Graphing calculator

Functions: type sin(x), a x^2 - 2, x(x+1), 2sin(3x)/x. Implicit multiplication works, as do ^ (right-associative), !, and constants pi, e, tau, phi. Functions include the trigonometric and hyperbolic families, sqrt, cbrt, abs, exp, ln, log (base 10), log2, floor, ceil, round, sign, min, max, mod, hypot, gamma, erf, and sigmoid.
Parametric curves take x(t) and y(t); polar curves take r(θ). Set the parameter range under each.
Parameters: any other single letter (a, b, k…) becomes a slider.
Navigate: drag to pan, scroll or pinch to zoom around the cursor, double-click to reset; Equal axes makes circles round.
Points: roots, local maxima and minima, and intersections of y = f(x) curves in the visible range are found numerically and listed; click one to copy it.
Derivative and integral: tick f′(x) (dashed) or ∫₀^x f (dotted) under a function; the definite integral panel uses Simpson’s rule, and “shade ∫_a^b” fills the area.
Export the view as PNG or SVG. The calculator evaluates expressions in radians or degrees, with ans and history.
⛶ Full screen (or F) gives the graph the whole screen — the browser’s full screen where it is allowed, otherwise a full-window layer (iPhone); it is redrawn as the window changes, and ◫ Panels hides the functions column. Escape leaves.

Numerical methods sample the visible range, so very narrow roots or features smaller than a pixel can be missed — zoom in to check.

Worked solutions, with each step explained, for the equations you plot: algebra step by step (its Transformations tab slides a, b, h and k on a parent function).

Share link (under the title) copies a URL that reopens this tool exactly as you have it — every tab’s inputs, with the current tab selected. Opening such a link replaces the inputs this browser had saved for the tool.

Linking to an example

Companion to Mathematics, Reconnected: chapters 5–19 and 33 link straight to the graphs below. You can write such a link by hand too, for example /tools/graph/?f=a x^2 + b x + c&a=1&b=2&c=-3&x=-6. Opening a link replaces the functions this browser had saved for the tool.










Parameter
Meaning
Example




f
functions y = f(x), separated by ;
f=sin(x);x^2/4


r
polar curves r(θ), separated by ; (write θ as t)
r=cos(k t)


xy
parametric curves x(t), y(t), separated by ;
xy=cos(t), sin(t)


t
range of θ or t for r and xy (default 0,2pi)
t=0,pi


a … z
a slider’s value: any single letter except e, f, i, r, t, x, y
k=3


x, y
the visible range, low,high (y defaults to fit x)
x=-1,7&y=-2,2


equal
1 makes the axes equal, so circles are round
equal=1


shade
shade ∫ₐᵇ of the first function and fill in the definite-integral panel
shade=0,pi


deriv, integral
show f′ or ∫₀ˣ f for function number n (1 = the first)
deriv=1


table
table of values: from,step
table=-3,1


points
0 hides the roots, extrema and intersections
points=0


example
one of the presets below; other parameters override it
example=ch13-polar-rose&k=5




Ranges and slider values accept expressions such as 2pi or sqrt(2). In the expression parameters
(f, r, xy, t, x, y, shade, table) a + typed into the address means plus, so
?f=x^2+2x+1 works; a value fully percent-encoded (encodeURIComponent, or spaces written %20) is
read exactly as encoded. Share link writes every setting into a compressed ?s= instead.


Presets:




ch05-slope-intercept — y = mx + b with sliders for m and b


ch06-two-lines — Two lines and their intersection


ch08-four-views — h(t) = 2 + 15t − 4.9t² with sliders for a, b, c


ch08-discriminant — Slide c and watch the two roots merge and vanish


ch10-conics — Conics from a focus at the origin and directrix x = −d: r = kd/(1 − k cos θ), k is the eccentricity


ch10-unit-circles — Unit circle in the Lᵖ metric: diamond (p = 1), round (2), square (large p)


ch11-families — Quadratic family a x² + b x + c with a table of values


ch11-four-sliders — a f(b(x − h)) + k on the parent x², book example g(x) = −2(x − 3)² + 4


ch11-four-sliders-abs — a |b(x − h)| + k, book example g(x) = |2x + 6| − 1


ch11-four-sliders-sqrt — a √(b(x − h)) + k


ch11-four-sliders-cube — a (b(x − h))³ + k


ch11-four-sliders-floor — a ⌊b(x − h)⌋ + k


ch11-mirror — y = x² and its reflection in y = x (fails the vertical line test)


ch12-growth-race — 1.01ⁿ against n³ on a log scale: n ln b against k ln n, crossing near 2,340


ch13-unit-circle — The unit circle unwrapped into sin and cos


ch13-polar-rose — Rose r = cos(kθ): k or 2k petals


ch14-geometric-series — Partial sums of a geometric series and their limit a/(1 − q)


ch14-gauss-staircase — Gauss’s staircase: 1 + 2 + … + n (steps) against n(n + 1)/2


ch15-euler — e^(iθ) on the unit circle, with its shadows cos θ and sin θ


ch16-secant — Secant of d(t) = 21t² at t = 1.5; slide h towards 0


ch17-secant-abs — Secants of |x| at 0 from either side: slopes +1 and −1


ch18-box — Open box from an a × b sheet: V(x) = x(a − 2x)(b − 2x)


ch19-riemann — Left Riemann sum of x² on [0, 2] with n rectangles


ch19-accumulation — f and its accumulation A(x) = ∫₀ˣ f


ch33-logistic — Sigmoid σ(wx + b) with sliders for w and b

Works with

Sharing

Linking to an example