Math

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Polar Form Calculator.

Convert a complex number to magnitude and argument.

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01

Set your values

Results update as you type.

Magnitude: 5

Magnitude

0.000000
Angle (degrees): 53.130102

Angle (degrees)

0.000000
Angle (radians): 0.927295

Angle (radians)

0.000000

Results update automatically as you type.

Use Cases

Engineering and Physics Calculations

Simplify AC circuit analysis, signal processing, and wave mechanics by converting complex impedances or phasors to polar form.

Example: Convert impedance Z = 3 + 4j to polar form for circuit analysis.

Mathematics and Education

Check your homework or learn how to convert complex numbers to polar form, which is essential for understanding complex analysis and trigonometry.

Example: Verify that 1 + i converts to √2 ∠ 45°.

Frequently Asked Questions

What does the polar form of a complex number represent?
The polar form represents a complex number as a magnitude (distance from origin) and an angle (direction from the positive real axis). It is an alternative to the rectangular form (a + bi).
How do I use this calculator?
Simply enter the real part and the imaginary part of your complex number in the provided fields. The calculator will compute the magnitude (r) and the angle (θ) in both degrees and radians.
What units are used for the angle?
The calculator provides the angle in both degrees and radians, so you can use whichever unit you need for your calculations.

Tips & Common Mistakes

Tips

  • Ensure you enter the imaginary part without the 'i' or 'j' suffix; just the numeric coefficient.
  • If your complex number has no imaginary part, enter 0 for the imaginary part.
  • Remember that the angle is measured from the positive real axis, counterclockwise for positive angles.
  • Use the polar form to easily multiply or divide complex numbers by adding or subtracting angles.

Common Mistakes to Avoid

  • Forgetting to include the sign of the imaginary part; a negative imaginary part will result in a negative angle.
  • Confusing degrees and radians; check which unit you need for your specific problem.
  • Entering the imaginary part with the 'i' symbol (e.g., '3i' instead of '3').

Last updated: August 13, 2026