Point Plotter: Free Cartesian & Polar Coordinates Plotter
Discover the world's most advanced Cartesian and polar point plotter—the only point grapher that also lets you visualize point graphs with rotated coordinate axes, forming an oblique coordinate system.
What is a point plotter?
A point plotter (aka point grapher) is a coordinate plotter (or coordinate grapher) designed to plot one or more points simultaneously in a coordinate system. These points are specified using ordered pairs, which determine their exact location.
A User-Friendly Free Online Cartesian & Polar Point Plotter
Our Cartesian / polar point plotter graphs ordered pairs (a,b) in two primary types of two-dimensional coordinate system: the Cartesian and the polar coordinate system. Each ordered pair uniquely identifies a point on either a Cartesian plane or a polar plane, with the components of the pair referred to as the point's coordinates.
To plot points using our Cartesian and polar point grapher, input the ordered pair (a,b) in the format a,b;.
For instance, to graph the points (1,2), (3,4) you would enter them as (spaces are optional): 1,2; 3,4;
Note: The components of the ordered pairs may represent Cartesian coordinates or the polar coordinates. By toggling the Polar checkbox, our Cartesian and polar point grapher plots the points based on the selected coordinate system.
The coordinate grapher also allows you to connect the points with line segments to form line graphs and polygons.
Polar Point Plotter
By selecting the Polar checkbox, our coordinate plotter switches to the polar coordinate system, allowing you to plot ordered pairs as points in polar coordinates, typically represented as (r,θ). Our polar points plotter accepts angles (θ) in radians, degrees, and grades for maximum flexibility.
Rotate Axes and Plot Points
Featuring the most sophisticated 2D Cartesian and polar coordinate systems, our point plotter is the world's only point grapher that is capable of rotating any of the coordinate axes. This unique capability allows you to plot points, create point graphs, or connect them to form line graphs in oblique coordinate systems (non-orthogonal Cartesian and generalized polar coordinate systems). Axes can be rotated to any angle and oriented in any direction, making this a truly groundbreaking point plotter for visualization..
To copy or save graphs right click on the image of a saved graph below and select "Copy image" or "Save image" from the pop-up menu.
Tips - as you type:
pi is replaced by π.
Note: Our graphing software allows you to use constant expressions, such as π or 1+√(2) wherever you can use a literal number.
Instructions for point plotter (Cartesian and Polar)
Our advanced free online Cartesian and polarpoint 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°.
Point plotter:Plot points and form line graphs in Cartesian coordinate system.
Oblique point plotter: Plot points and form polylines (polygon) in oblique Cartesian coordinate system.
Polar point plotter: Plot points and create line graphs in polar coordinate system.
Oblique polar point plotter: Plot points and form line graphs in oblique polar coordinate system.
Polar point plotter: Plotting in the Polar Coordinate System
To draw the points(rn,θn) in the polarcoordinate 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 an 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).
Mouse Operations in Our Graphing Software
Our point plotter allows you to use your mouse to perform unique operations as outlined below.
How to Rotate Axes
Our point plotter also makes it possible to use your mouse to rotate an axis: Hold down the Alt key and click on or near the axis. This will select the axis, and its color will change to red. Move the mouse. The selected axis will rotate accordingly, and the graphs are redrawn to reflect the rotation of the axis. Click again with the Alt key pressed, to release the axis.
To restore the coordinate system to its normal state press the Reset button (if hidden, press the ▼ icon).
How to Change Scales
To change the scale (zoom in one direction), hold down the ctrl key and click on an axis. The point that was clicked will be labeled "1" if clicked on the positive side, or "-1" if clicked on the negative side of the axis; it becomes the new unit for that axis, and the point grapher immediately updates the graphs.
How to Translate the Coordinate system
You can move the coordinate system in one of the following ways:
Click on the canvas and drag the mouse; this will translate the origin and the graphs together.
Double-click on the canvas to move the origin to the location where you clicked; the point plotter redraws the graphs.
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, distinct from its rectangular counterpart.
Our graphing tool uniquely allows 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.
While many texts use "Cartesian" and "rectangular" coordinate systems interchangeably, both typically refer to the rectangular Cartesian coordinate system with 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 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.
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