Impedance Calculator
Enter resistance R and reactance X, impedance Z, phase angle θ, and power factor are calculated instantly. Formula: Z = √(R² + X²). Positive X = inductive, negative X = capacitive.
Last updated: May 2026
Enter resistance R and/or reactance X above.
Z = √(R² + X²), positive X = inductive, negative X = capacitive
Impedance, formula and use
Impedance Z is the total opposition to AC current in a circuit containing both resistance and reactance. It combines the energy-dissipating effect of resistance (R) with the energy-storing effect of reactance (X), from inductors (positive X) or capacitors (negative X). The phase angle θ shows how much the current leads or lags the voltage, and the power factor gives the ratio of real to apparent power. Impedance is usually the last step in an AC analysis, after the reactance figures from the rest of the Electronics Hub have given you the value of X to enter here.
Formula reference
| Quantity | Formula | Example (R=100 Ω, X=100 Ω) |
|---|---|---|
| Impedance Z (Ω) | Z = √(R² + X²) | Z = √(100² + 100²) = 141.4 Ω |
| Phase angle θ (°) | θ = arctan(X / R) | θ = arctan(100/100) = +45.00° |
| Power factor PF | PF = cos(θ) = R / Z | PF = 100 / 141.4 = 0.7071 |
Sign convention
- Positive X (inductive): current lags voltage; θ > 0°. Use XL from the Inductor Reactance Calculator.
- Negative X (capacitive): current leads voltage; θ < 0°. Use XC from the Capacitor Reactance Calculator and enter it as a negative value.
- X = 0 (pure resistive): voltage and current in phase; θ = 0°; PF = 1.
Where the AC side of the chain begins
The DC build chain starts at Ohm's Law, where voltage, current, resistance and power are all pure real numbers and everything stays in phase. Impedance is the point where that simplicity ends and the AC world begins. Once a circuit contains a capacitor or an inductor, resistance alone no longer tells the full story: reactance adds a phase shift between voltage and current, and impedance is how you combine resistance and reactance into a single magnitude. You are here: AC: resistance plus reactance. Before entering a value here, you will normally have used the Capacitor Reactance Calculator or the Inductor Reactance Calculator (or both) to find X at your operating frequency. Those two tools feed directly into this one: X from either page goes straight into the reactance field above, and Z comes out below. From DC, the chain ran through LED resistors, voltage dividers, supply sizing and wiring losses; the AC sub-chain branches here and the same impedance triangle governs filters, audio crossovers, and any mains or RF load that is not purely resistive.
Working with AC components has made the phase-shift piece click for me in a way that pure DC work never did: in DC circuits resistance is the only opposition and everything stays in phase, but as soon as you add a capacitor to an audio or filter circuit you can measure the current leading the voltage and feel the difference Z makes compared to bare R.
Frequently Asked Questions
What is the difference between impedance and resistance?
Resistance R dissipates energy as heat and applies equally to DC and AC. Impedance Z is the AC equivalent: it includes resistance and the frequency-dependent opposition from inductors or capacitors (reactance X). At DC (f = 0 Hz), inductors are short circuits (XL = 0) and capacitors are open circuits (XC → ∞), so only resistance remains. At AC, all three must be combined: Z = √(R² + X²).
How do I combine inductive and capacitive reactance in one circuit?
When a circuit has both inductance and capacitance in series, their reactances partially cancel: Xnet = XL − XC. Calculate XL using the Inductor Reactance Calculator and XC using the Capacitor Reactance Calculator, subtract (XL − XC), then enter the result as X here. At resonance XL = XC, so Xnet = 0 and Z = R.
What does the phase angle tell me about a circuit?
The phase angle θ is how many degrees the current waveform is shifted relative to the voltage. A positive angle (0° to +90°) means the current lags voltage, the circuit is inductive. A negative angle (0° to −90°) means current leads voltage, capacitive. At θ = 0° the circuit is purely resistive and power transfer is maximised. At θ = ±90° no real power is consumed, all power is reactive and returns to the source each cycle.
When does power factor actually affect what I build on the bench?
For resistive loads (heaters, LED drivers with a resistive ballast, incandescent bulbs) power factor is close to 1 and you can ignore it. It becomes a real design concern when you add inductors or capacitors: a motor or transformer draws reactive current that does no work but still heats the supply wiring. In audio work, a PF well below 1 at the crossover frequency signals that the filter is loaded reactively, which shifts the corner frequency away from the design value. In mains installations, a PF of 0.5 means the supply must deliver twice the current of a fully resistive load at the same real power, so fusing and cable sizing must account for the apparent power (V x I), not just the watt figure. A PF of 0.707 corresponds to θ = 45°, the −3 dB point of an RC or RL filter, so the calculator's power-factor output doubles as a quick filter sanity check.
Methodology and sources
This tool combines resistance R and reactance X into the AC impedance Z, then derives the phase angle and power factor. It follows the standard series-circuit relationship in which R and X are the legs of a right triangle and Z is the hypotenuse.
- Method: Z = √(R² + X²); phase angle θ = arctan(X / R); power factor PF = cos(θ) = R / Z. Positive X is treated as inductive (θ above 0°), negative X as capacitive (θ below 0°).
- Standards and sources: Standard AC-circuit physics, the Pythagorean combination of resistance and reactance with trigonometric phase and power-factor relations. No external wiring or product standard is implemented; the math is the textbook impedance triangle.
- Assumptions and limits: Assumes a single series combination of R and X at one frequency, with X already net of any inductive and capacitive parts (X = XL − XC). It does not compute reactance from component values or frequency, and it does not model parallel networks, transmission lines, or complex source/load matching.
Reviewed and maintained by Rick Oosterling, who builds and wires 12 V, solar and EV systems hands-on. Last reviewed: June 2026. This calculator is a planning and learning aid, not engineering advice; verify critical design figures against your component datasheets and an authoritative reference before relying on them.
Next step in this workflow
AC circuit analyzed: explore all electronics calculators.