AC Circuits / CALCULATOR
Phasor Calculator
Convert phasors between polar and rectangular form, perform complex phasor operations, calculate series/parallel impedances, and generate balanced three-phase phasors.
Input Parameters
Edit the example values. Results update as you type.
Results
- Rectangular Form
- 8.6603 + j5
- Polar Form
- 10 ∠ 30°
- Rectangular Form
- 8.6603 + j5
- Magnitude
- 10
- Phase Angle
- 30°
Angles use degrees, normalized to (−180°, 180°]. The angle of a zero phasor is undefined. Parallel cancellation uses a relative tolerance of 10⁻¹² of the sum of admittance magnitudes.
Formula
a = M cosθ; b = M sinθ; M = hypot(a,b); θ = atan2(b,a)Substitution
A = 8.6603 + j5 = 10 ∠ 30° · a = 10 cos(30°) = 8.6603; b = 10 sin(30°) = 5 · a = M cosθ; b = M sinθ; M = hypot(a,b); θ = atan2(b,a) · = 8.6603 + j5 = 10 ∠ 30°Calculation Steps
- A = 8.6603 + j5 = 10 ∠ 30°
- a = 10 cos(30°) = 8.6603; b = 10 sin(30°) = 5
- a = M cosθ; b = M sinθ; M = hypot(a,b); θ = atan2(b,a)
- = 8.6603 + j5 = 10 ∠ 30°
Result Explanation
Rectangular form is usually simplest for addition/subtraction; polar form is usually simplest for multiplication/division.
Formulas and FAQ
a + jb = M∠θ · Zeq = 1 / Σ(1/Zk)Why is the phase angle of a zero phasor undefined?
A zero vector has no direction. Parallel impedance uses the reciprocal sum of complex impedances; use the RLC tool to derive impedance from circuit parameters.