# What is the impedance?

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.

- Page: https://www.acalculator.org/physics/impedance-calculator
- JSON spec: https://www.acalculator.org/physics/impedance-calculator.json
- Version: b380a591d969

## Default answer

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°.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| conn | Connection | Whether the parts are in series (one after another) or in parallel (side by side). |
| R | Resistance | The resistor. Leave empty if there is none. |
| L | Inductance (mH) | The inductor, in millihenries (1 H = 1,000 mH). Leave empty if there is none. |
| C | Capacitance (µF) | The capacitor, in microfarads (1 µF = 1,000 nF). Leave empty if there is none. |
| f | Frequency | The frequency of the AC supply or signal. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| z | Impedance (Ω) | The size of the impedance, \|Z\|, in ohms. |
| angle | Phase angle (°) | How far the voltage leads the current: positive for an inductive circuit, negative for a capacitive one. |
| resistive | Resistive part (Ω) | The real part of Z: \|Z\| × cos φ. |
| reactive | Reactive part (Ω) | The imaginary part of Z: \|Z\| × sin φ. |
| xl | Inductive reactance X_L (Ω) | 2π × f × L. |
| xc | Capacitive reactance X_C (Ω) | 1 ÷ (2π × f × C). |
| f0 | Resonant frequency (Hz) | 1 ÷ (2π × √(L × C)), when both L and C are given. |

## 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)).

## Assumptions

- 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.

## Worked examples

1. conn = series, R = 100, L = 100, C = 10, f = 60 gives z = 248.562178, angle = -66.277093, xl = 37.699112, xc = 265.258238, f0 = 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. conn = series, R = 3, L = 6.366198, f = 100 gives z = 5, 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. conn = parallel, R = 100, L = 100, C = 10, f = 60 gives z = 40.231382, 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).

## FAQ

### 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.

## Sources

- 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)
- OpenStax, University Physics Volume 2, §15.3 RLC Series Circuits with AC: Z = √(R² + (X_L − X_C)²) and 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)
- Wikipedia, "RLC circuit": the parallel circuit’s admittance and the resonant frequency 1 ÷ (2π√(LC)). https://en.wikipedia.org/wiki/RLC_circuit (retrieved 2026-10-05)