Point Plotter | Cartesian & Polar Point Grapher

Use our free online integrated Cartesian and polar point plotter to create point and line graphs with either Cartesian or polar coordinates. This unique Cartesian and polar point grapher is the world's only plotter that allows you to rotate axes, enabling you to plot points in an oblique coordinate system.

Instructions for point plotter (Cartesian and Polar)

Our advanced free online Cartesian and polar point plotter is easy to use; simply enter the coordinates of a set of points with the following syntax. The point grapher plots the set of points as you type (default).

Entering Points

To use our point grapher, the points (a₁,b₁),(a₂,b₂),... must be entered as a₁,b₁; a₂,b₂; ... In other words, separate the coordinates of each point by a comma and the points themselves by a semicolon (note that parentheses are excluded); blank spaces are optional. The last semicolon is optional, see the note below.

You can use constant expressions such as 1/2+sin(π/3) for point coordinates.

Example: 1,2; 3/4,4; -2,sin(π/6); (this will plot three points). If you choose the degrees mode, you can simply type in sin(30) since π/6 (radians) is equal to 30°.

Cartesian Point Plotter: Graph points with Cartesian coordinates. — **Point plotter**:Graph points and form line graphs in Cartesian coordinate system.

Oblique Cartesian (Parallelogrammatic) Points Plotter: Graph points with coordinate axes rotated. — **Oblique point plotter**: Graph points and form polylines (polygon) in **oblique (parallelogrammatic)** Cartesian coordinate system.

Polar Points Plotter: Graph points with polar coordinates. — **Polar point plotter**: Graph points and create line graphs in polar coordinate system.

Oblique Polar Points Plotter: Graph points with polar axis rotated. — **Oblique polar point plotter**: Graph points and form line graphs in **oblique** polar coordinate system.

Polar point plotter: Plotting in the Polar Coordinate System

To draw the points (r_n,θ_n) in the polar coordinate system, select the Polar checkbox. Our versatile polar point plotter enables you to input angular coordinates (radial angles) in various units—radians, degrees, and grades by selecting the corresponding angle mode..

Connecting Points

The point grapher allows you to connect the points and form line graphs by pressing the Connect button. This toggle button will connect the points in the focused expression box. Press it again to Unconnect the points.

Note: When connecting the points, if the last point is followed by a semicolon, the point plotter will connect it to the first point to form a (closed) polygon.

Graphing Multiple Sets of Points

The point plotter allows you to graph multiple sets of points. Press the » button to show the multi-graph pane. In each expression panel you can enter a set of points to plot. You can also do the following actions:

Add or delete panels with the + or × buttons if necessary.
Select or deselect checkboxes to show or hide graphs.

Labeling Axes

To label an axis, click on the ▼ icon at the top right of the canvas. Type in any number for which you want to label the axes, and press the Label button. The point grapher allows you to use constants like π, or even constant expressions such as 1+3π/2 to label an axis.

Rotating Axes

Our graphing software is the world's only point plotter that allows you to rotate axes. This unique feature allows you to visualize the graph of a given set of points in the oblique (non-perpendicular) coordinate system. To rotate an axis, click on the ▼ icon at the top right of the canvas, and then enter the angles by which you want to rotate each axis and press the Rotate button. The axis will rotate and the graphs will be redrawn to reflect the rotation. Our point plotter also allows you to use your mouse to rotate an axis by dragging it—see below to learn how.

Copying & Saving Graphs

Click the Copy/Save graph button. The point plotter will create an image of all graphs on the canvas (graphing area), which will appear below the plotter.
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).

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):

The point plotter allows you to change graph thickness using the slider.
The point plotter allows you to select the angle mode (radians - default, degrees, grades).
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 plotter, to update the graphs whenever you make any changes to the expressions or the coordinate plane (i.e., move the origin, rotate axes, etc.).
You have the option to display controls that will automatically rotate the axes.
The point grapher remembers the expressions so that you can use them in future visits. You can press Reset Calculator to clear them.

Points in Cartesian and Polar Coordinate Systems

Cartesian: The Cartesian coordinate system uses two perpendicular axes, customarily named x and y for plotting the point (a,b). The components a and b are called the x- and y-coordinates of the point. They represent the signed distances of the point from the origin (the point of intersection of the axes) along these axes.
Polar: In the polar coordinate system, a single axis, called the polar axis (typically denoted by θ = 0), serves as a fixed angular reference. The ordered pair (a,b) then locates a point at a signed distance, a, from the origin, called the pole, along a ray (called radial axis) starting from the pole and rotated by an angle of b relative to the polar axis (θ = 0).

Points in Oblique Cartesian Coordinate System

One of the most interesting features of our point grapher is the ability to rotate the axes. The standard Cartesian coordinate system, typically referred to as the rectangular coordinate system, employs two perpendicular axes, one horizontal, the other vertical. By rotating these axes, we create a Cartesian coordinate system where the axes intersect at any angle. This is known as an oblique Cartesian coordinate system or parallelogrammic Cartesian coordinate system, distinct from its rectangular counterpart.

Our graphing tool allows unique exploration of how point graphs appear in this generalized Cartesian coordinate system, which we term the oblique Cartesian coordinate system or simply the oblique coordinate system or parallelogrammic coordinate system, due to the parallelograms formed by grid lines, which are parallel to coressponding axes.

While many texts use "Cartesian" and "rectangular" coordinate systems interchangeably, both typically refer to the rectangular Cartesian coordinate system, which is characterized by perpendicular axes. To differentiate it from the oblique Cartesian coordinate system we introduce, we use the full term rectangular Cartesian coordinate system.

Given the novelty of this feature in our software and the lack of specific online resources for oblique coordinate systems, we categorize an oblique coordinate system as a specialized type of Cartesian coordinate system. To distinguish it from the rectangular Cartesian coordinate system, we have coined the term oblique Cartesian coordinate system.

By accommodating oblique axes, our point plotter offers fresh perspectives for data visualization and analysis, particularly in fields like physics, engineering, and geometry, and for development of game apps, where non-orthogonal coordinate systems can streamline complex problems.

Points in Oblique Polar Coordinate System

In the standard polar coordinate system, the polar axis is drawn horizontally. However, our polar point plotter allows you to position it at any angle and orientation by rotating the polar axis. This enables you to plot any set of points in an oblique polar coordinate system.