Point Grapher: Cartesian & Polar Points Plotter

About the Point Grapher

This online point grapher (aka coordinate plotter or point plotter) is designed to plot 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 plotter makes graphing simple in both Cartesian and polar coordinate systems. To graph points given by ordered pairs (a,b), just enter them as a,b;

These pairs can represent points in either Cartesian coordinates or polar coordinates, and our 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 plotter is the world's only plotter that supports axis rotation, enabling you to graph points in oblique coordinate systems (parallelogrammatic coordinate systems—non-rectangular Cartesian, and generalized polar coordinate systems).

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

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.

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.

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°.

Connecting Points

The point grapher allows you to connect the 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).