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Complex Number Calculators

Polar Form Calculator

Convert a complex number from rectangular form a + bi to polar form r∠θ and exponential form re^(iθ).

Enter values

Results update as you type.

Result

Polar form

1.41421356 ∠ 45°

Exponential form
1.41421356·e^(0.78539816i)
r
1.4142135624
θ (radians)
0.7853981634
θ (degrees)
45

About the Polar Form Calculator

Convert a complex number from rectangular form a + bi to polar form r∠θ and exponential form re^(iθ).

Also known as: rectangular to polar, complex to polar, polar form of complex number, euler form.

How to use this calculator

  1. Enter z = a + bi.
  2. The result updates instantly as you type — press Calculate (or Enter) at any time.
  3. Review the breakdown shown under the main result.
  4. Use Copy result or Share to save the answer or send a link with your inputs.

Formula

r = √(a² + b²) · θ = atan2(b, a)

Worked example

Using the values pre-filled in the calculator above:

  • z = a + bi: 1 + 1i

the calculator returns:

  • Polar form: 1.41421356 ∠ 45°
  • Exponential form: 1.41421356·e^(0.78539816i)
  • r: 1.4142135624
  • θ (radians): 0.7853981634