When to Use This Calculator
Use this calculator when all values are sinusoidal steady-state quantities at the same frequency and you need to move between polar notation, rectangular notation, or basic phasor operations.
Enter Phasors
Formula Summary
a + jb = M∠θ M = √(a² + b²) θ = atan2(b, a)
Add and subtract in rectangular form. Multiply magnitudes and add angles; divide magnitudes and subtract angles.
Practical Examples
AC voltage reference
A 120∠-30° voltage becomes approximately 103.923 - j60 V. The negative imaginary part shows the voltage lags the reference axis.
Series impedance check
A circuit impedance of 8 + j6 Ω converts to 10∠36.87° Ω, which helps compare impedance magnitude and phase angle before current calculations.
Common Mistakes
- Mixing RMS and peak magnitudes in the same operation.
- Adding polar phasors directly instead of converting to rectangular form first.
- Combining phasors from different frequencies or transient waveforms.
- Using degrees when another tool or reference expects radians.
Assumptions and Limits
Phasors represent sinusoidal steady-state quantities at one common frequency. They do not directly represent transients or mixtures of different frequencies.
Use a consistent RMS or peak convention across all phasors. Mixing RMS and peak magnitudes produces incorrect power and circuit results.
Reference Notes
These relationships are standard complex-number and sinusoidal steady-state AC circuit formulas, commonly covered in circuit analysis and power systems textbooks. Confirm sign conventions with the specific software, meter, or study method you are comparing against.