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Polar to Rectangular Online Calculator

Below is an interactive calculator that allows you to easily convert complex numbers in polar form to rectangular form, and vice-versa. There's also a graph which shows you the meaning of what you've found.

For background information on what's going on, and more explanation, see the previous pages,

Complex Numbers and Polar Form of a Complex Number

Additionally we've created this video, where we delve into the conversion between polar and Cartesian coordinates. With a straightforward approach, we illustrate the correlation between points in the coordinate plane and their representation in both systems.

Whether you're familiar with mathematics or just starting out, this explanation aims to simplify the concept for easy understanding. Join us as we demystify the connection between polar and Cartesian coordinates.

Interactive Graph - Convert polar to rectangular and vice-versa

In the following graph, the real axis is horizontal, and the imaginary (`j=sqrt(-1)`) axis is vertical, as usual.

Point P represents a complex number.

Things to do

  1. Choose whether your angles will be in degrees or radians first.

  2. Enter your values for either radius and angle, or real value and imaginary value and click "Calculate" to see the equivalent result (or you can press <Enter> on your keyboard).

  3. You can also drag point P to change the radius of the circle, and/or the angle to your desired values.

    You can zoom the graph in or out using the navigation icons at the bottom of the graph, and pan left-right, up-down by holding down the <Shift> key while dragging the graph.

  4. You can change the precision of all the calculations by changing the "Decimal places" option.

  5. Go back to the examples on the Polar Form page and try them here in the calculator, and compare the results.

Polar to Rectangular

Enter radius: Enter angle: o

Rectangular to Polar

Enter real: Enter imaginary: j

Using a hand-held calculator

See our review of the TI-NSpire here: TI-NSpire: The Most Powerful Calculator

TI-NSpire Calculator

Then go back to this earlier page to see how to convert polar to rectangular form using a graphing calculator:

Convert polar to rectangular using calculator

Euler's Formula and Identity

See also the interactive that's based on the above:

Euler Formula and Euler Identity interactive graph

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