Enter the magnitude, frequency, and phase angle of a sinusoidal time domain signal into the calculator to determine its phasor representation in polar form.

Sinusoid โ†” Phasor Calculator

Convert time-domain sinusoids to phasors and convert phasors back to time-domain signals.
Time Domain โ†’ Phasor
Phasor โ†’ Time Domain
Cosine
Sine
Peak
RMS
Degrees
Radians
Optional. If entered, angular frequency is filled automatically.
Optional. If entered, frequency is filled automatically.
RMS
Peak
Degrees
Radians
Cosine Output
Sine Output
Enter frequency or angular frequency.
Enter angular frequency or frequency.

Related Calculators

Time Domain To Phasor Formula

The following formula is used to convert a time domain signal to its phasor representation:

P = Mโˆ ฮธยฐ

Variables:

  • P is the phasor representation (Aโˆ ยฐ or Vโˆ ยฐ)
  • M is the magnitude of the time domain signal (A or V)
  • ฮธ is the phase angle in degrees

To convert a time domain signal to its phasor representation, use the magnitude and phase angle to create a polar form representation of the signal. The frequency is not used in the conversion to phasor form but is important for understanding the signal’s behavior over time.

Frequency โ†” Period โ†” Angular Frequency Conversion Table (T = 1/f, ฯ‰ = 2ฯ€f)
Frequency (Hz) Period (ms) Angular Frequency (rad/s)
11000.0006.283
10100.00062.832
5020.000314.159
6016.667376.991
10010.000628.319
2005.0001256.637
4002.5002513.274
4402.2732764.602
5002.0003141.593
10001.0006283.185
20000.50012566.371
50000.20031415.927
100000.10062831.853
120000.08375398.224
200000.050125663.706
327680.031205887.416
441000.023277088.472
480000.021301592.895
500000.020314159.265
1000000.010628318.531
Formulas: T (ms) = 1000 / f (Hz); ฯ‰ (rad/s) = 2ฯ€ f. Rounded to 3 decimals.

What is a Phasor?

A phasor is a complex number used to represent the magnitude and phase of a sinusoidal function in the frequency domain. It simplifies the analysis of linear electrical circuits that operate in steady state. Phasors are used extensively in electrical engineering, especially in the context of alternating current (AC) circuits.

How to Calculate a Phasor from Time Domain?

The following steps outline how to convert a time domain signal to its phasor representation:

  1. First, determine the magnitude (M) of the time domain signal.
  2. Next, determine the phase angle (ฮธ) in degrees.
  3. Use the formula P = Mโˆ ฮธยฐ to find the phasor representation.
  4. Finally, enter the magnitude and phase angle into the calculator to get the phasor.

Example Problem :

Use the following variables as an example problem to test your knowledge.

Magnitude (M) = 5 A

Frequency (f) = 60 Hz (not used in phasor calculation)

Phase Angle (ฮธ) = 30 degrees