Graphing Calculator Online

AI-Powered Free Online Calculus Built-In 50+ Presets

Describe any graph in plain English ("heart shape", "3D saddle", "Gaussian with mean 3") — or paste a homework problem and let AI extract the expressions. Plot functions, 3D surfaces, derivatives, integrals, limits, polar, parametric, equations, and inequalities. Built-in CAS for symbolic calculus, 50+ presets, sliders, animation. Our engine handles every calculation — AI only translates your description into expressions. A powerful Desmos alternative — no signup, works on any device.

Expressions
✨ AI Assistant

AI translates English to expressions. All math (plotting, derivatives, zeros, asymptotes) is computed by our engine.

Presets & Examples ▼
Quick Start
Calculus
Systems of Equations
Graph
Loading graphing engine…

We fix a=0 and use f(x)=x2. Move b and switch steps to see how area accumulation and primitive values match.

2.00

All Features & How to Use

Expression Types

Type any expression and the calculator auto-detects the type. You can also pick the type manually from the dropdown.

Type Example Input What It Does
Cartesian x^2, sin(x), y = 2x+1 Plots y = f(x) curves. Supports domain restrictions like x^2 {x > 0}
Equation x^2+y^2=25, y^2=4ax Solves symbolically via CAS — circles, ellipses, parabolas, any implicit curve
Parametric cos(t), sin(t) Plots x(t) and y(t) as a curve. Uses variable t
Polar 2+2*cos(theta), sin(3*θ) Plots r = f(θ). Type theta or use θ
Inequality y > x^2, x+y <= 5 Shades the region satisfying the inequality
Piecewise x<0: -x, x>=0: x^2 Define different formulas for different domains
Limit sin(x)/x at x→0 Computes the limit symbolically and annotates it on the graph
3D Surface sin(x)*cos(y) Auto-detected when both x and y appear. Interactive WebGL 3D plot
Point(s) (2, 3), [(1,2),(3,4)] Plot labeled scatter points. Also accepts (1,2), (3,4) without brackets
Vector(s) <3, 4>, <2,3> @ (1,1) Draw arrows from an origin. Use @ (ox,oy) to set the starting point
Vector Field <-y, x>, F(x,y) = <x, -y> Grid of arrows showing a 2D vector field. Presets: rotation, radial, vortex, wave
Table CSV data: 1,2 \n 3,4 Plot raw x,y data from a table
Regression CSV data + type dropdown Fit linear, quadratic, exponential, log, or power curves to your data
Distribution Normal, Poisson, Binomial… Plot probability distributions with adjustable parameters

Calculus Toggles (Cartesian expressions)

Each Cartesian expression has toggle checkboxes in its toolbar. Click any to enable:

Toggle What It Shows
f'(x) First derivative curve overlaid in a dashed line
f''(x) Second derivative curve overlaid in a dotted line
Min/Max Critical points (local minima and maxima) marked on the graph
Inflect Inflection points where concavity changes
∫ Definite integral with shaded area. Set bounds a and b, choose Riemann sum method (left, midpoint, right, trapezoidal) and number of rectangles
F(x) Symbolic antiderivative computed by the CAS engine and plotted as a separate curve
Table Editable table of values (Desmos-style). Type custom x-values, see computed y-values, and plot the points on the graph. Works for all expression types including polar and parametric
Zeros Finds and marks the roots (x-intercepts) of the function as green markers with coordinates
V.Asym Detects vertical asymptotes (where f(x) → ±∞) and draws red dashed lines
Tangent Draws a tangent line at a specified x-value. Enter the x-coordinate and see the tangent line, slope, and point of tangency
LaTeX Copies the expression as LaTeX notation to your clipboard (e.g., \sin(x), \frac{x}{2})

Parameter Sliders & Animation

Function Composition

Define named functions and compose them across expressions:

  1. In expression 1, type: f(x) = x^2 — this defines f and plots x²
  2. In expression 2, type: f(f(x)) — this auto-resolves to x⁴ and plots it
  3. You can also define g(x) = sin(x) and then use f(g(x)) to get sin²(x)

Tip: the function definition both defines the name and plots the RHS. Composition works up to 10 nesting levels.

Summation, Product & Fourier Series

Syntax Example Description
sum(var, start, end, body) sum(n, 1, 10, x^n/factorial(n)) Σ summation. Body can contain both the loop variable and x (plotted as a function of x)
prod(var, start, end, body) prod(k, 1, 5, 1-x/k) Π product notation. Same rules as sum
fourier(f(x), N) fourier(x, 5) Computes and plots the first N terms of the Fourier series approximation of f(x) on [−π, π]

Vectors & Vector Fields

Input Result
<3, 4> Arrow from origin (0,0) with direction (3,4), with arrowhead
<2, 3> @ (1, 1) Arrow starting from point (1,1) instead of origin
<1,0>, <0,1>, <1,1> Multiple vectors drawn from the same origin
<-y, x> Vector field: 15×15 grid of arrows showing the rotation field
F(x,y) = <x^2, -x*y> Named vector field with explicit F(x,y) prefix

Trace Mode & Annotations

Keyboard Shortcuts

Shortcut Action
Ctrl+Z / ⌘Z Undo last expression add/delete/change (when not typing in an input)
Ctrl+Shift+Z / ⌘Y Redo
Ctrl+Enter / ⌘Enter Add a new expression
Escape Exit trace mode

Expression Folders

Export & Sharing

Math Input Tips

You Type Interpreted As
2x2*x (implicit multiplication)
xyx*y
2(x+1)2*(x+1)
2sin(x)2*sin(x)
e^xexp(x)
ln(x)log(x) (natural log)
|x|abs(x)
π or piπ ≈ 3.14159
θ or thetaPolar angle variable
x^2 {x > 0}Domain restriction: plot only where x > 0

A live KaTeX math preview renders below each input as you type, so you can verify the expression is parsed correctly.

Frequently Asked Questions

This graphing calculator supports 8 plot types: Cartesian functions y=f(x) like sin(x) and x², equations solved symbolically such as x²+y²=25 or 2x+3y=8, parametric curves x(t) & y(t), polar graphs r=f(θ), limits with visual annotations, piecewise functions, inequalities with shaded regions, and statistical distributions. Just type any expression — it auto-detects the type.
For any Cartesian function, use the calculus toggles next to the expression input. Toggle f'(x) to overlay the derivative curve, click ∫ to shade the area under the curve with adjustable a and b bounds, or toggle F(x) to plot the symbolic antiderivative computed by the built-in CAS engine (Nerdamer). All three can be shown simultaneously on the same graph.
Select the Limit type from the dropdown, enter a function like sin(x)/x, and set the approach value (e.g., 0). The calculator uses a symbolic CAS to compute the exact limit, plots the function, and annotates the limit point with an open circle marker, a dashed horizontal line at y=L, and a dotted vertical line at x=a. Try the built-in presets: lim sin(x)/x → 1, lim (ex−1)/x → 1, lim (x²−1)/(x−1) → 2.
Yes. Add multiple equations such as y=x² and y=2x+3 and the calculator graphs both curves. Use the Intersections button to find where they cross. The Equation type uses Nerdamer CAS to solve any equation symbolically, including circles, ellipses, hyperbolas, and higher-degree polynomials. Over 15 system presets are built in, from linear 2×2 to circle+line and parabola+line.
Yes. Type any single letter like a, b, or c in your expression and a slider appears automatically. Drag to change the parameter in real time. Press the play button to animate and watch the graph evolve continuously. This works for all plot types including polar, parametric, and implicit equations.
Presets are organized by category: Quick Start (sin, parametric, polar), Calculus (antiderivative of x², FTC demo, Area-to-Primitive visual, limit sin(x)/x), Systems of Equations (linear 2×2, circle+line, parabola+line), Creative Curves (spirograph, lissajous, butterfly, cardioid, golden spiral), Physics (damped oscillation, projectile, wave interference), Machine Learning (activation functions, loss functions, gradient descent, Gaussians), and Classic & Historical curves (Witch of Agnesi, folium, cissoid, nephroid). Click any preset chip to load instantly.
100% free with no signup, no usage limits, and no ads blocking the graph area. All computation runs entirely in your browser using Math.js, Plotly.js, Nerdamer CAS, and KaTeX. Export graphs as PNG or SVG, save expression sets to local storage, or generate shareable URLs to send to classmates or colleagues. Works on desktop, tablet, and mobile.
The calculator analyzes your input as you type. If you enter an equation with y and an equals sign like 2x+3y=8, it automatically switches to Equation mode and solves symbolically. If you type an inequality like y > x², it switches to Inequality mode with shaded regions. Plain expressions like sin(x) stay in Cartesian y=f(x) mode. You can always override by selecting the type manually from the dropdown. A live KaTeX math preview shows the rendered expression as you type.

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