Welcome to our world's most advanced free online graphing calculator, designed to graph the most common types of mathematical expressions — functions, equations, parametric curves, point sets, and it's the only graphing tool that can graph in oblique coordinate systems. Furthermore, it can also find the x-intercepts, calculate and graph symbolic derivatives.

Our online graphing calculator is a sophisticated and feature-rich graphing software application for drawing the graphs of functions, equations (including implicitly defined functions), parametric curves and points in the Cartesian and polarcoordinate systems.

This graphing calculator has features that enable you to animate the graphing process in a unique way that helps you understand it better. It is also unique in its ability to visualize graphs in an oblique coordinate system where each axis can be rotated independently. These features provide an interactive way to learn about graphing.

It can easily find the x-intercepts (also known as zeros or roots of a function), and also calculate the 1^{st} and 2^{nd} order symbolic derivatives of functions and parametric expressions, and graph the derivatives.

In particular, you can use this graphing calculator to:

Graph linear functions and linear equations in point-slope form and slope-intercept form.

Graph conic sections in the standard form such as (x-h)^2 + (y-k)^2 = r^2, and the general form (Ax^2 + Bxy + Cy^2 - Dx + Ey + F = 0), which can be a circle, ellipse, parabola, hyperbola, or some degenerate graphs.

Graph level curves, which are in the form F(x,y) = c.

Our powerful graphing calculator lets you graph functions, equations, parametric curves, and point sets. Simply type the expression into any expression box, and the software will automatically detect the type of expression and generate the graph instantly (default) using the Cartesian coordinate system (either rectangular or oblique) or polar coordinate system. You can easily switch between them by selecting/deselecting the Polar checkbox. The software is designed to automatically adjust the variables according to the expression type and coordinate system, so you don't have to worry about which variable (x, y, t, or θ) to use. Non-advanced users can also use one of these graphers to graph a single type of expression.

Our graphing calculator is designed to be intelligent and user-friendly. When you enter an expression, it automatically detects its type:

Function: If you use x as the independent variable, the graphing tool will display the expression as f(x)= or f(θ)= depending on the coordinate system.

Equation: If your expression includes an equal sign (=), the calculator will switch to equation mode and display Eq: in the label.

Points: If your expression uses both commas and semicolons, it will switch to points mode, displaying x,y; or r,θ;, depending on the coordinate system

Parametric: A single comma indicates a parametric expression. The graphing calculator displays p(t)= and replaces x with t in the expression. Deleting the comma switches back to function mode, replacing t with the appropriate variable.

When graphing functions or parametric expressions, if you don't specify a domain (interval), the graphing calculator automatically sets a suitable domain to ensure proper graphing. It uses dom=(-∞, ∞) for functions in the Cartesian coordinate system, and dom=(0, 2π) otherwise. You can change the endpoints of the interval if desired, but they must be finite for polar or parametric graphing. The calculator will automatically adjust any infinities to finite values.

Visualize how graphs are constructed step-by-step! Our graphing calculator offers the most powerful animation feature for function graphs in the polar coordinate system and parametric graphs in bothCartesian and polar coordinate systems. The animation allows you to observe whether any loops or sections of the graph are traced multiple times.

The animation uses a step-by-step approach to draw these graphs. You can control the speed of the animation, allowing you to see the construction process in detail. Pause/resume at any speed to tailor the animation to your pace. To activate the animation feature, press the ► button at the bottom of the graphing tool (if hidden, press Animate first).

The graph animator starts the animation for the focusedfunction or parametric curve. The animation progressively draws the graph, from the initial value to the final value of the independent variable or parameter.

When animating in the polar coordinate system, you can optionally show or hide the rotating radial axes by checking or unchecking the Show radial axes checkbox (by default, it's checked). By showing the rotating radial axes, the polar graphing calculator animates the polar graph construction in a way unmatched by any other polar graphing tools.

You can press ‖ to pause the animation, or Done to stop it. This also closes the animation interface. To display the animation interface again, press the Animate button.

Use the slider to adjust the animation speed.

Graphing Multiple Expressions

To graph multiple functions, equations, parametric curves or point sets, press the » button to show the multi-graph pane containing the expression panels, and type your expressions in expression fields on any of the available panels.

Add or remove panels: Use the plus ( +) button to add more expression panels or the delete (×) button to remove panels if needed.

Show/hide graphs: Select or deselect the checkbox next to an expression to show or hide its corresponding graph.

Graph Accuracy Setting

Select an option in Graph Fineness. This controls how smooth and detailed the graph will be. Higher accuracy creates a smoother curve with more detail but takes longer to graph. Choose the level that best suits your needs.

Copying & Saving Graphs

Click the Copy/Save graph button. This will create a copy of all the graphs on the canvas (graphing area) which will appear as an image below the graphing calculator..

Right-click on the image and select the appropriate option from the context menu. Depending on your device and preferences, you might be able to:

Copy: Create a copy of the image to your clipboard for pasting elsewhere.

Save image as... : Save the image as a file on your device in a chosen format (e.g., PNG, JPG).

Evaluating Functions & Parametric Expressions

To evaluate a function or parametric expression, type a literal number or numerical expression in the provided box. The calculator will display the calculated value, rounded to the number of decimal places set by the slider.

Finding X-Intercepts

Our calculator can be used as an equation solver to find the x-intercepts (also known as zeros or roots) of a function. To do this, press the Solve button. The equation solving calculator will then find the x-intercepts of the function in focus by solving the equation f(x) = 0 and display them on the screen. Notes on finding x-intercepts

Calculating and Graphing Symbolic Derivatives

In addition, the calculator can be used as a derivative graphing calculator. To calculate the first and second order derivatives of a function or parametric expression in focus, press the Derivative button.

After the derivatives are displayed, you can press Graph f, f' or Graph f, f', f'', which also appear on the screen, to draw the graphs of the function or parametric expression and their derivatives in a new window. You can also add the calculated derivatives to new panels by selecting them (selected by default). These panels will be appended to the bottom of the multi input pane. This will allow you to use them to find, for example, the critical points of the function by pressing the Solve button as described above. Press the OK button to close the derivative window.
Find out more about first & second order derivatives.

Interesting Curves

Graph any of the predefined expressions under the Interesting Graphs selections, located on the multi-input pane, to render some cool Cartesian and polar graphs by selecting it. For best results, you may need to select Graph Fineness as "+1" or higher.

Settings

Press the ⚙ (gear) button to set options (if the button is hidden, first click on the ▼ icon at the top right of the canvas):

Graph Thickness: Change graphthickness using the slider.

Angle Mode: Select the angle mode (radians - default, degrees, grades) — you can also change angle modes by using the buttons provided on the top of the Canvas.

Graphing Mode: If you deselect the Graph as you type option, you will have to press Graph selected expressions, which then appears at the bottom of the calculator, to update the graphs whenever you make any changes to the expressions or the coordinate plane (i.e., move the origin, rotate axes, etc.).

Automatic Axis Rotation: You have the option to display controls that will automatically rotate the axes.

Expression History: The graphing calculator remembers expressions between visits. You can press Reset Calculator to clear them.