Point Grapher: Cartesian & Polar Point Plotter

The world's most advanced point grapher that you can use for free online to create both point graphs and line graphs by connecting points with either Cartesian or polar coordinates. This unique Cartesian and polar point grapher allows you to rotate the axes and graph points in an oblique coordinate system.

About the Point Grapher

This online point grapher (aka point plotter, coordinate grapher, or coordinate plotter) is designed to graph points in a plane. You'll provide the points as ordered pairs—with a simple format as described below.

A User-Friendly Cartesian & Polar Point Grapher

Our integrated Cartesian and polar point grapher makes plotting simple in both Cartesian and polar coordinate systems. To graph points given by ordered pairs (a,b), simply enter them as a,b;

These pairs can represent points in either Cartesian coordinates or polar coordinates, and our point plotter will graph them based on the coordinate system you choose.

By default, points are plotted in the Cartesian coordinate system. However, simply select the Polar checkbox, and our coordinate grapher will seamlessly switch to its built-in polar coordinate system. This means the components of your ordered pairs will be treated as polar coordinates—typically represented as (r,θ)—and plotted accordingly.

Our polar point plotter offers maximum flexibility, accepting angles (θ) in radians, degrees, or grades—which you can easily select.

Point Plotting in Oblique Coordinate Systems Capability

Our advanced online point grapher is the world's only point plotter that supports axis rotation, enabling you to graph points in oblique coordinate systems (aka parallelogrammatic coordinate systems—non-rectangular Cartesian, and generalized polar coordinate systems).

With this powerful capability, our oblique point grapher lets you rotate individual axes, automatically updating the point graphs, line segments, or polygons formed by connecting the points.

Note: You can even rotate an axis using your mouse: Hold down the Alt key, click on the axis, and move your mouse to rotate it. Click again (with the Alt key pressed) to lock the axis into its new position. For a complete guide to all mouse controls, refer to MouseMatics.

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Cartesian Point Plotter: Graph points with Cartesian coordinates.
Point grapher: Plot points and form line graphs in Cartesian coordinate system.
Oblique Cartesian (Parallelogrammatic) Points Plotter: Graph points with coordinate axes rotated.
Oblique point grapher: Plot points and form polylines (polygon) in oblique (parallelogrammatic) Cartesian coordinate system.
Polar Points Plotter: Graph points with polar coordinates.
Polar point grapher: Plot points and create line graphs in polar coordinate system.
Oblique Polar Points Plotter: Graph points with polar axis rotated.
Oblique polar point grapher: Plot points and form line graphs in oblique polar coordinate system.
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To copy or save graphs right click on an image of the graph(s) below and select "Copy image" or "Save image ..." from the pop-up menu.

Entering Points into Point Plotter

To use our online Cartesian and polar point plotter, simply enter the points (a1,b1),(a2,b2),... 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.

Connecting Points

The point grapher allows you to connect points with line segments to form line graphs or polygons 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—forming a (closed) polygon.

Point Graph in Oblique Cartesian Coordinate System

One of the most intriguing features of our point grapher is its unique ability to rotate axes. The standard Cartesian coordinate system, typically referred to as the rectangular coordinate system, employs two perpendicular axes: one horizontal and one vertical. By rotating these axes, we create a Cartesian coordinate system where the axes can intersect at any angle. This is called an oblique Cartesian coordinate system or parallelogrammic Cartesian coordinate system. This naming is due to the parallelograms formed by grid lines, which are parallel to the corresponding axes.

While many texts use Cartesian coordinate system and rectangular coordinate system interchangeably, we specifically use the full term rectangular Cartesian coordinate system to distinguish it from the oblique Cartesian coordinate system that we introduce.

Our point plotter allows for unique exploration of how point graphs appear in this generalized Cartesian coordinate system, which we refer to as the oblique Cartesian coordinate system (or simply the oblique or parallelogrammic coordinate system).

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

Point Graph in Oblique Polar Coordinate System

In the standard polar coordinate system, the polar axis is drawn horizontally. However, our polar point grapher 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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