Graphing Calculator
Plot y = f(x) for one or several functions on the same axes. Type expressions such as sin(x) or x^2/8 - 3, then drag to pan and scroll to zoom toward the pointer; trig, logs, roots and exponentials are built in.
How to Use
- Type a function of x after “y =”. The page opens with sin(x) and x^2/8 - 3 plotted together.
- Press “+ Add function” for another row; each function gets its own colour, and × removes a row.
- Or click a preset: sin & cos, x² & x³, 1/x or damped wave.
- Drag the graph to pan and scroll to zoom toward the pointer. The grid and axis numbers rescale as you go.
- Press Reset view to return to x from −10 to 10 and y from −8 to 8.
Drag to pan · scroll to zoom ·
Worked Example
The starting graph. The parabola x^2/8 − 3 has its lowest point at (0, −3) and crosses the x-axis at ±√24 = ±4.899. It can only meet sin(x), which stays between −1 and 1, where x² is between 16 and 32, so for 4 ≤ |x| ≤ 5.657. It does so twice: at x ≈ −5.4634 (y ≈ 0.7310) and x ≈ 4.1508 (y ≈ −0.8464). Zoom in on either crossing to read it more closely.
The damped-wave preset. exp(-x^2/4)*sin(4x) crosses zero every π/4 = 0.7854 and stays inside the envelope ±exp(−x²/4). By x = 2 the envelope is e−1 = 0.368, and by x = 4 it is e−4 = 0.0183, too small to see at the starting scale.
The common mistake: 1/2x. Typed without brackets, 1/2x means (1/2)·x, a straight line through the origin with slope 0.5, not the curve 1/(2x). At x = 4 the first gives 2 and the second 0.125. Brackets around the whole denominator, 1/(2x), give the hyperbola.
Show Work
Formulas
From Coordinates to Graphing Calculators
Drawing an equation as a curve goes back to René Descartes, whose La Géométrie of 1637 tied algebra to geometry with coordinates; Pierre de Fermat reached the same idea independently at about the same time. The x and y axes on this page are the system that still carries Descartes’s name.
Casio’s fx-7000G of 1985 was the first calculator that could draw graphs, and Texas Instruments followed with its first graphing model, the TI-81, in 1990.
About This Tool
This graphing calculator is for seeing the shape of y = f(x): where a function rises and falls, where it crosses zero or another curve, and where it breaks off. It plots as many functions as you add, in up to six colours, and redraws as you type, pan or zoom. It finds the roots and crossings in view numerically, to about five significant figures, but does not solve exactly: the Quadratic Formula Calculator gives exact roots of ax² + bx + c, the Calculus Workbench finds derivatives and integrals, and the Scientific Calculator evaluates a single expression.
Everything runs in your browser; nothing is uploaded.
Related tools: Scientific Calculator, Quadratic Formula Calculator, Calculus Workbench, and Derivative Calculator.
Frequently Asked Questions
What can I type?
+, −, *, / and ^ with brackets, x, the constants pi, e and tau, and the one-argument functions sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, sqrt, cbrt, abs, exp, ln, log (base 10), log2, floor, ceil, round and sign. A number or bracket next to a name multiplies: 2x, 3sin(x), (x+1)(x-1). Powers come before a leading minus, so -x^2 is the downward parabola −(x²). Write 1000 rather than 1e3; E notation is not read.
Are angles in degrees or radians?
Radians. sin(x) crosses zero at multiples of π = 3.14159 and repeats every 2π = 6.28319, so the starting window from −10 to 10 shows about 3.2 waves. For degrees, write sin(x*pi/180); its period is then 360, so zoom out a long way to see a full wave.
How do I find where two graphs cross?
Plot both and zoom in on the crossing until the axis numbers give the precision you need. The starting pair, sin(x) and x^2/8 - 3, cross twice: at x ≈ −5.4634 (y ≈ 0.7310) and x ≈ 4.1508 (y ≈ −0.8464). For a crossing to many decimal places, solve f(x) − g(x) = 0 in the Numerical Methods Lab.
Why is there a gap in 1/x or tan(x)?
The function is not defined there. The curve is lifted wherever a value is not a finite number or jumps by more than 1.5 graph heights between neighbouring pixels, so 1/x is not joined across x = 0 and tan(x) is not joined across its asymptotes at ±π/2 = ±1.5708.
How do zoom and pan work?
Each scroll step makes the window 10% larger (zoom out) or 10% smaller (zoom in) around the point under the pointer, and dragging moves it. Grid lines are spaced at 1, 2 or 5 times a power of 10, about a tenth of the window: 2 units in the starting −10 to 10 view.
How do I use the Graphing Calculator?
Simply type your numbers and read the result, which refreshes the instant you change something. There is nothing to submit and nothing to wait for.
Do I need to install or sign up for anything?
Not at all — it runs in the browser with nothing to install and no account. After it loads once, it even works without an internet connection.
Is my information private?
Yes. Everything happens in your browser. Nothing you type is sent to a server or saved anywhere.
Common Use Cases
Solving by graph
x^2 - 5x + 6 crosses the x-axis at 2 and 3, its two roots.
Comparing growth
Plot 2^x and x^3 and zoom out: the exponential overtakes the cube for good at x ≈ 9.94.
Transformations
sin(2x) repeats every π = 3.14159, half the period of sin(x); sin(x) + 1 moves the wave up by 1.
Damped oscillations
exp(-x^2/4)*sin(4x) shrinks to e⁻¹ = 0.368 of its size by x = 2.
Checking homework
Compare a sketch with the real curve: x^2/8 - 3 has its vertex at (0, −3) and crosses zero at ±4.899.
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