Point Plotter | Cartesian & Polar | Point & Line Graphs

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 points 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 points 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 Points 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 points plotter is the world's only points 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 points plotter for visualization..

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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 points plotter (Cartesian and Polar)

Our advanced free online Cartesian and polar points plotter is easy to use; simply enter the coordinates of a set of points with the following syntax. The points 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.

Cartesian Points Grapher
Point plotter:Plot points and form line graphs in Cartesian coordinate system.
Oblique Cartesian Points Grapher
Oblique point plotter: Plot points and form polylines (polygon) in oblique Cartesian coordinate system.
Polar Points Grapher
Polar point plotter: Plot points and create line graphs in polar coordinate system.
Oblique Polar Points Grapher
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 (rnn) 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 points 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 points plotter will connect it to the first point to form a (closed) polygon.

Graphing Multiple Sets of Points

The points 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:

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 points 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 points 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 points plotter also allows you to use your mouse to rotate an axis by dragging it—see below to learn how.

Copying & Saving Graphs

  1. 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.
  2. 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 points 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 points grapher immediately updates the graphs.

How to Translate the Coordinate system

You can move the coordinate system in one of the following ways:

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):

Points in Cartesian and Polar Coordinate Systems

Points in Oblique Cartesian Coordinate System

One of the most interesting features of our points 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 points 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.

Insert on the bottom of multi-input panel: