acalculator

What is the impedance?

Choose series or parallel, then enter the resistance, inductance, capacitance and frequency (leave out a part that is not there). The impedance calculator shows the impedance, phase angle, reactances and resonant frequency.

Your numbers

Units
Connection
Impedance (Ω)
248.562

The impedance is 248.562 Ω at a phase angle of −66.28°.

Phase angle (°)
−66.28
Resistive part (Ω)
100
Reactive part (Ω)
−227.559
Inductive reactance X_L (Ω)
37.6991
Capacitive reactance X_C (Ω)
265.258
Resonant frequency (Hz)
159.155

Impedance (Ω): 248.562. The impedance is 248.562 Ω at a phase angle of −66.28°.

How to calculate

Works out the impedance of a resistor, inductor and capacitor in series or in parallel at a given frequency, with the phase angle, the reactances, and the resonant frequency.

Example with the default inputs (Connection Series, Resistance 100 Ω, Inductance (mH) 100, Capacitance (µF) 10, Frequency 60 Hz): The impedance is 248.562 Ω at a phase angle of −66.28°.

Method: X_L = 2πfL, X_C = 1 ÷ (2πfC). Series: Z = R + j(X_L − X_C), |Z| = √(R² + (X_L − X_C)²). Parallel: Y = 1/R + j(2πfC − 1/(2πfL)), Z = 1 ÷ Y. φ = the angle of Z. f₀ = 1 ÷ (2π√(LC)).

  • Ideal parts: a pure resistor, inductor and capacitor, at one sine-wave frequency.
  • A part left empty is not in the circuit: in series it is a plain wire, in parallel an open branch.

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Connection Series, Resistance 100 Ω, Inductance (mH) 100, Capacitance (µF) 10, Frequency 60 Hz gives Impedance (Ω) 248.562178, Phase angle (°) -66.277093, Inductive reactance X_L (Ω) 37.699112, Capacitive reactance X_C (Ω) 265.258238, Resonant frequency (Hz) 159.154943.Source: OpenStax, University Physics Volume 2, §15.3 RLC Series Circuits with AC (Z = √(R² + (X_L − X_C)²), φ = tan⁻¹((X_L − X_C) ÷ R)), https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac (retrieved 2026-10-05); OpenStax, University Physics Volume 2, §15.2 Simple AC Circuits (X_L = ωL, X_C = 1 ÷ ωC, ω = 2πf), https://openstax.org/books/university-physics-volume-2/pages/15-2-simple-ac-circuits (retrieved 2026-10-05)
  2. Connection Series, Resistance 3 Ω, Inductance (mH) 6.366198, Frequency 100 Hz gives Impedance (Ω) 5, Phase angle (°) 53.130102.Source: OpenStax, University Physics Volume 2, §15.3 RLC Series Circuits with AC (Z = √(R² + (X_L − X_C)²), φ = tan⁻¹((X_L − X_C) ÷ R)), https://openstax.org/books/university-physics-volume-2/pages/15-3-rlc-series-circuits-with-ac (retrieved 2026-10-05)
  3. Connection Parallel, Resistance 100 Ω, Inductance (mH) 100, Capacitance (µF) 10, Frequency 60 Hz gives Impedance (Ω) 40.231382, Phase angle (°) 66.277093.Source: Wikipedia, "RLC circuit", Parallel circuit (admittance of R, L and C in parallel; resonance at 1 ÷ (2π√(LC))), https://en.wikipedia.org/wiki/RLC_circuit (retrieved 2026-10-05)

How it works

With ω = 2πf (f in hertz), L in henries (the box takes millihenries, ÷ 1,000) and C in farads (the box takes microfarads, ÷ 1,000,000):

  • inductive reactance X_L = ωL
  • capacitive reactance X_C = 1 ÷ (ωC)

Series. Z = R + j(X_L − X_C). A part left empty counts as a plain wire (R = 0, X_L = 0, or X_C = 0).

  • |Z| = √(R² + (X_L − X_C)²)

Parallel. Add admittances: G = 1 ÷ R and B = ωC − 1 ÷ (ωL), with a part left empty counted as an open branch (its term is 0). Then Z = 1 ÷ (G + jB):

  • resistive part = G ÷ (G² + B²), reactive part = −B ÷ (G² + B²)
  • |Z| = 1 ÷ √(G² + B²)

The phase angle φ is the angle of Z, from −90° to 90°: atan2(reactive part, resistive part). The resonant frequency, shown when both L and C are given, is f₀ = 1 ÷ (2π√(LC)).

Rules

  • Give at least one of R, L and C. Resistance from 1 µΩ to 1,000 MΩ; inductance from 0.000001 to 1,000,000 mH; capacitance from 0.000001 to 1,000,000 µF; frequency from 0.001 Hz to 1,000 MHz.
  • In parallel, if G² + B² is 0 (an inductor and capacitor at resonance with no resistor), the impedance is infinite and the page gives no answer.
  • Every step uses π, so values are floats, shown to 6 significant figures and the angle to 2 decimals.

Worked examples by hand

100 Ω, 100 mH and 10 µF in series at 60 Hz. ω = 2π × 60 = 376.991. X_L = 376.991 × 0.1 = 37.6991 Ω. X_C = 1 ÷ (376.991 × 0.00001) = 265.258 Ω. X_L − X_C = −227.559 Ω. |Z| = √(100² + 227.559²) = √61,783.3 = 248.562 Ω. φ = tan⁻¹(−227.559 ÷ 100) = −66.28° (capacitive). f₀ = 1 ÷ (2π√(0.1 × 0.00001)) = 159.155 Hz.

3 Ω in series with 4 Ω of inductive reactance. |Z| = √(3² + 4²) = 5 Ω; φ = tan⁻¹(4 ÷ 3) = 53.13°. (At 100 Hz, 4 Ω is an inductance of 4 ÷ (2π × 100) H = 6.366 mH.)

The same 100 Ω, 100 mH and 10 µF in parallel at 60 Hz. G = 0.01 S. B = 1 ÷ 265.258 − 1 ÷ 37.6991 = 0.00376991 − 0.0265258 = −0.0227559 S. G² + B² = 0.0001 + 0.000517831 = 0.000617831. |Z| = 1 ÷ √0.000617831 = 40.2314 Ω. Reactive part = 0.0227559 ÷ 0.000617831 = 36.8319 Ω, resistive part = 0.01 ÷ 0.000617831 = 16.1856 Ω, so φ = tan⁻¹(36.8319 ÷ 16.1856) = 66.28° (inductive).

Other questions people ask

How do I calculate impedance?

Work out the reactances first: X_L = 2πfL for the inductor and X_C = 1 ÷ (2πfC) for the capacitor. In series, Z = √(R² + (X_L − X_C)²). A 3 Ω resistor in series with 4 Ω of inductive reactance has an impedance of √(9 + 16) = 5 Ω.

What is the difference between impedance and resistance?

Resistance opposes current the same way at every frequency and turns energy into heat. Impedance also includes reactance, which comes from inductors and capacitors, changes with frequency, and stores energy instead of using it. In a DC circuit or a pure resistor, impedance equals resistance.

What does the phase angle tell me?

How far the current is out of step with the voltage. A positive angle means the circuit is inductive (the current lags); a negative angle means it is capacitive (the current leads). At 0° the circuit acts like a pure resistance, and the power factor is the cosine of the angle.

What happens at resonance?

At the resonant frequency, 1 ÷ (2π√(LC)), the inductive and capacitive reactances are equal and cancel. A series circuit then has its lowest impedance, equal to R. A parallel circuit has its highest impedance; with no resistor in parallel it would be infinite, so the page gives no answer there.

How do I calculate impedance in parallel?

Add the parts as admittances: 1 ÷ R for the resistor, and 2πfC − 1 ÷ (2πfL) for the capacitor and inductor together. The impedance is 1 ÷ √((1/R)² + (2πfC − 1/(2πfL))²). The page does this for you when you choose Parallel.

Why does the impedance change with frequency?

An inductor’s reactance grows with frequency, and a capacitor’s falls. So a coil blocks high frequencies and passes low ones, and a capacitor does the opposite. Filters and tuned circuits use this.