How to use the AC Impedance and Phasor Calculator
- 1. Pick a modeSeries RLC, parallel RLC or phasor maths.
- 2. Enter valuesR, L, C and f, or two phasors like 3+j4 and 10∠−30.
- 3. See the answerZ in both forms, θ, power factor, currents and a diagram.
How AC impedance is calculated
In AC circuits each element has an impedance: Z_R = R, Z_L = jωL and Z_C = 1/(jωC) = −j/(ωC), with ω = 2πf. Series impedances add: Z = R + j(XL − XC). For parallel branches, add the admittances: Y = 1/R + j(ωC − 1/ωL), then Z = 1/Y. In polar form |Z| = √(R² + X²) and θ = tan⁻¹(X/R). The power factor is cos θ, lagging for inductive circuits and leading for capacitive ones.
Worked example: R = 30 Ω in series with L = 127.3 mH at 50 Hz gives XL = 314.16 × 0.1273 = 40 Ω. So Z = 30 + j40 = 50∠53.13° Ω. On 230 V, I = 4.6 A, the power factor is 0.6 lagging, P = 635 W, Q = 846 VAR and S = 1.06 kVA.
Phasor maths tips for exams
- Add and subtract in rectangular form. Multiply and divide in polar form (multiply magnitudes and add angles).
- Two parallel impedances: Z = Z1Z2/(Z1 + Z2).
- Check your calculator mode: angles here are in degrees.
- In a series circuit VL and VC are 180° apart, so you cannot add their magnitudes directly.
Phasor mode accepts 3+j4, 3+4j, −j10, 5∠53.13 and 5<53.13.
Frequently asked questions
How do I enter a complex number?
Rectangular as 3+j4, 3+4j or −j10, and polar as 5∠53.13 or 5<53.13 (angle in degrees). SI prefixes such as 4.7k also work.
What if my circuit has no capacitor?
Leave C blank. Blank elements are treated as not present: a missing series element adds nothing, and a missing parallel branch is open.
What do lagging and leading mean?
Lagging means the current lags the voltage (inductive, θ > 0). Leading means the current leads the voltage (capacitive, θ < 0).
Is this tool free?
Yes. You fill in a short form once to see your result, and the other Uncodemy tools then open without it. All the maths runs in your browser.