move it; pinch, use the + and − buttons, or hold Ctrl (⌘ on a Mac) and scroll to zoom. The house button resets the view. With the graph focused, arrow keys pan and + / − zoom.
- Hover over a curve (or tap it on a phone) to trace it. Click a key point on the graph, or in the list under it, to see its exact coordinates.
- Use Copy link to share the graph, or download it as SVG or PNG. The table under the graph lists values for any curve and downloads as CSV.
Examples
y = x^2 - 2x - 3
Zeros at x = −1 and x = 3, minimum at (1, −4), y-intercept (0, −3)
y = a sin(b x + c)
Add sliders for a, b and c, then drag them to change the amplitude, frequency and phase.
x^2 + y^2 = 25 y = x/2 + 1
The circle of radius 5 and a line crossing it
x^2 + y^2 < 9
The inside of a circle of radius 3, with a dashed edge (the edge is not included)
r = cos(3θ)
A three-petalled rose
Common uses
- Seeing what a function looks like and where it crosses the axes.
- Checking solutions of simultaneous equations by finding where graphs intersect.
- Exploring how a parameter changes a curve, with a slider.
- Making a clean graph image for homework, notes or a presentation.
What you can graph
- Functions:
y = f(x), or justf(x);x = g(y)for curves such as sideways parabolas. - Polar curves:
r = f(θ)(type θ or theta), with θ from 0 to 2π unless you change the range. - Parametric curves:
(x(t), y(t)), with t from 0 to 2π unless you change the range. - Equations in x and y:
x^2 + y^2 = 25,y^2 = x^3 − x,sin(x) = cos(y). - Inequalities:
y < 2x + 1,x ≥ 3,x^2 + y^2 ≤ 9. The region is shaded; a dashed edge means the edge is not included. - Points:
(2, 3)or a list(1, 2), (3, 4). - Sliders and functions:
a = 2makes a slider;f(x) = x^3 − xdefines a function you can use in other lines. - Piecewise:
y = x < 0 ? −x : x^2(condition ? value if true : value if false).
Typing tips
Multiplication can be implied: 2x, 3sin(x), ax^2 + bx + c (a·x²). Use brackets for functions — sin(x), not sinx. log is base 10 and ln is natural; √x, |x|, x² and π can be typed directly. Fractional powers of negative numbers give the real root when the denominator is odd, so x^(1/3) is drawn for negative x too. Trig functions use radians unless you switch to degrees.
How the graph is drawn
Each function is evaluated at least once per pixel across the screen. Where neighbouring values jump, the calculator looks closer: if the jump does not shrink as the gap narrows, the curve is broken there (an asymptote or a step) instead of being joined by a false vertical line, and where a function stops being defined (√x at 0) the end point is found precisely. Equations in x and y are traced with the marching-squares method on a fine grid, ignoring places where the expression jumps through infinity. Key points are found by bisection and golden-section search to about 10 significant figures.
Privacy and sharing
Everything is calculated in your browser. The share link stores the expressions and view in the part of the address after # — that part is never sent to any server, including ours, when the link is opened.
Limitations
- Key points are found for curves of the form y = f(x) and only within the current view; very many or very closely spaced points (such as sin(1/x) near 0) are not all listed.
- Equations in x and y are traced on a grid of a few pixels, so very thin features or isolated points can be missed — zoom in to see more detail.
- Complex numbers, 3D surfaces, regression and statistics plots are not included.
- Up to 40 expressions of up to 300 characters each. Functions you define can call each other, but a line may need at most 2,000 function calls for each point of the graph (and the whole graph 10,000), so deeply nested definitions such as f(x) = g(x) + g(x), g(x) = h(x) + h(x), … are refused rather than freezing the page.
Privacy
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.
Frequently asked questions
How do I graph a circle?
Type its equation in x and y: x^2 + y^2 = 25 is a circle of radius 5 centred at the origin, and (x − 2)^2 + (y + 1)^2 = 9 has centre (2, −1) and radius 3. Keep Equal scale on so it looks round.
How do I find where two graphs cross?
Graph both as y = … lines. Their intersections in view are marked as key points and listed under the graph; click one to see its coordinates.
How do sliders work?
Any single letter that is not x, y, t, r, e or i becomes a parameter. When a line uses one that is not defined yet, click Add slider, or type a = 1 yourself. Set the slider’s range and step in the boxes next to it, and press play to animate it.
Why does tan(x) not have vertical lines?
Many plotters join the last point before an asymptote to the first point after it, drawing a false vertical line. This calculator detects the jump and breaks the curve instead.
Can I use degrees?
Yes — choose Degrees above the graph and sin, cos, tan and their inverses work in degrees, so y = sin(x) repeats every 360 units.
Is my graph saved?
The link in the address bar updates as you work, so you can bookmark it or press Copy link to share it. Nothing is stored on a server.